fudom 2013 - bme műszaki mechanikai tanszék · this work was supported by the tÁmop...

FUDoM 2013

VI. FINNO-UGRIC INTERNATIONAL CONFERENCE OF MECHANICS

WITH SPECIAL SYMPOSIA

11-15 August, 2013 Rackeve (Budapest), Hungary

HAS-BUTE Research Group for Dynamics of Machines and Vehicles

Department of Applied Mechanics, Budapest University of Technology and Economics

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FUDOM 2013 PROGRAMME AND ABSTRACTS

EDITOR: Balázs Fekete

CONFERENCE SECRETARIAT: Gábor Csernák

Balázs Fekete

EDITOR IN CHIEF: Andras Szekeres, LOC FUDoM

Dept.Applied Mechanics, Budapest University of

Technology and Economics

H-1521 Budapest, Hungary

Phone: (36 1) 463 1231

Fax: (36 1) 463 3471

Email: [email protected]

[email protected]

INTERNATIONAL ORGANIZING COMMITTEE (IOC):

J.Engelbrecht (EST) – chairman

A.Szekeres (HUN) – executive chairman

K.Cirule (LV)

R.Hetnarski (USA)

D. Jou (ESP)

N. Kizilova (UKR)

W.Muschik (GER)

LOCAL ORGANIZING COMMITTEE (LOC):

Gy.Beda - honorary chairman,

A.Szekeres - general chairman,

G.Csernak and P.Van - executive chairmen,

T. Fulop,

B.Fekete – scientific secretary.

mailto:[email protected]


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VI. FINNO-UGRIC INTERNATIONAL CONFERENCE OF MECHANICS

WITH SPECIAL SYMPOSIA

Organized by:

HAS-BUTE RESEARCH GROUP FOR DYNAMICS OF MACHINES AND

VEHICLES

DEPARTMENT OF APPLIED MECHANICS, BUDAPEST UNIVERSITY OF

TECHNOLOGY AND ECONOMICS

Supported by:

BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS

INSTITUTE OF CYBERNETICS AT TALLINN TECHNICAL UNIVERSITY

SOCIETY FOR THE UNITY OF SCIENCE AND TECHNOLOGY/ EGYESÜLET

A TUDOMÁNY ÉS TECHNOLÓGIA EGYSÉGÉÉRT

KAYSER AUTOMOTIVE HUNGÁRIA KFT.

This work was supported by the TÁMOP 4.2.4.A/1-11-1- 2012- 0001 project. The project is

co-financed by the European Union and the European Social Fund.

A kiadvány az Európai Unió és Magyarország támogatásával a TÁMOP 4.2.4.A/1-11-1- 2012- 0001 azonosító

számú „Nemzeti Kiválóság Program – Hazai hallgatói, illetve kutatói személyi támogatást biztosító rendszer

kidolgozása és működtetése országos program” című kiemelt projekt keretei között valósult meg.

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CONFERENCE PROGRAMME

11 AUG SUNDAY

15:00- Registration

18:00-19:00 Folklore

19:00- Welcome banquet

12 AUG MONDAY

9:00-9:20 Opening

9:20-11:00 STEPAN 60/1

11:00-11:30 Coffee

11:30-13:30 STEPAN 60/2

13:30-14:30 Coffee

14:30-16:30 STEPAN 60/3

13 AUG TUESDAY

9:00-12.00 Interdisciplinarity

12:00-12:30 Coffee

12:30-14:30 KAYSER Session

15:00-22:00 Puszta visit

14 AUG WEDNESDAY

9:00-11:00 Farmer market

11:00-13:15 Thermo-Hygro-Mechanics

13:15-14.00 Coffee

16:00-17:00 Greek Orthodox church visit

17:30-20:30 Special pub (Wine and palinka taste)

15 AUG THURSDAY

9:00-11:00 CPEA/1

11:00-11:30 Coffee

11:30-13.30 CPEA/2

13:30-14:30 Coffee

18:00-19:00 Classical music concert

19:00- Farewell banquet

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DETAILED PROGRAMME

12 AUG MONDAY

CHAIR: W.V. WEDIG STEPAN 60 /1

TIME AUTHORS TITLE OF PRESENTATION

9:20-11:00

N.D. Stoica NONLINEAR DYNAMIC EVALUATION FOR

EXISTING BUILDINGS

W.V. Wedig

MULTI-TIME-SCALE DYNAMICS OF HALF-CAR

MODELS UNDER STOCHASTIC EXCITATIONS

WITH TIME-DELAYS

T. Outtas

NUMERICAL SIMULATION OF FRONTAL OFFSET

CRASH TEST FOR THE VEHICLE FRAME USING LS

DYNA

D. Takács, G. Stépán SELF-EXCITED VIBRATIONS OF HIGH SPEED

ROLLING WHEELS

B. Várszegi, D. Takács SKATEBOARD, THE SELF-BALANCING

NONHOLOMIC SYSTEM

12 AUG MONDAY

CHAIR: L. YUAN STEPAN 60 /2


11:30-13:30

T. Kalmár-Nagy, Y. S.

Lee

STABILITY ANALYSIS FOR DELAY-

DIFFERENTIAL EQUATIONS BY ROOT COUNTING

L.Yuan, V.-M.

Järvenpää, S. Virtanen

PARAMETRIC STABILITY CONDITION STUDY FOR

GRINDING CONTACT DELAY EQUATIONS

T.Insperger, J. Milton,

G. Stépán

ON THE STABILIZATION EFFECT OF

ACCELERATION FEEDBACK FOR DELAYED

FEEDBACK SYSTEMS

D. Bachrathy, G.

Stépán

FAST STABILITY CHART COMPUTATION BY

HARMONIC BALANCE FOR DELAYED SYSTEM

M. Kidd, G. Stépán TIME DELAY MODEL FOR CONTROLLED

CONTINUUM BEAM

T. G. Molnár, T.

Insperger

ON THE STABILIZATION BY FINITE SPECTRUM

ASSIGNMENT IN CASE OF PARAMETER

UNCERTAINTIES

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12 AUG MONDAY

CHAIR: T. KALMÁR-NAGY STEPAN 60 /3


14:30-16:30

D. Hajdu, T. Insperger TIME DOMAIN ANALYSIS OF THE SMITH

PREDICTOR

P.B. Béda

STABILITY AND BIFURCATIONS IN DELAYED

AND ANTICIPATORY SYSTEMS OF APPLIED

MECHANICS

G. Gyebrószki, P. T.

Nagy, G. Csernák

NUMERICAL EXPLORATION OF MICRO-CHAOTIC

BEHAVIOUR

V.-M. Järvenpää,

L.Yuan

MULTIBODY SIMULATION OF GRINDING

PROCESS

G. Csernák, Z. Pálmai BUILT-UP EDGE INDUCED CHAOTIC CHIP

FORMATION DURING TURNING

13 AUG TUESDAY

CHAIR: J. VERHÁS INTERDISCIPLINARITY


9:00-12:00

A. Szekeres INTERDISCIPLINARITY AND THERMO-HYGRO-

MECHANICS - GENERAL INTRODUCTION AND HUMOR

IN SCIENCE

J. Verhás THERMAL NOISE IN MECHANICS

Y. Schwartz „HUMAN ENGINEERING” IN THE NEW HEBREW

CULTURE

N. Kizilova PHYSICS OF LIVING MATTER

D. Kartofelev, J.

Engelbrecht

ALGORITHMIC MELODY COMPOSITION BASED

ON FRACTAL GEOMETRY OF MUSIC

J. Engelbrecht

COMPLEXITY: FROM GENERAL ISSUES TO

MECHANICS

13 AUG TUESDAY

CHAIR: I. NEMES KAYSER


12:30-14:30

G. Lámer

THE ROLE OF TOPOLOGY AND METRICS IN THE

MECHANICAL MODELLING OF CONTINUOUS

MEDIA

N. Kizilova,

A.Szekeres

PLANT LEAVES GIVE NATURE INSPIRED

SOLUTION FOR ENGINEERED OPTIMAL HEAT

AND MASS EXCHANGERS

A. Yaghoobi, M.

Yildiz

PERIDYNAMIC EVALUATION OF J-INTEGRAL FOR

INTERACTING CRACKS IN A PLATE UNDER

TENSION

C.-P. Wu, H.-Y. Li,

FINITE CYLINDRICAL PRISM METHODS FOR THE

ANALYSIS OF LAMINATED COMPOSITE HOLLOW

CYLINDERS

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14 AUG WEDNESDAY

CHAIR: L. ÉCSI THERMO-HYGRO-MECHANICS


11:00-13:15

L. Écsi, P. Élesztős, R.

Jančo

A UNIVERSAL HEAT EQUATION TO PREDICT

DUCTILE MATERIAL BEHAVIOUR AT WIDE

RANGE OF STRAIN RATES – VERIFICATION OF

THE EQUATION AT LOW STRAIN RATES

Gy. Béda, P. B. Béda CONDITIONAL LAGRANGE DERIVATIVE WITH

GIBBS FUNCTION

N. Kizilova, A.

Szekeres

COUPLED THERMOMECHANICAL AND ELECTRIC

PHENOMENA IN BONE TISSUE

S. M. Hosseini

TWO DIMENSIONAL COUPLED NON-FICK

DIFFUSION-THERMOELASTICITY ANALYSIS

(BASED ON GREEN – NAGHDI THEORY)

EMPLOYING MESHLESS LOCAL INTEGRAL

EQUATIONS (LIES)

Á. Kovács, A. Kovacs INCREASE OF LOAD-CAPACITY OF A SQUARE-

FORM NANOFILTER

V. Petrova, A.

Szekeres

THEORETICAL MODELING OF THERMO-HYDRO-

MECHANICAL FRACTURE OF A MEDIA WITH

CRACKS

M. Fabrizio THERMODYNAMICS OF NON-LOCAL MATERIALS:

EXTRA FLUXES AND INTERNAL POWER

15 AUG THURSDAY

CHAIR: J. ENGELBRECHT CPEA /1


9:00-11:00

T. Fülöp, P. Ván, A.

Csatár

ELASTICITY, PLASTICITY, RHEOLOGY AND

THERMAL STRESS – AN IRREVERSIBLE

THERMODYNAMICAL THEORY

E. Ruszinko

PECULIARITIES OF PLASTIC STRAINING UNDER

MULTIAXIAL STRESS STATES: FEIGEN’S

EXPERIMENTS

A. Berezovski, J.

Engelbrecht, P. Ván

WEAKLY NONLOCAL THERMOELASTICITY WITH

DUAL INTERNAL VARIABLES

B. Czél, Gy. Gróf, T.

Fülöp, J. Verhás, P.

Ván

EXPERIMENTAL AND THEORETICAL WEAKLY

NONLOCAL HEAT CONDUCTION

M. Grmela NONLOCAL MULTISCALE DYNAMICS AND

THERMODYNAMICS

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15 AUG THURSDAY

CHAIR: M. GRMELA CPEA /2


11:30-13:30

N. Mitsui, P. Ván THERMODYNAMICAL MODEL OF FRICTION

J. Engelbrecht, T.

Peets, D. Kartofelev

NEGATIVE GROUP VELOCITY MAY APPEAR IN

MICROSTRUCTURED SOLIDS

P. Ván CONCEPTS AND METHODS OF WEAKLY

NONLOCAL CONTINUUM THEORIES

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FUDoM 2013

ABSTRACTS

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STEPAN 60 /1

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NONLINEAR DYNAMIC EVALUATION FOR EXISTING BUILDINGS

Nicolae Daniel Stoica, Technical University of Civil Engineering Bucharest

A major shortcoming of the first Romanian seismic design codes consisted in the fact that they did not

allow direct assessment of the behaviour of structures in inelastic domain and does not contain the

concept and principles on this issue. Major earthquakes from 1977, 1986, 1990 and 2004 showed large

incursion in inelastic domain for the structures, highlighting some degradation and damage in non-

structural elements, primarily (due to exceeding the allowable deflection and dissipation of part of the

amount of energy induced by the earthquake) and in structural elements (beams, frames, coupling beams,

columns, reinforced concrete structural walls, foundations) due to inadequate structural conformation.

