impact and crash modelling of composite structures

8/7/2019 IMPACT AND CRASH MODELLING OF COMPOSITE STRUCTURES

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IMPACT AND CRASH MODELLING OF COMPOSITE STRUCTURES:

A CHALLENGE FOR DAMAGE MECHANICS

Alastair F. Johnson

German Aerospace Center (DLR)

Institute of Structures and Design, Stuttgart, Germany

e-mail: [email protected]

Anthony K. Pickett

Engineering Systems International GmbH

Eschborn, Germany

e-mail: [email protected]

Key words: composites materials, damage mechanics, delamination, impact, crash modelling

___________________________________________________________________________

Abstract: The paper describes recent progress on the materials modelling and numerical

simulation of the impact and crash response of fibre reinforced composite structures. The

work is based on the application of explicit finite element (FE) analysis codes to composite

aircraft structures under both low velocity crash and high velocity impact conditions.

Detailed results are presented for the crash response of helicopter subfloor box structures

using a strain based damage and failure criterion for fabric reinforced composites. In order

to obtain better agreement with measured impact response, an improved composites damagemechanics model with damage parameters as internal state variables is presented. Improved

models for predicting delamination are also considered and a novel approach is presented in

which a composite laminate is modelled numerically by stacked shell elements with contact

interfaces whose delamination is controlled by fracture mechanics criteria.

___________________________________________________________________________



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1. Introduction

Composite materials are now being used in primary aircraft structures, particularly in

helicopters, light aircraft, commuter planes and sailplanes, because of numerous advantages

including low weight, high static and fatigue strength and the possibility to manufacture large

integral shell structures. Future transport aircraft will contain composites for primary and

secondary wing and fuselage components. Materials such as carbon fibre/epoxy are inherently

brittle and usually exhibit a linear elastic response up to failure with little or no plasticity.

Thus composite structures are vulnerable to impact damage and have to satisfy certification

procedures for high velocity impact from runway debris or bird strike. When suitably

triggered to fail by delamination and compression crushing, composites may exhibit high

energy absorption and are of interest for light weight energy absorbing structural elements

such as subfloors in helicopters and transport aircraft. Thus for the further development of

composite aircraft structures, especially in safety critical components, it is important tounderstand the mechanisms of energy absorption and failure, and to have predictive design

tools for simulating the response of composite structures under impact and crash loads. This

paper describes current research aimed at the development and validation of FE simulation

methods for composites, and their application in impact and crashworthiness studies on

composite aircraft structures.

Conventional metallic structures absorb impact and crash energy through plastic deformation

and mechanisms such as geometric folding. Modern explicit FE codes are able to model these

effects and are being successfully applied to simulate the collapse of metallic aircraft and

automotive structures. This paper is concerned with the validity of such codes for modelling

the response of composite structures under low and high velocity impact. Emphasis is given to

composite materials models suitable for implementation into FE codes, which can adequately

characterise the nonlinear damage progression and different failure modes that occur in

composites [1]. Such effects are now included in recent mathematical theories of composites

damage mechanics [2]. The challenge for the damage mechanics approach is to implement

these models into commercial FE codes and to develop procedures for experimentally

determining the many materials parameters required from manageable test programmes.

Section 2 summarises some of the models available for composites in-plane properties. In the

paper measured stress-strain data were used to calibrate the 'degenerate bi-phase model' in the

explicit code PAM-CRASH [1] and to determine the appropriate damage parameters as

functions of the strains.

Examples of FE simulations for the impact response of helicopter subfloor structural elements

based on this materials model were described in [3]. This work is extended here in Section 3

to include hybrid carbon/aramid fabric/epoxy subfloor boxes which are designed to absorb

crash energy by both folding and crushing modes. The results of the dynamic simulations of

vertical impacts on the subfloor elements showed excellent agreement between the predicted

modes of failure and those observed in tests, however simulated load levels, and hence the

total energy absorbed in the structure, is often found to be below test results.



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Thus improvements to the models are required for better agreement with the measured

dynamic response and to extend the simulation capability to high velocity impacts. An

improved composites damage mechanics model with damage parameters as internal state

variables is under development, based on [2]. This model has a number of features notincluded in the simpler 'degenerate bi-phase' model. It allows damage parameters for in-plane

and through-thickness shear failure modes, as well as failures along and transverse to the fibre

directions. Delamination models and strain rate dependence may also be incorporated in the

damage mechanics framework. Some of this ongoing work is presented in Section 4. Here a

novel numerical approach for delamination modelling is presented using stacked shell

elements with a contact interface condition based on fracture mechanics principles. With this

approach the delamination energy is included in the crash or impact simulation. Examples are

given in which the delamination model is calibrated for a double cantilever beam specimen.

Comparison of these simulations with the simpler modelling approaches above and test data,

will show whether damage and fracture mechanics are viable in practice as a basis for moreaccurate impact simulations and crashworthiness studies on composite structures.