REFERENCES

[1] D. Stoica, A. Pretorian - Basic concepts in the R/C retrofitting solutions of P13 (first Romanian

aseismic design code) existing buildings. Braila ten levels block of flats case study - 1992 – AICPS

Review

[2] D. Stoica, A. Pretorian - P13 existing buildings nonlinear dynamic behaviour. M1f8 and soft and weak

level repeatable “name-code” layouts. – 1993 - AICPS Review

[3] D. Stoica, A. Pretorian - Dynamic Non-linear Analysis Methodologies in the R/C P13 existing

buildings. – 1993 - AICPS Review

[4] D. Stoica, E. Titaru, A. Pretorian Technical and economic aspects regarding the put in safe against

earthquakes of the existing buildings retrofitting solution. 1998 – First Romanian Earthquake Engineering

Conference

[5] D. Stoica, S. Majewski - General considerations about the behaviour and retrofitting solutions for the

existing buildings with masonry structures – Gliwice – Zakopane - REPROCITY International Meeting –

April 2008

MULTI-TIME-SCALE DYNAMICS OF HALF-CAR MODELS UNDER STOCHASTIC

EXCITATIONS WITH TIME-DELAYS

W.V. Wedig, KIT-Universität Karlsruhe Institut für Technische Mechanik

The paper introduces high order simulation schemes and correspondingly extended covariance equations

[1]. Both are derived by multiply iterated integrals [2] and applied to the dynamics of road-vehicle

systems. Running on roads, vertical car vibrations are generated in dependence on the car velocity. The

car vibrations become resonant when the vehicle speed times the road frequency approaches the natural

frequencies of the car.

Systematic simulation errors, caused by finite time steps of the applied discrete integration scheme, are

discussed in dependence on the car speed. They are compared with strong solutions of the linear road-

vehicle systems calculated for vanishing step sizes by means of the classical covariance equations [3]. To

avoid numerical instabilities in case of stiff frequency situations, multi-time scales are introduced into the

associated bi-linear moments’ equations.

These investigations are extended to the dynamics of half car models under stochastic base excitations

with time delays [4]. Provided the car models are symmetric, the vertical car vibrations are decoupled

from the rotational ones. Evaluations of the stationary root-mean-squares over the related car speed show

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typical sub-resonances for increasing wheel axle distances. In the classical case of vanishing time delays,

however, there is only one resonance peak near the natural frequency of the decoupled half-car model.

REFERENCES

[1] W. Wedig, Dynamics of Cars Driving on Stochastic Roads. In: Proceedings of Computational

Stochastic Mechanics, Spanos, PD and Deodatis, G editors. Millpress, Rotterdam, 647-654, 2003.

[2] W. Wedig . Resonances of Road-Vehicle Systems with Nonlinear Wheel Suspensions. In: Dynamics,

Modeling and Interaction Control in Real and Virtual Environments. Stépán G, Kovács LL and Tóth A,

editors. Springer: 2010. p.83-90.

[3] W.Wedig, Simulation of Road-Vehicle Systems. Prob Eng Mech 2012; 27(1) p.82-87.

[4] W. Wedig, Stochastic Vibrations of Half Car Models under Base Excitations with Time Delays . In:

CD-Proceedings of the 7th EUROMECH Solid Mechanics Conference, Warschau , 2009.

NUMERICAL SIMULATION OF FRONTAL OFFSET CRASH TEST FOR THE VEHICLE

FRAME USING LS DYNA

T. Outtas, mechanical structures and materials laboratory, university of Batna - Algeria

A. Benhizia, mechanical structures and materials laboratory, university of Batna - Algeria

In the crash-test, keeping the space around the occupants remains the subject of research for the

automobile manufacturers. The analysis of the crash-test with explicit finite element programs such as

LS-DYNA helps us to reduce the actual testing on prototypes in the automotive industry. The frontal

crash is extremely fast, it is about 120ms, the physical knowledge of the frame leader sheets are very

difficult to obtain and control during this time. We are interested to study and optimize the nonlinear

dynamic behaviour of a frame leader model examining the influence of local changes on the geometry of

the frame rail and the configuration of assembly. The model of the frame chosen, it consists mainly of

two beams connected with ties. We have used "solid works" for the design of the model parts. Three

configurations represent the model’s geometry of the frame studied. The dynamics resulting In the 3

configurations, shows that the vulnerable areas caused the initiation of lateral deflection, this does not

allow the absorption of shock causing a large deformation of the frame. The results lead us to conclude a

preliminary choice of a complete tubular structure for the frame parts, the proper choice of the shape of

the frontal part allows starts the buckling in a predetermined direction, This is numerically stabilized in

the model by using a small crease, putting the part of the carrier more rigid than the frontal one.

REFERENCES

[1] Reid JD, Towards the understanding of material property influence on automotive crash structures,

Thin-Walled Structures, 24:285–313, 1996

[2] Recep Gumruk, Sami Karadeniz, A numerical study of the influence of bump type triggers on the

axial crushing of top hat thin-walled sections, Thin-Walled Structures 46, 1094–1106, 2008

[3] Yong-Bum Cho, Chul-Ho Bae, Myung-Won Suh, Hyo-Chol Sin, Thin-Walled Structures 44 ,415–

428, 2006

[4] Yuxuan Li, Zhongqin, Lin, Aiqin Jiang, Guanlong Chen, Use of high strengthsteel sheet for

lightweight and crashworthy car body,Materials and Design 24, 177- 182. 2003

[5] Shujuan Hou, Qing Li, Shuyao Long, Xujing Yang, Wei Li, Crashworthiness design for foam filled

thin-wall structures, Materials and Design 30 , 2024–2032,2009

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SELF-EXCITED VIBRATIONS OF HIGH SPEED ROLLING WHEELS

Takács, D., Research Group on Dynamics of Machines and Vehicles, Hungarian Academy of Sciences

Stépán, G., Department of Applied Mechanics, Budapest University of Technology and Economics

The nonlinear dynamics of rolling wheels as ain spatial problemce is a challenging task of classical

dynamics. The rolling of elastic tyres has been an advanced research topic in vehicle dynamics since the

1920s. Improved modeling and analysis of rolling elastic tyres haves essential role in developing ABS

systems or in avoiding shimmy.

It was recognized already in one of the first scientific reports on shimmy dynamics that the tyre contact

patch is responsible for a kind of memory effect, but the theory of delay differential equations was not

available at that time. While an engineering approximation of the tyre lateral deformation in the contact

patch solved relevant industrial problems like real-time control of ABS braking systems, some vibration

phenomena of towed wheels like quasi-periodic wheel shimmy or micro-shimmy remained unexplained.

The stability and bifurcation analysis of the exact delay-differential equations that are originated in the

contact patch memory provides, however, experimentally validated description of the mentioned vibration

phenomena. The delayed tyre models should still be improved further, especially for the steered wheels of

high-speed motorcycles or airplane nose gears.

In classical mechanical models of shimmying tyres, the lateral tyre deformation is usually described in the

contact patch only; or in special cases, the deformation outside the contact patch is approximated by

steady state functions, for example, in case of the so-called stretched string tyre model. These

approximations neglect the dynamics of the tyre carcass. But the traveling deformation waves induced at

the trailing edge of the contact patch can propagate along the circumference of the tyre. This induces

another kind of delay effect (in other words, a regenerative effect) that may be the source of further self-

excited vibrations. The aim of this study is to construct the mechanical model which can capture this

regenerative effect of the tyre carcass and to show its effect on shimmy.

Acknoledgement: The research work was supported by the Hungarian National Science Foundation

under grant no. OTKA PD105442.

SKATEBOARD, THE SELF-BALANCING NONHOLOMIC SYSTEM

Várszegi, B., Department of Applied Mechanics, Budapest University of Technology and Economics

Takács, D., Research Group on Dynamics of Machines and Vehicles, Hungarian Academy of Sciences

The simplest vehicles sometimes show interesting unwanted instabilities. For example, the linear stability

of bicycles and skateboards are investigated even nowadays in several studies of vehicle dynamics (see

for example, [1] and [2]). The aims of this study are the investigation of the motion of the skateboard and

the stability analysis of its straight stationary motion.

A low degree-of-freedom, very simple mechanical model of the skateboard is constructed using mass

point, massless rods and torsion spring element. Kinematic constraints of rolling play key role in the

motion of the skateboard, thus, even the simplest model has to consider them. Namely, our mechanical

model is nonholonomic, and the equations of motion of the system are derived with the help of the

Appell-Gibbs equations.

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By means of the composed conservative mechanical model, the linear stability of the straight stationary

rolling was analyzed. Based on our results, it can be established that the straight stationary rolling of the

skateboard can be stable at great speed even if it is unstable at smaller speeds. This was also confirmed by

simple experiments on the dependence of the stability limits on the speed of the skateboard. Similar

results are published about a simplified mechanical model of the bicycle in [1]..

Since, the composed model is unable to show the well-known instability problem of skateboard at large

speeds, the control loop of the rider was also considered in the mechanical model. The reaction time was

implemented into the model by means of the time delay in the control. The stability of the skateboard was

studied for different speeds and control parameters.

Acknoledgement: The research work was supported by the Hungarian National Science Foundation

under grant no. OTKA PD105442.

REFERENCES

[1] Kooijman, J. D. G., at al…: 2011 A Bicycle Can Be Self-Stable Without Gyroscopic or Caster

Effects, Science 332, 339 (2011).

[2] Kremnev, A. V., Kuleshov, A. S.: 2008, Dynamics and simulation of the simplest model of

skateboard, ENOC-2008, Saint Petersburg, Russia, June, 30–July, 4 2008

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STEPAN 60 /2

17


STABILITY ANALYSIS FOR DELAY-DIFFERENTIAL EQUATIONS BY ROOT COUNTING

Tamás Kalmár-Nagy, Mitsubishi Electric Research Laboratory

Young S. Lee, Department of Mechanical and Aerospace Engineering

New Mexico State University

One of the main practical problems for delay equations is to determine the stability of the zero solution of

the system as a function of parameters. Stability is determined by the location of the zeroes (roots) of the

characteristic equation. The system is unstable if the rightmost root is in the right half plane and stable

otherwise. The characteristic equation for delay systems is transcendental with infinitely many roots, thus

computing all the roots to establish stability is not possible. However, counting the roots in the right half

plane would settle the stability question. Such approach was taken by Stépán [1], Hassard [2] and Olgac

and Sipahi [3].

Since it is easier to count roots in a bounded domain, we utilize a conformal map to map the right half

plane into the interior of the unit circle. The number of roots of the transformed characteristic equation

within the unit circle can be expressed as a complex contour integral (by the argument principle). Instead

of evaluating this integral, we present an equation that governs the evolution of the characteristic function

(together with necessary auxiliary equations) and augment this system with the differential form of the

complex contour integral (based on the "imbedding method" of Kalaba et al. [4] for ordinary differential

equations). Integrating this system from along the unit circle then yields the number of roots of the

characteristic equation within the unit circle. The method is demonstrated on several systems.

REFERENCES

[1] Stépán, G. Retarded Dynamical Systems. Longman: Harlow, UK, 1989.

[2] Hassard, B. D., Counting Roots of the Characteristic Equation for Linear Delay-Differential Systems,

Journal of Differential Equations, 136, pp. 222-235, 1997.

[3] Olgac, N., and Sipahi, R., An Exact Method for the Stability Analysis of Time-Delayed LTI Systems,

IEEE Trans. Autom. Control, 47(5), pp. 793--797, 2002.

[4] Kalaba, R. and Mease, K., An imbedding method for matrix eigenvalue problems, Computers &

Mathematics with Applications, 4(1), pp. 53--59, 1978.

PARAMETRIC STABILITY CONDITION STUDY FOR GRINDING CONTACT DELAY

EQUATIONS

Lihong Yuan, Tampere University of Technology

Veli-Matti Järvenpää, Tampere University of Technology

Seppo Virtanen, Tampere University of Technology

In this work, a roll grinding machine has studied. In paper machine industry, the grinding machine is

either used for finishing or maintaining the surfaces of metal rolls. Excellent surface finish should be

homogenous one with silky sheen, free of scratches and any other blemishes. Precision roll provides more

efficient roll operation and better paper quality. However, the chip removal process by grinding is often

accompanied by a violent instability that is so called regenerative chatter[1]. Such kind of chatter may

cause low quality surface, grinder damaged. To understand the dynamic behaviour of grinding machine

18


towards these aspects is very important. A typical grinding machine consists of work piece-roll (metal)

and grinding wheel (stone) which keep contact interaction during the process. The contact vibration

problem of such kind of system will be investigated. In order to ensure the finishing the entire surface of

on roll, technically there are always overlaps between the revolution paths related the width of the

grinding wheel. The overlap rate is associated with the axial speed of the grinding stone’s sledge which

starts from one end of the roll to another end in one completed process. Therefore the delay effects from

both the roll and the grinder have been taken into account[2]. The grinding forces in normal and

tangential directions might be associated with friction factor as well. The nonlinear mathematic model has

been established, which the delay effects from both the roll and the grinder. Based on stability theory, the

characteristic equation for linearized stability at equilibrium is conducted[3]. Moreover, the super and

subcritical bifurcations have been identified[4]. The effects from the parameters of interest in rolling

contact will be analysed accordingly[5]. At the end, the influences of the roughness from the contact

surfaces also will be discussed.

REFERENCES

[1] R.A. Thompson, On the Doubly Regenerative Stability of a Grinder:Theory of Chatter Growth,

Journal of Engineering for Industry, 1986, Vol.108/75.

[2] G. Stepan, Retard Dynamical Systems: Stability and Characteistic Functions,john Wiley& Sons, Inc.,

1989.

[3] M.S. Fofana, Sufficient conditions for the stabolity of single and multiple regenerative chatter,

Chaoas, Solitions and Fractals 14 (2002) 335-347, Pergamon.

[4] F.C. Moon, Dynamics and Chaos in Manufacturing Process, Wiley, New York,1998.

[5] L. Yuan, E. Keskinen, V.M. Järvenpää, Stability Analysis of Roll Grinding System with Double Time

Delay Effects, IUTAM Symposium on Vibration Control of Nonlinear Mechanisms and Structures, 2005,

Germany, Kluwer Academic Publishers.

ON THE STABILIZATION EFFECT OF ACCELERATION FEEDBACK FOR DELAYED

FEEDBACK SYSTEMS

Tamás Insperger, Budapest University of Technology and Economics

John Milton, W. M. Keck Science Center, Claremont Colleges, CA

Gábor Stépán, Budapest University of Technology and Economics

A model for human postural balance is considered in which the time-delayed feedback depends on

position, velocity and acceleration (PDA feedback). It is shown that a PDA controller is equivalent to a

predictive controller, in which the prediction is based on the most recent information of the state, but the

control input is not involved into the prediction. A PDA controller is superior to the corresponding

proportional-derivative (PD) controller in the sense that the PDA controller can stabilize systems with

~40% larger feedback delays. The addition of a sensory dead zone to account for the finite thresholds for

detection by sensory receptors results in highly intermittent, complex oscillations that are typical feature

of human postural sway. The presentation is based on the paper [1].

REFERENCES

[1] Insperger T, Milton J, Stepan G, Acceleration feedback improves balancing against reflex delay,

Journal of the Royal Society Interface, 10(79) (2013), Article No. 20120763.

19


FAST STABILITY CHART COMPUTATION BY HARMONIC BALANCE FOR DELAYED

SYSTEM

Daniel Bachrathy, HAS-BUTE Research Group on Dynamics of Vehicles and Machines


The fast and reliable calculation of the stability of systems with time delay is of high importance in many

applications like traffic jams, wheel shimmy, cutting processes and even in human balancing.

An efficient and robust method was implemented in a Matlab package to analyze the general form of

delayed linear systems with time-periodic coefficients. The stability is determined based on the harmonic

balance for delayed system which leads to an infinite determinant of Hill type. The stability boundaries

are computed by the Multi Dimensional Bisection Method which is able to determine the stable and

unstable islands automatically. This method calculates the values of the approximated Hill’s determinant

above a coarse mesh first, then it refines the mesh in each iteration steps along the stability boundaries

where both the sign of the real part and the sign of the imaginary part of the determinant change. In each

step of the refinements, the accuracy is doubled.

In the developed freeware Matlab package, the governing equation has to be defined by the time periodic

coefficient matrices, the corresponding time delays, the orders of time derivatives of the general

coordinate vector, as well as the range of the parameters and the resolution of the stability chart. The

method is optimized for 2 parameters, which is a typical case in engineering applications, but 1 and 3

parameter stability charts are also supported. The algorithm is tested by means of numerous examples.

TIME DELAY MODEL FOR CONTROLLED CONTINUUM BEAM

Milan Kidd, Budapest University of Technology and Economics


A metal beam with a force actuator at an unfixed end and a force feedback with gain from the other,

fixed, end is modeled first with a finite degree-of-freedom delay differential equation and then with a

continuous delay partial differential equation. In each case a stability map is constructed for the

parameters of delay, gain and damping in the manner presented in Insperger/Stépán [1].

REFERENCES

[1] „Semi-Discretization for Time-Delay Systems.” Insperger, Tamás and Stépán, Gábor. Springer Press,

2011.

ON THE STABILIZATION BY FINITE SPECTRUM ASSIGNMENT IN CASE OF

PARAMETER UNCERTAINTIES

Tamás G. Molnár, Budapest University of Technology and Economics


An application of the Finite Spectrum Assignment (FSA) control technique is presented for an inverted

pendulum with feedback delay. The FSA controller predicts the actual state of the system over the delay

20


period using an internal model of the real system. If the internal model is perfectly accurate then the

feedback delay can be compensated. However, slight parameter mismatch of the internal model may

result in an unstable control process. In this paper, stabilizability of the inverted pendulum for different

system and delay parameter mismatches are analyzed. It is shown that, for the same parameter

uncertainties, the FSA controller allows stabilization for significantly larger feedback delays than a

conventional delayed proportional-derivative controller does. In the analysis, it is assumed that the

controller input is piecewise constant (sampled), this way the destabilizing effect of the difference part of

the governing neutral functional differential equation is eliminated. The relation of the FSA controller to

the Smith predictor is also described in time domain. The presentation is based on the conference paper

[1].

REFERENCES

[1] Molnár TG, Insperger T, On the stabilizability of the delayed inverted pendulum controlled by finite

spectrum assignment in case of parameter uncertainties, Proceedings of the ASME 2013 International

Design Engineering Technical Conferences & Computers and Information in Engineering Conference,

Portland, Oregon, USA, DETC2013-12316.

21


STEPAN 60 /3

22


TIME DOMAIN ANALYSIS OF THE SMITH PREDICTOR

Dávid Hajdu, Budapest University of Technology and Economics


Time domain representation of the original Smith Predictor is presented for systems with feedback delays.

It is shown that if the parameters in the internal model of the predictor are not equal to the parameters of

the real system, then the dimension of the closed loop system is double of the dimension of the open-loop

system. Furthermore, the time-domain representation of the corresponding control law involves terms of

integrals with respect to the past similarly to the Finite Spectrum Assignment control technique. The

results are demonstrated for a second order system (pendulum) subjected to the Smith Predictor. It is

demonstrated that stability diagrams can be constructed using the D-subdivision method and Stepan’s

formulas. The sensitivity of the stability properties with respect to the parameter uncertainties in the

predictor’s internal model is analyzed. It is shown that the original Smith Predictor can stabilize unstable

plants for some extremely detuned internal model parameters. Thus the general concept that the Smith

Predictor is not capable to stabilize unstable systems is technically not true. The presentation is based on

the conference paper [1].

REFERENCES

[1] Hajdu D, Insperger T, Time domain analysis of the Smith predictor in case of parameter uncertainties:

a case study, Proceedings of the ASME 2013 International Design Engineering Technical Conferences &

Computers and Information in Engineering Conference, Portland, Oregon, USA, DETC2013-12324.

STABILITY AND BIFURCATIONS IN DELAYED AND ANTICIPATORY SYSTEMS OF

APPLIED MECHANICS

Péter B. Béda, Budapest University of Technology and Economics

In applied mechanics several papers concentrate on the comparison of delayed and non-delayed

approaches of controlled machines. We may study both continuous and discrete time systems, by using

both numeric and analytic methods. These analytic methods are from the qualitative theory of differential

equations like Lyapunov’s indirect method, or the use of monodromy operator of discrete mappings and

the basic bifurcation theory. The principal points of interest in the paper are how continuous time system

differs from its representation as some discrete time system in stability and robustness and how the

discretization of a continuous time subsystem acts on the stability properties and bifurcation of the

coupled system.

23


NUMERICAL EXPLORATION OF MICRO-CHAOTIC BEHAVIOUR

Gergely Gyebrószki, Budapest University of Technology and Economics

Péter Tamás Nagy, Budapest University of Technology and Economics

Gábor Csernák, HAS-BUTE Research Group on Dynamics of Machines and Vehicles

In [1] and [2] the micro-chaotic behaviour of digitally controlled systems was investigated. Micro-chaos

is a phenomenon, when digital effects (sampling, round-off and processing delay) lead to small-amplitude

chaotic oscillations. The so-called micro-chaos maps of various digitally controlled unstable linear

mechanical systems were derived, and it was shown, that several disconnected attractors may exist in the

phase-space of these maps. Although the size of these attractors is usually negligible, the distance of the

farthest attractor from the desired state can be rather large. It has also been proved mathematically that in

a couple of simple cases the evolving vibrations are indeed chaotic. Our current goal is to compile a set of

numerical methods which can be used to quickly examine the micro-chaotic behaviour of realistic

digitally controlled systems. For example, cell mapping techniques can be applied for the exploration of

the phase-space or the duration of transients can be estimated, based on Lyapunov exponent calculation

algorithms. In the present paper, these numerical methods are used on PD- and PID-controlled unstable

linear systems to qualify the chaotic behaviour in a broad range of control parameters.

ACKNOWLEDGMENTS

This research was supported by the Hungarian National Science Foundation under grant no. OTKA K

83890.

The work reported in the paper has been developed in the framework of the project „Talent care and

cultivation in the scientific workshops of BME" project. This project is supported by the grant TÁMOP-

4.2.2.B-10/1--2010-0009.

REFERENCES

[1] G. Csernák, G. Stépán: Digital Control as Source of Chaotic Behavior, International Journal of

Bifurcation and Chaos, 20(5), pp. 1365-1378, 2010.

[2] G. Csernák, G. Stépán: Sampling and Round-off, as Sources of Chaos in PD-controlled Systems,

Proceedings of the 19th

Mediterranean Conference on Control and Automation, June 20-23, 2011, Corfu.

MULTIBODY SIMULATION OF GRINDING PROCESS

Veli-Matti Järvenpää, Tampere University of Technology

Lihong Yuan, Tampere University of Technology

The grinding is a maching operation in which material is removed from a work piece to produce a part

with quality surface finish. The contact dynamics of the grinding process is sensitive to instabilities,

which are related to the regenerative chatter resulting from the unstable interaction between the machine

tool and the workpiece [1-3]. Two chatter excitation sources can be considered. The first one is on the

grindstone surface. All surface error shapes on it from the previous rounds will carry on and become an

excitation source. The resulting phenomena can be expressed mathematically by a time delay term. The

second chatter source is on the work piece side due to an overlap of the grinding path. The two delay

terms make the vibration system of the cylindrical grinding process self-excited. The grinding vibration

24


system can be modeled for example as a two-degree-of-freedom system. However, more comprehensive

approach should be introduced for the vibration responses of a whole cylindrical grinding machine unit.

In this paper a multibody simulation (MBS) of the grinding machine unit is considered. The focus is in

the contact force description of the grinding process in the MBS model. The MBS model is derived by

describing the grindstone and the workpiece as individual flexible bodies. The modeling is based on

component mode synthesis by utilizing finite element meshes and modal vector sets. The cutting force is

replaced by a distributed contact load, which is calculated according to the total penetration on the

surfaces. The grindstone moves in the model horizontally along the work piece axis during grinding. The

vibration histories on the workpiece and grindstone surfaces are stored during the solution and the time

integration procedure includes variable time delays. The simulation results of are for verification purposes

only at the current state of this research. More improvements are needed, which will be our future work.

REFERENCES

[1] R. A. Thompson, On the Double Regenerative Stability of Grinder: The Theory of Chatter Growth,

Journal of Engineering for Industry, Vol. 108/75 (1986)

[2] Y. Altintas, Manufacturing Automation, Cambridge University Press, 2000

[3] V. Järvenpää, L .Yuan, Active Vibration Control of Multibody Rolling Contact System, Motion and

Vibration Control, Selected papers from MOVIC 2008, edited by H. Ulbrich et al., Springer(2009).

BUILT-UP EDGE INDUCED CHAOTIC CHIP FORMATION DURING TURNING

Gábor Csernák, HAS-BUTE Research Group on Dynamics of Machines and Vehicles, Budapest,

Hungary

Zoltán Pálmai, Budapest University of Technology and Economics, Dept. of Manufacturing Science

Built-up edge (BUE) is the accumulation of the cut material against the rake face, close to the tip of the

cutting tool. As the BUE periodically develops and breaks off, the thickness of the cut layer changes,

leading to poor surface quality. We developed a thermo-mechanical model for the description of the chip

formation during turning [1,2] that takes into account the variation of the cutting depth. The model

comprises a set of delay-differential equations, thus, the phase-space of the system is infinite dimensional.

The formation of BUE provides an excitation for the cutting dynamics. According to our experimental

and numerical investigations, the resulting vibrations can be chaotic. To prove the occurrence of chaos,

we determined the largest Lyapunov exponent by two different methods [3].

REFERENCES

[1] Z. Pálmai, G. Csernák, Chip formation as an oscillator during the turning process. Journal of Sound

and Vibration 326 (2009) 809-820.

[2] G. Csernák, Z. Pálmai, Exploration of the chaotic phenomena induced by fast plastic deformation of

metals. International Journal of Advanced Manufacturing Technologies 40 (2009) 270-276.

[3] Z. Pálmai, G. Csernák, Effects of built-up edge induced oscillations on chip formation during turning.

Journal of Sound and Vibration, in press (2013). http://dx.doi.org/10.1016/j.jsv.2012.08.015

http://dx.doi.org/10.1016/j.jsv.2012.08.015

25


INTERDISCIPLINARITY

26


INTERDISCIPLINARITY AND THERMO-HYGRO-MECHANICS – GENERAL

INTRODUCTION AND HUMOR IN SCIENCE

Andras Szekeres, Budapest University of Technology and Economics, Department of Applied Mechanics,

Hungary

Interdisciplinarity (Idy) is one of the most contemporary notions. Generally accepted that Idy means first

of all application of different field of sciences. A very good example is the thermo-mechanics (TM) that

is composed of mechanics (M) and thermo-dymanics (TD). Both M and TD are several hundred years old

and they mutually apply each other, i.e. there is no M without TD and vice versa. Even though, the TM

and first of all its engineering application is new, younger, maybe much younger than 100 years old [1].

TM has two roots from the theoretical and practical needs. Both are clear, the first one has already been

mentioned. Neither the second one needs any proof if we think about the material properties. All the

materials are deformable and heat sensitive. This makes the practical root of the TM. Beeing at the

application and at the materials, most of them, first of all up-to-date ones, e.g. composites, bio tissues

concrete etc. are also hygroscopic. This makes the need of the thermo-hygro-mechanics (THM) [2], i.e.

the triple coupled field of mechanics, an other frequent Idy.

Based on what has been told so far, the presentation is going to give a brief summary on the foundation of

the THM, on the possible application of the electrical analogy, some application, e.g. amphora and also

the wider side of the Idy.

REFERENCES

[1] Hasselmann DPH, Heller RA: Thermal stresses in severe environments. Plenum Press, NY, 1980

[2] Szekeres A., Engelbrecht J.: Coupling of Generalized Heat and Moisture Transfer. Periodica

Polytechnica Ser. Mech. Eng. Vol. 44. No. 1, pp. 161-170 (2000).

THERMAL NOISE IN MECHANICS

Prof. Dr. Verhás József, Budapest University of Technology and Economy

The thermal noise was observed experimentally at the first quarter of twentieth century in radio

receivers and amplifiers and remained assumed a proprietary phenomenon in electric networks.

Nowadays, more and more authors draw the attention to the existence of thermal noise in other kinds of

work, especially, in mechanical interactions. The arguing refers, usually, to nanotechnology as the small

size involves more considerable effect. The treatment is mostly statistical and is based on fluctuations; the

essential role of dissipation remain partially hidden. Here a more intuitive method is presented closely

related to the traditional kind of argumentation in classical thermodynamics.

An idealized transducer joins electricity to mechanical work; further on, the methods of electric

networks—worked out well—is applied. The theory of Nyquist–noise is built up with a one dimensional

analogue of thermal radiation. The radiating body is replaced by an electric two pole, the field of radiation

by a transmission line; even by a couple of parallel wires. The Nyquist– formula analogous to Kirchhoff's

radiation law; studying the work on a moving end of the transmission line results the form of temperature

dependence, moreover, the Doppler effect displays Wien’s distribution. The spectral distribution can be

obtained either by Planck's or Einstein's procedure.

27


A very important corollary is that If we assume the thermal noise of dissipating elements as their

inherent behavior and being rather the cause of fluctuations than the opposite, we may get an image of

statistical theories without ergodic problem and Loschmidt's paradox.

„HUMAN ENGINEERING” IN THE NEW HEBREW CULTURE

Yigal Schwartz, Ben-Gurion University of the Negev, Israel

The Jews have existed as a people for approximately 5000 years. During this period, they may have gone

through many significant and fascinating changes. But only int he mid-nineteenth century did some of the

members of one of the dominant elites of this nation decided to reinvent it. They chose to throw away two

thousand years of Diaspora history and to create, in place of the “old Jew”, who was marked by some of

the prominent characteristics of ani-Semitic rhetoric, a “new Hebrew”- stronger, more handsome, and

more suitable to the modern world.

The process of “human engineering” – a term that I borrow from the field of generic engineering, took

place for the most part in the New Hebrew literature, which took over in many ways the place and

authority of religion. A large number of Hebrew writers, from 1850 onward, undertook the national

mission and offered in their works models of human “hybrids” that yielded diverse, unusual, and

sometimes very strange “new Hebrews”.

In this lecture, I will address a number of these “hybrids”. I will base my talk on a combination of tools

from literary theory, humanistic geography, and comparative mythology.

PHYSICS OF LIVING MATTER

Natalya Kizilova, Kharkov National University, Ukraine

Seventy years ago, in February 1943 Erwin Schrodinger gave his brilliant lectures on the topic and his

famous book [1] was published and widely discussed. Since then ’mathematical biology’ and ’medical

physics’ became common teaching courses at universities, biophysics reached unbelievable success. We

speak of biotechnologies based on physical phenomena, genetic modification by physical factors.

Mathematical models describing living matter at any scale from molecules to cells, tissues, organs,

systems, whole organisms, collectives and ecosystems have been developed and are successfully works

helping in quite different areas from medical diagnostics and treatment to ecology and economics.

Periodic journals are dedicated to the subject [2]. What is special for the living matter in nature?

Mathematicians, philosophers, biologists, doctors pondered deeply of it [3,4]. When the laws of

thermodynamics were discovered, Laplace and Lavoisier rushed to check validity of the laws in

biosystems and reported on the succes of their experiments. In mathematical models it is assumed the

same general mass, momentum and energy balance equations are valid for the living bodies, but validity

of the second law in biosystems is still discussed.

Living matter appeared during the evolution and many biosystems and biomaterials exhibit optimal

properties. Evolutionary optimization considered as algorythm can be examined by numerical

computations verifying whether the optimal structures could appear during the random variation and

selection process. Nonliving matter also follows optimal ways, for instance, riverbeds correspond to the

ways of minimal enegry expences in the gravity field on the complex surface landscape. As it was

proclaimed in [5] biology is a branch of condensed matter physics and life is an emergent phenomena

28


that occurs in systems that are far out of equilibrium. In the paper a series of hypothesis, experimental

data and provocative statements are presented for discussions.

REFERENCES

[1] Schrodinger E. What is life? The physical aspect of the living cell. Dublin. 1955.

[2] http://www.journals.elsevier.com/physics-of-life-reviews/

[3] Vernadsky V.I. Living mater. Moscow. 1978.

[4] Presman A.S. Electromagnetic fields and living matter. Moscow. 1968.

[5] Goldenfeld N., Woese C. Life is Physics: Evolution as a Collective Phenomenon Far From

Equilibrium. // Annu. Rev. Condens. Matter Phys. - 2011. v.2. – P. 375–399.

ALGORITHMIC MELODY COMPOSITION BASED ON FRACTAL GEOMETRY OF MUSIC

Dmitri Kartofelev and Jüri Engelbrecht, Tallinn University of Technology, Institute of Cybernetics,

Centre for Nonlinear Studies (CENS), Tallinn, Estonia

There are almost as many styles of music as there are composers, as each composer imparts their own

creative preferences and ideas when working on a composition. However, beyond this variety and

individuality, are there rules or an underlying structure that essentially differentiates a musical

composition from completely random and meaningless collections of notes? It is said that music is the

right balance of the predictability (orderliness) and surprise (randomness). Quantitative study of that right

balance can be performed by appealing to the notion of the fractal geometry. It has been previously

demonstrated that music can be characterized by the fractal geometry, obeying a 1/fD power law, where D

can be understood as the fractal dimension [1]-[3]. This suggestion holds for the pitch, melody and

rhythm structure as well as for the loudness fluctuation of music [4].

The aim of the current presentation is to make evident the properties of the fractal geometry and the scale-

independency of music [1]. In addition introduction and demonstration of the basic methodology of the

algorithmic music composition is presented. Algorithmic music composition is based on the chaotic

nonlinear dynamic systems, self-similar iterative maps or on the more complicated iterative schemes

taking advantage of the “structured spontaneity” of the nonlinear dynamics by directly transforming the

mathematical objects (fractals) to the musical entities. Resulting scores incorporate enough self-similar

chaotic structural complexity for the listener to perceive as being musical. It is shown that the fractal

geometry is capable of quantifying and describing the human composed music of the different styles and

eras [3]. This underlying structure may explain why music sounds generally pleasing, and shows how

music composed by the human conciseness harmonizes with the nature at large [2]. It is well known that

numerous natural phenomena exhibit fractal geometry. Further it has been shown that on the level of

neurons human brain resonates more efficiently with the input stimulus that has fractal geometry cf. [5].

REFERENCES [1] K. J. Hsü and A. Hsü, “Self-similarity of the “1/f noise” called music,” Proc. Natl. Acad. Sci., vol. 88,

pp. 3507—3509, 1991.

[2] K. J. Hsü, “Applications of fractals and chaos,” Springer-Verlag, pp. 21—39, 1993.

[3] D. J. Levitina, P. Chordiab, and V. Menonc, “Musical rhythm spectra from Bach to Joplin obey a 1/f

power law,” PNAS, vol. 109, no. 10, pp. 3716—3720, 2012.

[4] R. V. Voss and J. Clarke, “’1/f noise’ in music and speech,” Nature, vol. 258, pp. 317—318, 1975.

[5] Y. Yu, R. Romero, and T. S. Lee, “Preference of sensory neural coding for 1/f signals,” Phys. Rev.

Lett., vol. 94, pp. 108103-2—108103-4, 2005.

29


COMPLEXITY: FROM GENERAL ISSUES TO MECHANICS

J.Engelbrecht, Centre for Nonlinear Studies (CENS), Institute of Cybernetics at Tallinn University of

Technology

Complexity in contemporary sense is understood as emergence of collective properties in systems with

large number of parts (constituents, cells, etc.) that interact with each other and with their environments

[1]. Nonlinearity is an important property of nonlinear systems. The recent studies include many

interesting cases starting from physical examples to networks in society and technology, economic and

financial systems, etc.[2]. In mechanics, although not stressed in classical studies, complexity plays also

an important role. In solids, there are interaction forces between the micro-structural constituents and

internal fields, in fluids (soft matter) there is turbulent mixing where features are defined by the statistics

of deformation of material elements, in tissues the intracellular process must be taken into account. The

effects of complexity have been analysed in the context of nonlinear wave motion [3,4] where due to

coupling of nonlinear and dispersive effects the emergence of solitons is possible. Interaction of solitons

leads again to new effects – amplification of interaction solitons which is effectively seen in water waves

[5].

REFERENCES

[1] G.Nicolis and C.Nicolis, Foundations of Complex Systems. World Scientific, 2007.

[2] P.Ball, Why Society is a Complex Matter. Springer, 2012.

[3] J.Engelbrecht, Nonlinear wave motion and complexity. Proc Estonian Acad Sci, 2010, 59, No 2, 66-

71.

[4] J.Engelbrecht, F.Pastrone, Non linear waves in complex microstructured solids, Acc. Sc.Torino,

Memorie Sc. Fis., 2011, 35, 23-36.

[5] T.Soomere, J.Engelbrecht, Extreme elevations and slopes of interacting solitons in shallow water.

Wave Motion, 2005, 41, No 2, 179-192.

30


KAYSER

31


THE ROLE OF TOPOLOGY AND METRICS IN THE MECHANICAL MODELLING OF

CONTINUOUS MEDIA

Géza Lámer, Dr., Faculty of Engineering, University of Debrecen, HUNGARY

Rátz László u. 20. IV. 20. 1119 Budapest XI, Email: [email protected]

Continuous media commonly refers to solid bodies, fluids and gases. Granular materials were also

regarded as a special form of solid bodies, primarily during soil mechanical modelling. At the same time,

it is obvious that solid bodies, granular materials, fluids and gases are continuous in a different sense. The

emphasis or question is on the term continuous: how can or how does continuum have to be interpreted. It

has to be interpreted in a number of different ways. Is the material itself continuous from a physical

aspect or are the mathematical objects reflecting and modelling the material continuous? Is the behaviour

of the material itself continuous or are the mappings of mathematical objects reflecting and modelling the

behaviour of the material continuous?

Continuity, or to be more precise the continuity of mappings are interpreted in mathematics.

Continuity is a fundamental idea that if there is a mapping in a point then mapping a bit further away only

changes slightly. Continuity is interpreted firstly in the metric space then it is generalised in a topological

space. The question regarding the continuity of continuous media can be redefined from a topological

point of view whether material and its behaviour can be described with the tools of topology and whether

the topology provides an opportunity for modelling the variety of material behaviour.

In the first part of the lecture we examine the role of topology in modelling of continuous media. This

includes three topics:

T1. Topology in the cases of point-set, point and point-set, point-sets. Description of (physical, or

rather mechanical) bodies with the help of topology.

T2. Consequences of the existence of topology: the independent set of elements becomes a solid body.

The location of elements in the examined body can be determined by coordinates.

T3. Classification of body motions by the tools of topology. Motions that can be described in the

existence of topology and motions that can be described with local or global “disintegration” of topology.

Deformations and vibrations, rearrangements, flows and heat-motions.

In the second part of the lecture we examine how topology provides an obvious opportunity for the

classification of the internal structure of continuous media and motion types of continuous media.

Topology is unable to separate the motion types of solid bodies from the aspect of deformation. The

assessment of metric characteristics is also required for the description of deformation. The second part of

the lectures includes the examination of the role played by metrics in the modelling of continuous media.

Three topics are covered:

M1. Metric: position vector, (local) basis vector, metric, affine connection, curvature.

M2. Metric mapping: displacement, extension and rotation of basis vectors, changes of affine

connection, compatibility relationships.

M3. The restricting each other relationship of topology and metric: large displacements come about at

small deformations.

PLANT LEAVES GIVE NATURE INSPIRED SOLUTION FOR ENGINEERED OPTIMAL

HEAT AND MASS EXCHANGERS


Andras Szekeres, Budapest University of Technology and Economics, Hungary

Leaves perform vital for plants photosynthetizing and transport functions. Sun radiation, water and CO2

are converted in organic assimilates needed for plant growth and development. Ground water being

absorbed by the roots is transported along the whole plant due to evaporation from the leaf surface,


32


which produce negative pressure driving the water transport. Coupling of different functions demands

special mechanical and transport properties of the leaves that are provided by a network of veins.

Venation systems of leaves exhibit some regularities in geometry and correspond to optimal pipelines

providing delivery and uniform distribution of water and assimilates at minimal total energy cost [1].

Branching design of veins can be used for optimization the fuel cells [2] and other engineered heat and

mass transfer systems [3-5]. There are several essentially different types of leaf venation appeared at

different evolution stages, namely pinnate, palmate, arcuate and parallel.

In this paper efficiency of different venation types as heat and mass transporting systems is estimated.

Water movement along the veins is studied as filtration in anizotropic porous media with double porosity.

The propelling force is the hydrostatic and osmotic pressure differences between the petiole and the

atmosphere. Total energy expences for condective and diffusive motion and entropy production are

computed for the simplified round and oval leaf shapes with different types of venations. It was shown

the evolutionary old types of both leaf shapes and venation patterns needs more energy for the

transportation than the evolutionary younger species. Possible engineering applications are proposed.

REFERENCES

[1] Kizilova N. Computational approach to optimal transport network construction in biomechanics. //

Lecture Notes in Computer Science. – 2004. - Vol.3044. – P.476-485.

[2] Kjelstrup S., Coppens M.-O., Pharoah J.G., Pfeifer P. Nature-Inspired Energy- and Material-Efficient

Design of a Polymer Electrolyte Membrane Fuel Cell. // Energy Fuels, 2010, v.24 (9), pp. 5097–5108.

[3] Kizilova N. Optimal Fiber-Reinforced Composites: Solutions Given by the Nature. // Structural

Analysis of Advanced Materials. Eds: M. Karama, C. Atanasiu, G. Papanicolaou, G.Horia. Tarbes. -

2009. – P.72-78.

[4] Kizilova N., Szekeres A. Biothermohygromechanics: biomimetic comosites with optimal properties //

Intern.conf. “Contemporary problems of mathematics and its applications in natural sciences and

information technologies”. Book of abstracts. – Kharkov. – 2011. – P. 13-14.

PERIDYNAMIC EVALUATION OF J-INTEGRAL FOR INTERACTING CRACKS IN A

PLATE UNDER TENSION

Amin Yaghoobi, Mehmet Yildiz

Sabanci University, Faculty of Engineering and Natural Sciences,

Advanced Composite and Polymer Processing Laboratory (AC2PL)

Orhanli-Tuzla, 34956, Istanbul, Turkey

Defects might form in structural components in the form of isolated or interacting cracks under the

operating conditions. If cracks have a close proximity with respect to each other, the stress field around

the tip of a given crack will be magnified thereby accelerating the crack growth rate. Understanding that

isolated cracks may not pose a threat to structural integrity of the component, interacting cracks however

may significantly degrade the damage tolerance of the structure. Thus, a good understanding of the

behavior of crack interaction and coalescence is vital for reliable design and structural integrity

assessment.

To investigate multiple crack interaction, many of the existing studies have used classical continuum

mechanics formulations based on Finite Element Method (FEM) to compute the fracture parameters such

as stress intensify factor (SIF), energy release rate and J-integral which indicate the magnification of

stress field at the front of crack tip [1,2]. Nevertheless, the classical theory of continuum mechanics is

poorly suited to modeling of this type of problem since it uses partial differential equations as a

mathematical description. The required spatial derivatives, by definition, do not exist on the surfaces of

33


discontinuity, thus, the entire formulation breaks down when such discontinuities exist. Although much

work has been devoted to the development of special techniques to circumvent this problem, these

techniques are not fully satisfactory either in principle or in practice as general descriptions of fracture.

To be able to model materials with discontinues, a nonlocal theory, known as Peridynamic (PD), has been

proposed by Silling [3] which avoids the fundamental mathematical difficulty by using integral equations

as a description of material motion rather than differential equations [4, 5].

In this paper, we have developed a PD formulation for the J-integral to be able investigate crack

interactions in a brittle body subjected to the Mode I type loading. The detailed description of the

algorithm for computing the nonlocal version of the J-integral is provided. A plate with finite thickness

containing double cracks positioned in series with respect to each other is modeled, and the numerical

results are validated with those obtained by using FEM and the classical J-integral.

REFERENCES

[1] F.Z. Xuan, J. Si, S.T. Tu, Evaluation of C* integral for interacting cracks in plates under tension,

Engineering Fracture Mechanics, 76 (2009) 2192-2201.

[2] R. Daud, A.K. Ariffin, S. Abdullah, A.E. Ismail, J-Integral Evaluation in Two Dimensional

Interacting Cracks, Advanced Materials Research, 214 (2011) 55-59.

[3] S.A. Silling, Reformulation of elasticity theory for discontinuities and long-range forces, J Mech

Phys Solids 48 (2000) 175–209.

[4] Y. Ha, F. Bobaru, Characteristics of dynamic brittle fracture captured with peridynamics,

Engineering Fracture Mechanics 78 (2011) 1156–1168.

[5] W. Liu and J. Hong, Discretized peridynamics for brittle and ductile solids, Int. J. Numer. Meth.

Engng 89 (2012) 1028–1046.

FINITE CYLINDRICAL PRISM METHODS FOR THE ANALYSIS OF LAMINATED

COMPOSITE HOLLOW CYLINDERS

Wu, Chih-Ping, National Cheng Kung University, Taiwan

Li, Hao-Yuan, National Cheng Kung University, Taiwan

In recent decades, the fiber-reinforced composite materials (FRCMs) have attracted considerable

attention in advanced engineering applications. In order to achieve a reliable design to enhance the

working lifetime of FRCM structures, various three-dimensional (3D) numerical modeling have been

proposed to assess the performances of assorted two-dimensional (2D) ones, while most of these existing

3D ones were obtained for the plates/shells with fully simple supports, and few for other boundary

conditions, such as fully clamped edges, and combinations of clamped, and simply-supported ones.

Based on the Reissner mixed variational theorem (RMVT), Wu and Li [1], and Wu and Chang [2]

developed the unified formulations of the finite rectangular layer methods (FRLMs) and the finite

cylindrical layer methods (FCLMs) for the 3D analysis of simply-supported, multilayered composite

plates and cylinders, respectively, in which the relative orders used for expansion of the displacement and

transverse stress components through the thickness coordinate can be freely chosen, while the FRLMs

and FCLMs are applicable to the 3D problems of multilayered plates/shells with fully simple supports

only. The current study therefore aims at developing a unified formulation of the RMVT-based finite

cylindrical prism methods (FCPMs) for the approximate 3D analysis of multilayered composite cylinders

with combinations of clamped and simply-supported conditions at the edges. The accuracy and

convergence of these FCPMs are examined by comparing these FCPM solutions with both the 3D

elasticity solutions of simply-supported, multilayered composite cylinders and the accurate solutions

34


obtained using the ANSYS commercial software for these cylinders with various boundary conditions. In

addition, a parametric study with regard to various effects on the displacement and stress components

induced in multilayered composite cylinders is carried out, such as radius-to-thickness ratio, length-to-

thickness ratio, and different boundary conditions.

REFERENCES

[1] Wu CP, Li HY. The RMVT- and PVD-based finite layer methods for the three-dimensional analysis

of multilayered composite and FGM plates. Compos Struct 2010;92:2476-2496.

[2] Wu CP, Chang YT. A unified formulation of RMVT-based finite cylindrical layer methods for

sandwich circular hollow cylinders with an embedded FGM layer. Compos Part B Eng 2012;43:3318-

3333.

35


THERMO-HYGRO-MECHANICS

36


A UNIVERSAL HEAT EQUATION TO PREDICT DUCTILE MATERIAL BEHAVIOUR AT

WIDE RANGE OF STRAIN RATES – VERIFICATION OF THE EQUATION AT LOW STRAIN

RATES

L. Écsi, Faculty of Mech. Engrg., STU Bratislava, Nám. slobody 17, 812 31 Bratislava, SK

P. Élesztős, Faculty of Mech. Engrg., STU Bratislava, Nám. slobody 17, 812 31 Bratislava, SK

R. Jančo, Faculty of Mech. Engrg., STU Bratislava, Nám. slobody 17, 812 31 Bratislava, SK

In contemporary computations ductile materials use different material models depending on the

maximum strain rate of deformation that the body experiences. At low strain rates elastic-plastic material

models are used, while at high strain rates viscoplastic material models are employed [1]. The

fundamental difference in the formulation of the two classes of material models restricts the usage of the

models either into a low strain rate deformation region, or a high strain rate deformation region with no

transitional region between them. In this paper a universal heat equation to predict ductile material

behaviour at wide range of strain rates, including ductile-to-brittle failure mode transition is presented [2],

[3]. The equation has been verified in numerical examples by modelling material tests of a ductile

material at low strain rates. The verification results are briefly outlined and discussed.

REFERENCES

[1] SIMO, J. C., HUGHES, T. J. R., Computational inelasticity, Springer, NY, 1998..

[2] Écsi, L., Élesztös, P., An improved thermal-structural finite element model for ductile-to-brittle failure

mode transition to model ductile material behavior at high strain rates. In: ECCOMAS 2012: 6th

European Congresss on Computational Methods in Applied Sciences and Engineering. Vienna, Austria,

September 10-14, 201,. CD-ROM, s. 1-15.

[3] ÉCSI, L., ÉLESZTÖS, P., Moving toward a more realistic material model of a ductile material with

failure mode transition. Materialwissenschaft und Werkstofftechnik. Vol. 43, No. 5 (2012), s. 379-387.

CONDITIONAL LAGRANGE DERIVATIVE WITH GIBBS FUNCTION

Gyula Béda, Budapest University of Technology and Economics

Péter B. Béda, Budapest University of Technology and Economics

By using the first and second laws of thermodynamics equations were given for the stress σ [1].

Assuming a uniaxial stress field and by using Gibbs function in the equations of thermodynamics small

strain ε can be obtained. By comparing the two groups of possible constitutive equations we obtain such

equations which can be expressed by the same equations by varying both stress and strain fields.

REFERENCES

[1] Béda Gy. Thermomechanical stress from conditional Lagrange derivative, Periodica Polytechnica,

Mechanical Engineering 56/1 (2012) pp. 7-8.

37


COUPLED THERMOMECHANICAL AND ELECTRIC PHENOMENA IN BONE TISSUE



Bone tissue is a solid material composed of the porous skeleton made of the collagen fibers and crystals

of calcium salts and filled with interstitial fluid. The live cells of the bone are located in lacunas and need

nutrition. Bone is a piezoelectric material due to piezoelectricity of collagen [1] and electric phenomena

play important role in bone physiology [2]. Within the linear electrodynamics theory the direct and

reverse piezoelectric effects are

ik iklm lm kij k ij i ikl kl ij j ip G e E T, P e E T

where iklmG , ij , kije and ij are tensors of elastic (Young), thermoelastic, piezoelectric and dielectric

coefficients, i are pyroelectric coefficients, eE is electric-field strength, )4/()ˆˆ( EIP

is

polarization.

In this paper the coupled mechanical, thermal and electric phenomena in application to interstitial

transport and cell nutrition in bone tissue are studied. The relative input of thermodiffusion,

electrodiffusion and other cross-coupled effects in the heat T TT TM TE eJ L T L M L , mass

M TT MM ME eJ L T L M L and electric charge E ET EM EE eJ L T L M L fluxes in bones are

estimated on recent experimental data. The electrokinetic phenomena such as electrophoresis,

electroosmosis, flow potential and polarization in lacunas, meso- and microchannels of bones appeared at

constant and periodic mechanical compression are studied basing on the developed approach.

REFERENCES

[1] Fukada E., Yasuda I. On the piezoelectric effect in bone. J. Phys. Soc. Japan. 1957. vol.12, N10.

P.1158-1162.

[2] Avdeev Yu.A., Regirer S.A. Electromechanical properties of bone tissues. // Modern problems of

biomechanics. Vol.2. Riga, Zinatne. – 1983. – pp. 103-131.

TWO DIMENSIONAL COUPLED NON-FICK DIFFUSION-THERMOELASTICITY

ANALYSIS (BASED ON GREEN – NAGHDI THEORY) EMPLOYING MESHLESS LOCAL

INTEGRAL EQUATIONS (LIES)

Seyed Mahmoud Hosseini, Industrial Engineering Department, Faculty of Engineering, Ferdowsi

University of Mashhad, PO Box: 91775-111, Mashhad, Iran.

This work presents the application of meshless local integral equations (LIEs) based on meshless local

Petrov-Galerkin (MLPG) method to two dimensional coupled non-Fick diffusion-thermoelasticity

analysis. The governing equations of thermoelasticity are based on Green – Naghdi theory of coupled

thermoelasticity (without energy dissipation). A unit step function is used as the test functions in the

local weak-form. It leads to local integral equations (LIEs). The analyzed domain is divided into small

subdomains with a circular shape. The radial basis functions are used for approximation of the spatial

variation of field variables. For treatment of time variations, the Laplace-transform technique is utilized.

38


The molar concentration diffuses through 2D domain with a finite speed similar to thermoelastic wave.

The propagation of mass diffusion and thermoelastic waves are obtained and discussed at various time

instants. The MLPG method has a high capability to track the diffusion and thermoelastic wave fronts at

arbitrary time instants in 2D domain. The profiles of molar concentration and displacements in two

orthogonal directions are illustrated at various time instants.

INCREASE OF LOAD-CAPACITY OF A SQUARE-FORM NANOFILTER

Ádám Kovács, Budapest University of Technology and Economics, Faculty of Mechanical Engineering,

Department of Applied Mechanics

Andras Kovacs, Furtwangen University, Faculty of Computer and Electrical Engineering

Porous membranes are often used for filtering purposes in micro-electromechanical systems. Investigated

membranes are made from perforated silicon-nitride (SiN) on a porous polysilicon (PS) layer, which is

supported and reinforced by single-crystal silicon. The performance of filters highly depends on the

porosity. In order to obtain higher filtration rate the porosity should be increased as much as possible

which, unfortunately, diminishes the strength, and consequently, the load capacity of the device. The

latter effect can be compensated by application of support layers or columns as a support grid within the

porous Si-layer.

The load capacity of the module can be defined as the critical (bursting) pressure pcrit, that causes failure

of the membrane. Adequate methods should be used in the design to estimate this critical pressure. For

the investigated structures the side-length of membranes is some order of magnitude larger than the

thickness (L/h >> 1), therefore classical thin plate theories can not be applied effectively to perform

strength analysis. A challenging mechanical problem is the treatment of the complicated two-layer

structure combined by thin vertical columns. Exact solution for this problem is not known.

Finite element simulations have been performed to investigate the effect of Sireinforcement on the stress

state in the case of different reinforcement topology. The results of simulations have been compared and

verified with measurements made on square-form silicon-nitride and polysilicon structures. After

verification the load-capacity has been estimated using the maximum stress failure criterion. Computed

and measured critical pressures are in good agreement.

REFERENCES

[1] Kovács, Á., Kovács, A., Mescheder, U. Estimation of elasticity modulus and fracture strength of thin

perforated SiN membranes with finite element simulations. Comp. Mat. Sci., 43 (2008) 59-64.

[2] Van Rijn, C.J.M. Nano and Micro Engineered Membrane Technology, Elsevier, (2004).

THEORETICAL MODELING OF THERMO-HYDRO-MECHANICAL FRACTURE OF A

MEDIA WITH CRACKS

Vera Petrova, Voronezh State University, Russia


Investigations of thermo-hydro-mechanical fracture of materials are important for many engineering

branches, in particular, in geotechnical and environmental engineering. Almost any of the engineering

materials are heat sensitive and hygroscopic because of their structure and the porosity. The latter

generally means voids, pores, cracks, etc. Dealing with the mechanics of these materials and structures,

39


the heat and moisture cannot be neglected; the problem has to be handled as coupled. General theory of

the cross-coupled heat and moisture transfer was presented in [1].

The governing equations of fluid flow in a porous media are similar to the heat transfer equation. This

analogy between the problems will be used in this work. The influence of a heat flux on a media with

cracks was considered in numerous papers, a particular problem of macro-microcrack interaction under

influence of a heat flux was studied in [2] and under the influence both heat flux and mechanical loading

in [3]; this technique will be used in the present investigation. To simplify the problem the plane problem

will be considered and some models for the fracture study of materials with cracks under influence of a

heat and a moisture will be presented. The variation of thermal intensity factors and hydro intensity

factors at crack tips with the changes of the main parameters of the problem (geometrical and material)

will be given. The influence of the thermal and hydro fluxes on the strain-stress state at the vicinity of the

cracks will be investigated.

REFERENCES

[1] Szekeres, A. Cross-coupled heat and moisture transport: Part 1-theory, Journal of Thermal Stresses 35

(1-3) (2012), 248-268.

[2] Ordyan M.G., Petrova V.E. Thermal problem of interaction of partially insulated cracks in a

bimaterial subjected by a heat flux (Russian). Vestnik of Voronezh State University. Series: Physics,

Mathematics, N 1 (2009), 141 - 149.

[3] Petrova V., Schmauder S. Interaction of a system of cracks with an interface crack in functionally

graded/homogeneous bimaterials under thermo-mechanical loading, Computational Materials Science,

Computational Materials Science 64 (2012), 229-233

THERMODYNAMICS OF NON-LOCAL MATERIALS: EXTRA FLUXES AND INTERNAL

POWER

Mauro Fabrizio. Università di Bologna

Abstract The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or

simple materials, while for non-local systems there are two di_erent ways: either modify this usual

formulation by introducing suitable extra fluxes or express the Laws of Thermodynamics in terms of

internal powers directly, as we propose in this paper. The first choice is subject to the criticism that the

vector fluxes must be introduced a posteriori in order to obtain the compatibility with the Laws of

Thermodynamics. On the contrary, the formulation in terms of internal powers is more general , because

it is a priori defined on the basis of the costitutive equations. Besides it allows to highlight, without

ambiguity, the contribution of the internal powers in

the variation of the thermodynamic potentials.

Finally, we consider some examples of non-local materials and derive the proper expressions of their

internal powers from the power balance laws.

REFERENCES

[1] M. Fabrizio, B. Lazzari, R. Nibbi. Thermodynamics of non-local materials: extra fluxes

and internal power. Continuum Mechanics and Thermodynamics. 23, Issue 6, 509-525. 2011.

http://link.springer.com/journal/161/23/6/page/1

40


CPEA /1

41


ELASTICITY, PLASTICITY, RHEOLOGY AND THERMAL STRESS – AN IRREVERSIBLE

THERMODYNAMICAL THEORY

T. Fülöp 1,2,4

, P. Ván 1,2,4

, A. Csatár 3,4

1 Wigner Research Centre for Physics, P.O.Box 49, H-1525 Budapest, Hungary

2 Dept. of Energy Engineering, Budapest Univ. of Technology and Economics,

Bertalan L. u. 4-6, H-1111 Budapest, Hungary 3

Hungarian Institute of Agricultural Engineering, Tessedik S. u. 4, H-2100 Gödöllő, Hungary 4

Montavid Thermodynamic Research Group, Igmándi u. 26, H-1112 Budapest, Hungary

We present a thermodynamical formulation of elastic, plastic, rheological and thermal stress phenomena

of solids that is based on two pillars. One of them is a novel definition of kinematic quantities [1] that

enables the description of finite deformation elastic, plastic and heat expansion changes in an objective

way, with no reference instant, no reference configuration and no reference frame. Solids are assumed to

possess a self-metric (natural metric) structure, with which their current metric coincides whenever the

body is in a stressless, totally relaxed state. The elastic kinematic quantity measures the deviation of the

current metric from the self-metric. Plasticity is a phenomenon when the self-metric is forced to change.

In parallel, heat expansion is conceived as the temperature dependence of the self-metric so a changing

temperature is another source of changing self-metric.

The other pillar of our approach is irreversible thermodynamics. The constitutive equations are chosen in

a way that positive definiteness of entropy production is ensured. The standard aspects of plasticity (flow

rule, etc.) are manifest in the formulation. In parallel, thermal stresses emerge as an elastic response to

heat expansion. The classic Duhamel-Neumann theory of thermal stress is recovered as a special limiting

case. At last, rheological effects are incorporated with the aid of an internal variable (dynamical degree of

freedom), a framework that has already proved successful for non-Fourier heat conduction [2], for

example.

After a brief explanation of the theory, we illustrate its use via discussing an experiment in which a

strongly stretched sample undergoes plastic deformation. The temperature of the sample is continuously

monitored so we can observe the initial nearly-adiabatic cooling – a consequence of the nonzero thermal

expansion coefficient –, and the subsequent heat dissipation accompanying the plastic change.

REFERENCES [1] T. Fülöp and P. Ván, Kinematic quantities of finite elastic and plastic deformation, Mathematical

Methods in the Applied Sciences 35 (2012) 1825-1841.

[2] P. Ván and T. Fülöp, Universality in heat conduction theory: weakly nonlocal thermodynamics,

Annalen der Physik 524 (2012) 470-478.

PECULIARITIES OF PLASTIC STRAINING UNDER MULTIAXIAL STRESS STATES:

FEIGEN’S EXPERIMENTS

Endre Ruszinko, Óbuda University

Researchers are concerned with the analytic description of Feigen’s results on plastic straining under

combined loading [1]. The model is developed in terms of the synthetic theory of irrecoverable

deformation [2,3] (taking into account [4]). Criterion to establish when Feigen’s phenomenon can be

observed is proposed. Feigin’s experimental results are of crucial importance to obtain further insight into

42


mechanisms of plastic deforming. Despite the fact that this phenomenon dates back to the 1950s of the

twentieth century, its modeling has not been completely solved yet.

Feigen’s experiment consists in the following loading regime: (i) a specimen plastically deforms in a

complex stress state, tension and torsion, (ii) the specimen is subjected to such a loading when the

torsional component decreases and the tension increases. Feigen reports an unexpected phenomenon is

observed. The torsional plastic deformation ( S ) accumulated in the initial combined loading decreases

during the torsional unloading, 0 S : the specimen is plastically “untwisting”. According to classical

ideas, a plastic strain developed in active loading remains unchangeable during the succeeding unloading.

This phenomenon can be explained by the fact that, during the unloading, the plastic shifts develop within

such slip systems giving a negative increment in torsional strain thereby resulting in the plastic untwisting

of specimen. At the same time, the fraction of grains, which produces positive torsional strains in the

initial loading, remains hardened during the unloading.

REFERENCES

[1] Feigen, M. (1954), Inelastic behavior under combined tension and torsion, 2nd

USNCAM, pp. 469-476.

[2] Rusinko, A., Rusinko, K. (2009). Synthetic theory of irreversible deformation in the context of

fundamental bases of plasticity, Int. J. Mech. Mater. 41: 106-120.

[3] Rusinko, A., Rusinko, K. (2011). Plasticity and Creep of Metals, Springer, Berlin.

[4] Fülöp, T., Ván, P. (2012). Kinematic quantities of finite elastic and plastic deformation, Mathematical

Methods in the Applied Sciences, 35 pp. 1825-1841

WEAKLY NONLOCAL THERMOELASTICITY WITH DUAL INTERNAL VARIABLES

Arkadi Berezovski, Jüri Engelbrecht, Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn

University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia

Peter Ván, Wigner Research Centre for Physics, Institute of Particle and Nuclear PhysicsH-1525

Budapest, P.O.Box 49, Hungary

The response of many materials of engineering interest to external loading is influenced by their

microstructure. The components of such a microstructure may have different material properties, resulting

in a highly anisotropic and inhomogeneous response of the material. Prediction of the thermoelastic

behavior of such materials is not an easy task, because a more general description of thermal processes is

needed in addition to the generalized continuum description extending the conventional continuum

mechanics for incorporating intrinsic microstructural effects.

In the conventional thermoelasticity, the free energy density is a function of the deformation gradient and

temperature only and cannot depend on the temperature gradient. However, in the presence of varying

temperature fields at the microstructure level, the temperature gradient influence on the

thermomechanical response of the material is expected due to the microheterogeneous nature of the

materials. It appears that in the framework of the internal variables theory it is possible to obtain a

hyperbolic evolution equation for microtemperatures keeping the parabolic evolution equation for the

macrotemperature. Effects of microtemperature gradients exhibit themselves on the macrolevel due to the

coupling of equations of macromotion and evolution equations for macro- and microtemperatures.

The overall description of thermomechanical processes in microstructured solids includes both direct and

indirect couplings of equations of motion and heat conduction at the macrolevel. In addition to the

conventional direct coupling, there exists the coupling between macromotion and microtemperature

evolution. This means that the macrodeformation induce microtemperature perturbations due to the

heterogeneity in the presence of a microstructure. These perturbations, propagating with finite speed, can

induce, in turn, corresponding changes in the macrotemperature. At last, the appeared changes in the

43


macrotemperature affect macrodeformations once more. Although the observed effect of the

microstructure is small, it exists in the case of realistic values of material parameters.

EXPERIMENTAL AND THEORETICAL WEAKLY NONLOCAL HEAT CONDUCTION

B. CZÉL2, GY. GRÓF

2, T. FÜLÖP

123, J. VERHÁS

3 AND P. VÁN

123

Recently a linear irreversible thermodynamic framework of heat conduction in rigid conductors was

introduced, were the deviation from local equilibrium is characterized by a single internal variable and by

the generalization of the entropy current density via a current intensity factor [1]. A general constitutive

evolution equation of the current density of internal energy was derived via introducing linear relationship

between the thermodynamic forces and uxes. The Fourier, Maxwell-Cattaneo-Vernotte, Guyer-

Krumhansl, Jeffreys type and Green-Naghdi type equations of heat conduction were obtained as special

cases [2].

The nonlocal, relaxation type constitutive equation of the energy current density qi was obtained in the

following form:

(

)

( )

(1)

Here, T is temperature, and we have introduced an index notation, with used for the gradient. The

material parameters , , , a1, a2, b1, b2 are nonnegative and not independent.

Based on these theoretical considerations, the universality of the proposed framework was demontrated

showing that various heat conduction mechanisms and material structures lead to the above form of the

constitutive relation. For example, material heterogeneity, with the possibility of two temperature or

different channels of heat are particular cases of the above equation. Therefore, (1) is interpreted as a

universal, effective approach to heat conduction.

In order to identify non-Fourier effects we performed and analysed two different simple heat conduction

experiments. A layered periodical heterogeneous structure is the subject of abrupt temperature jump at

one of boundaries and heat conduction measurements with ash method. In the presentation we show the

results of our analysis.

REFERENCES [1] V. A. Cimmelli and P. Ván. The effects of nonlocality on the evolution of higher order uxes in non-

equilibrium thermodynamics. Journal of Mathematical Physics, 46(11):112901{15, 2005. cond-

mat/0409254.

[2] P. Ván and T. Fülöp. Universality in heat conduction theory: weakly nonlocal thermodynamics.

Annalen der Physik, 524(8):470{478, 2012. arXiv:1108.5589.

¹Dept. of Theoretical Physics, Institute for Particle and Nuclear Physics, Wigner Research Centre for

Physics, HAS

²Dept. of Energy Engineering, Budapest Univ. of Technology and Economics, 3Montavid Thermodynamic Research Group

NONLOCAL MULTISCALE DYNAMICS AND THERMODYNAMICS

Miroslav Grmela ,École Polytechnique de Montréal, C.P.6079 succ. Centre-ville Montréal, H3C 3A7,

Québec, Canada, e-mail: [email protected]

Different types of experimental observations of macroscopic systems have led to different experiences

that in turn have led to different theoretical frameworks helping to organize and explain them. Initially,

the frameworks have been introduced independently one of the other (recall for instance the history of

44


fluid mechanics, thermodynamics, and kinetic theory). Subsequently, it has been realized that there are

macroscopic systems that can be describe simultaneously by several of the frameworks and that the main

difference in the descriptions is the amount of details that they involve. A description (we shall also use

the term a level of description and the symbol L1 to denote it) that involves more details than another

level of description L2 is called more microscopic (or equivalently less macroscopic) than the level L2.

The question then arises as to whether L2 can be derived from L1. By examining relations of many well

established levels of description, a general mathematical structure expressing the passage L1→L2 has

been identified. In the nutshell, the (fast) time evolution realizing the passage L1→L2 is a continuous

sequence of Legendre transformations in which a potential, interpreted as entropy emerging in the

investigation of L1→L2, is maximized (see e.g. [1,2]).

Let L1, L2, L3 be three levels ordered from the most microscopic to the least microscopic. In such

sequence we can investigate relations L1→L2→L3. These relations lead to two entropies on the level L2.

One, denoted s(2→3), emerges in the investigation of the passage L2→L3 as the potential generating the

fast time evolution in which the level L2 reduces to the level L3. The other, denoted s(2←1) is the entropy

s(1→2) (that emerges in the investigation of the passage L1→L2) evaluated at its maximum (i.e.

(2 1) (1 2)limts s

).

In the illustration discussed in the talk, the level L3 is the level of classical equilibrium

thermodynamics denoted ET, the level L2 is the level of local equilibrium thermodynamics denoted LET,

and the level L1 is the level of extended irreversible thermodynamics denoted EIT.

We make three observations:

1. We show that the entropy s(LET←EIT) emerging on the level LET of local equilibrium

thermodynamics is necessarily weakly nonlocal (see also [3]).

2. Given a weakly nonlocal entropy, we show a general way how to construct the time evolution that it

generates.

3. We explore a nonlocal extension of the classical fluid mechanics (called a two-point fluid

mechanics) in which the hydrodynamic fields are functions of two position vectors instead of one.

REFERENCES [1] Grmela, M. "Multiscale equilibrium and nonequilibrium thermodynamics in chemical engineering",

Advances in Chemical Engineering 39, 76-128 (2010)

[2] Grmela, M. "Role of Thermodynamics in Multiscale Physics", Computers and Mathematics with

Applications" DOI:10.10162? j.camwa.2012.11,019+ (2013)

[3] Grmela, M., Lebon, G., Dubois, C., "Multiscale thermodynamics and mechanics of heat", Phys.Rev.E

83, 061134 (2011)

45


CPEA /2

46


THERMODYNAMICAL MODEL OF FRICTION

Noa Mitsui, Wigner RCP, Hungarian Academy of Sciences, Hungary

Peter Van, Wigner RCP, Hungarian Academy of Sciences, Hungary

Property of rock friction have been investigated mainly by laboratory experiments, and empirical

equations have been proposed [1]. Many researches were looking for the mechanism described by the

equations, and most of the proposed models assume a special shape of the frictional contact surface [2].

The real contact surfaces, however, do not have any special shape but have small particles of the medium

between them. Thus their assumption is not sufficient and we aim at understanding the mechanism of the

friction in a thermodynamic framework. As a first of step, we focused the change in dynamic friction

depending on the shear loading rate [1]. First, we summarized the qualitative properties in experimental

data of rock friction. They are 1) frictional coefficient in a stable sliding condition with a constant loading

rate depends on the logarithm of the loading rate 2) instantaneous jump of the frictional coefficient is

caused by the loading rate change, 3) the following relaxation of frictional coefficients to a stable

stationary value, and 4) oscillation occurs in some cases (e.g., large loading rate, polished surfaces, thin

sand interface layer between the samples) [3]. Second, we construct a model based on thermodynamical

constitutive equations. In the presentation, the mentioned properties are compared with model predictions.

The advantege of the presented framework is the uniform background with dissipative continuum

theories. Therefore the different parameters can be calculated and compared with the continuum

equivalents and the role of weakly nonlocal extensions can be analysed.

REFERENCES

[1] Dieterich, J. H., J. Geophys. Res. 84, 2161-2168 (1979).

[2] Brechet, Y., and Y. Estrin, Scr. Metall. Mater., 30, 1449-1454 (1994).

[3] Marone, C., C. B. Raleigh, and C. H. Scholz, J. Geophys. Res. 95, 7007-7025 (1990).

NEGATIVE GROUP VELOCITY MAY APPEAR IN MICROSTRUCTURED SOLIDS

J.Engelbrecht, T.Peets, D.Kartofelev Centre for Nonlinear Studies (CENS) Institute of Cybernetics at

Tallinn University of Technology

The phenomenon of negative group velocity (NGV) is discovered by Sommerfeld and Brillouin in 1914

in optics. First it was considered as a theoretical possibility but later such a phenomenon was shown to

exist by many experiments. In optical materials the NGV is a direct consequence of interference between

different frequency components due to the changes in the refractive index. In solids the NGV is found for

Lamb waves in layered materials, in composite circular shells, in crystal lattices etc. The interest to such

materials is now increased in the context of metamaterials which are engineered with a purpose to create

effective macroscopic behaviour like in phononic crystals.

We report on NGV in microstructured materials which are widely used in contemporary technology. The

materials under consideration are of two types: hierarchical Mindlin-type materials (“a scale within a

scale”) [1] and wool felt [2]. In both cases basic mathematical models are presented together with the

corresponding dispersion relations. The analysis shows that there are certain ranges of physical

parameters which allow the NGV [3] in both materials. We stress that although NGV characterizes the

“backward propagation”, it has been shown [4] that the causality principle is not violated.

47


REFERENCES

[1] A.Berezovski, J.Engelbrecht, T.Peets. Multiscale modeling of microstructured solids. Mech. Res.

Commun., 2010, 37, 531-534.

[2] D.Kartofelev, A.Stulov. Propagation of deformation waves in wool felt (submitted)

[3] T.Peets, D.Kartofelev, J.Engelbrecht. Waves in microstructured solids and negative group velocity

(submitted)

[4]A.Dogariu, A.Kuzmich, L.Wang. Transparent anomalous dispersion and superluminal light-pulse

propagation at a negative group velocity. Phys.Rev. A, 2001, 63, 053806.

CONCEPTS AND METHODS OF WEAKLY NONLOCAL CONTINUUM THEORIES

P. Ván¹²³

Weakly nonlocal continuum theories are developed with different methods and concepts.

Phase field,

GENERIC,

Diffusive internal variables,

Weakly nonlocal irreversible thermodynamics,

are conceptual frameworks where weak nonlocality, the extension existing evolution equations and

creation of new ones, can be formulated and tested.

Why only space derivatives, that is nonlocality? What about time derivatives? How can we decide

between the different frameworks? Improved prediction and/or rigorous formulation?

The presentation survey the mentioned theories and formulate some comparative statements. It is argued

that second law, objectivity and effciency of weakly nonlocal theories cannot be separated. Some

benchmark open problems of continuum physics are collected.

¹Dept. of Theoretical Physics, Institute for Particle and Nuclear Physics, Wigner

Research Centre for Physics, HAS

²Dept. of Energy Engineering, Budapest Univ. of Technology and Economics, 3Montavid Thermodynamic Research Group

48


PHYSICAL AND MECHANICAL ASPECT OF FRACTURE COMPOSITE PROBLEMS

V.P. Tamuzh, Latvia University

B.A. Kozhamkulov, B.E.Akitay, A.I.Kupchishin , K.N.Jumadilaev, T.B.Tulendinov,

Latvia University, Kazakh National Pedagogical University after Abay, e-mail: [email protected]

In recent years, considerable interest in the kinetic theory of composites failure, based on the study of

physical and mechanical processes caused by mechanical loads and exposure. The processes of

deformation and fracture in polymers differ pronounced time dependence. This manifests itself in

particular statistical phenomena of fatigue and creep, rupture stress decreases with increasing duration of

action. A thorough study of these processes will allow the scientific approach to the creation of new high-

strength polymers and method of protection from radiation damage.

It should be noted that among the most important problems of condensed matter physics is also the task of

creating materials with predetermined physical properties. Require materials with high specific strength,

heat-resistant, wear-resistant, resistant to corrosive environment, all kinds of radiation. One of the

effective ways to solve this problem is the development of composites with different structures.

Composites, unlike alloys and high-strength structural crystals successfully combine high strength with a

greater toughness. To understand these processes need to take into account all the factors that affect the

physical and mechanical properties of the composite: the nature of the polymer and filler phase and the

physical state of the polymer, curing conditions and binding processes.

Phenomenological study of the mechanical properties of polymers in physics research continues to be

reduced to the study of the rate of accumulation of violations (the emergence and growth of cracks) or

return the integral value - load durability τ. As above [2] according by Zhurkov formula durability of the

applied voltage σ and the temperature T:

(1)

is given the deep physical meaning and the further development the kinetic concept of strength is both on

the basis the analysis of the physical meaning of this formula and its member coefficients , and on

the basis of direct methods of studying the nature of the elementary events underlying the process of

destruction. In development of destruction questions, there are two basic approaches: a) the destruction

caused by invasion of the most dangerous defect when stress concentration coefficient reaches a critical

value and b) the destruction caused by the gradual accumulation of small defects in the bulk material. The

crack germination it is the final stage of destruction.

It should be noted that our knowledge about the true shape very approximate defect; significant role in the

calculation averaged properties must play account viscoelastic properties may therefore be more

appropriate to determine the values of the coefficients k1, k2 of the experiment with a simple loading and

further found using the prediction coefficients for changing the properties material in the other modes of

loading.

Gratitude: this work was supported by grant for fundamental research the Ministry of Education and

Science of Republic of Kazakhstan. Theme: "The study of mechanical properties and processes of the

radiation damage of composites." Order is number 23 on the Science Committee of 25.09.2012. Contract

is number 171 on 25.09.2012.

REFERENCES

[1.] V.R. Regel, V.P. Tamuzs. Destruction and fatigue polymers and composites. Mechanics of

Polymers, 1977, № 3, -158-478.

[2.] Nuclear and Radiation Physics (Proceedings of the international conference dedicated to the 40th

anniversary of the Institute of Nuclear Physics NNC RK, Almaty, 8, 11 October 1997) - Almaty:

«PRINT-S», 1997. - 274 p

[3.] V. Kuksenko, V. Tamuzs. Fracture micromechanics of polymer materials. //Riga, Zinatne 1975 in

Russian, English translation - Martinus Nijhoff Publ. - 1981., pp. 310

49


CONSTITUTIVE MODELLING AND SIMULATION OF SHORT FIBRE REINFORCED

MATERIALS

Heiko Herrmann, Institute of Cybernetics at TUT, Estonia

Viktoria Berg, Dept. of Mathematics, University of Kassel, Germany

Marika Eik, Institute of Cybernetics at TUT, Estonia

Jari Puttonen, Aalto University School of Engineering, Finland

During the past decades short fibre reinforced materials have become important to many industries. This

includes a wide range of matrix and fibre materials, e.g. from resin to cementitious matrix and from glass

over cellulose to steel for fibres. The influence of the fibre orientation distribution on the material

properties has been a topic for research for a long time. In this presentation, a constitutive model for short

fibre reinforced concrete (SFRC) in the uncracked state will be presented, as an example. This model is

based on the hyperelastic St. Venant-Kirchhoff material and enriched by an anisotropic part to include the

fibre orientation distribution. Numerical FEM simulations with the proposed constitutive model and

fracture simulations using the DEM (discrete element method) will be presented, these demonstrate, how

important it is to control the fibre orientation distribution in the manufacturing process. As the

manufacturing process might involve casting, as e.g. in the case of SFRC, an outlook on simulations of

the manufacturing process in order to predict and to control the fibre orientation distribution will be

given.

50


LIST OF PARTICIPANTS

Bachrathy, Daniel [email protected]

Béda, B. Péter [email protected]

Béda, Gyula [email protected]

Berezovski, Arkadi [email protected]

Bhattacharyya, R.Kumar [email protected]

Cimmelli, Vito Antonio [email protected]

Czél, Balázs [email protected]

Csernák, Gábor [email protected]

Écsi, Ladislav [email protected]

Engelbrecht, Jüri [email protected]

Fabrizio, Mauro [email protected]

Fekete, Balazs [email protected]

Fülöp, Tamás [email protected]

Grmela, Miroslav [email protected]

Gróf, Gyula [email protected]

Gyebrószki, Gergely [email protected]

Hajdu, Dávid [email protected]

Herrmann, Heiko [email protected]

Insperger, Tamás [email protected]

Järvenpää, Veli-Matti [email protected]

Jou, David [email protected]

Jutas, Audrius [email protected]

Kalmar-Nagy, Tamas [email protected]

Kartofelev, Dmitri [email protected]

Kidd, Milan [email protected]

Kizilova, Natalya [email protected]

Kovács, Ádám [email protected]

Kozhamkulov, A.B. [email protected]

Lámer, Géza [email protected]

Mitsui, Noa [email protected]

Molnár, Tamás Gábor [email protected]

Petrova, Vera [email protected]

Ruszinko, Endre [email protected]

Schwartz, Yigal [email protected]

Seyed Mahmoud Hosseini [email protected]

Stépán, Gábor [email protected]

Stoica, Nicolae Daniel [email protected]

Szekeres, András [email protected]

Takács, Dénes [email protected]

Toufik, Outtas [email protected]

Ván, Peter [email protected]

Várszegi, Balázs [email protected]

Verhás, József [email protected]

Wedig, W.V. [email protected]

Wu, Chih-Ping [email protected]

Yaghoobi, Amin [email protected]

Yuan, Lihong [email protected]

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