2. Modelling composites properties

For metals there is extensive information in the literature on dynamic materials properties at

large strains and high strain rates, and appropriate constitutive equations have been

implemented into FE codes for structural impact simulations. For composite materials

dynamic failure behaviour is very complex due to the different fibres and matrices available,

the different fibre reinforcement types such as unidirectional (UD) fibres and fabrics, the

possibility of both fibre dominated or matrix dominated failure modes, and the rate

dependence of the polymer resin properties. Thus at present there are no universally acceptedmaterials laws for crash and impact simulations with composites. It was considered that a

homogeneous orthotropic elastic damaging material was an appropriate model for UD and

fabric laminates, as this is applicable to brittle materials whose properties are degraded by

microcracking. Constitutive laws for orthotropic elastic materials with internal damage

parameters are described in [2] and [4], and take the general form

εε = S σσ (1)

where σσ and εε are vectors of stress and strain and S the elastic compliance matrix. In the

plane stress case required here to characterise the properties of composite plies or shellelements with orthotropic symmetry axes (x1, x2), the in-plane stress and strain components

are

σσ = ( σ11 , σ22 , σ12 )T εε = ( ε11 , ε22 , 2ε12 )

T . (2)

Using a strain equivalent damage mechanics formulation, the elastic compliance matrix S may

then be written :



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S =

1 1 0

1 1 0

0 0 1 1

1 1 12 1

12 1 2 2

12 12

/ ( ) /

/ / ( )

/ ( )

E d E

E E d

G d

− −− −

−

ν

ν (3)

where ν12 is the principal Poisson's ratio, which for simplicity is assumed not to be degraded.

This general plane stress form for an orthotropic elastic material with damage has 3 scalar

damage parameters d 1 , d 2 , d 12 and 4 'undamaged ' elastic constants: the Young's moduli in the

principal orthotropy directions E 1 , E 2 , the in-plane shear modulus G12 , and the principal

Poisson's ratio ν12. The damage parameters have values 0 ≤ di ≤ 1 and represent modulus

reductions under different loading conditions due to progressive damage in the material. Thus

for unidirectional (UD) plies with fibres in the x1 direction, d 1 is associated with damage or

failure in the fibres, d 2 transverse to the fibres, and d 12 with in-plane shear failure. For fabricreinforcements then d 2 is associated with the second fibre direction.

In [2] conjugate forces Y 1 , Y 2 , Y 12 are introduced corresponding to driving mechanisms for the

damage parameters. It can be shown that with the compliance matrix chosen in (3) that for

elastic damaging materials:

Y 1 = σ112

/ (2E 1(1-d 1)2), Y 2 = σ22

2/ (2E 2(1-d 2)

2), Y 12 = σ12

2/ (2G12(1-d 12)

2) (4)

and it is assumed that the damage evolution equations have the general form:

d 1 = f 1 (Y 1 , Y 2 , Y 12), d 2 = f 2 (Y 1 , Y 2 , Y 12), d 12 = f 12 (Y 1 , Y 2 , Y 12). (5)

Multiaxial failure, or interaction between damage states, can be included in the model

depending on the complexity of the form assumed for the evolution functions f 1 , f 2, f 12. These

are determined from experimental test data. In [2] the theory is developed in detail for UD

plies in which it is assumed that the ply is undamaged in the fibre direction in tension thus d 1= 0, and a coupling is assumed between transverse fibre damage and in-plane shear damage.

Specific models are developed for f 2 and f 12 and appropriate parameters determined from test

data. In ongoing work under the EU funded HICAS project [5] a test programme on fabric

reinforced composite laminates is being carried out and specific forms of the evolution

functions are being determined.

PAM-CRASH [6] contains several materials models and special elements for laminated

composite materials, which are summarised in [1]. A general materials law as in (1) - (5) will

be implemented, but at present only the special form from [2] for UD plies with 2 damage

functions is available. Thus the damage mechanics formulation suitable for fabric laminates,

which are the reinforcements of interest here, is not yet available. Thus the crash simulations

of composite aircraft floor structures reported in Section 3 are based on an alternative

composites models available in PAM-CRASH. It is supposed that the damage parameters are

functions of the strain invariants, which can be determined by modelling measured stress-

strain curves. The elastic damaging materials law for fabric reinforcements is currently



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modelled in PAM-CRASH as a 'degenerate bi-phase’ model in which the UD fibre phase is

omitted, and the 'matrix' phase is assumed to be orthotropic. In the current version of the code

the simplifying assumption is made that d 1 = d 2 = d 12 = d , thus the composite fabric ply has

orthotropic stiffness properties, but a single 'isotropic' damage function d which degrades allthe stiffness constants equally. The code does however allow different damage functions in

tension and compression. Despite the approximations this model has been used successfully to

simulate the crash response of a quasi-isotropic carbon fabric/epoxy airframe structure in [7].

In this paper it is applied in a pragmatic way to a number of orthotropic and quasi-isotropic

fabric composite laminated structures.

Fig. 1 Schematic fracturing damage function and corresponding stress-strain curve.

The composites structures studied in the paper have been designed for high energy absorption

(EA), and consist of hybrid laminates of carbon and aramid fabric/epoxy for the subfloorelements of Section 3. A materials specimen test programme has been carried out to determine

the basic mechanical properties of the aramid, and carbon fabric/epoxy ply materials used.

Uniaxial stress-strain curves for fabric reinforced composites are modelled by a bilinear

damage function, in which there are two damage constants d1 and du to be determined, (note

d1 here should not be confused with the damage parameter d 1 .) Typical uniaxial stress-strain

curves have the general form shown in Fig. 1, where εi is strain at the onset of initial damage,

ε1 is the strain at the peak failure stress, and εu is a limiting strain above which the stress is

assumed to take a constant value σu. Measured test data for fabric composites are used to

calibrate the materials model and to determine the damage parameters d1 and du for the

analysis. The parameter d1 measures the departure from linearity at the first 'knee' in thestress-strain curves, and is thus small in tension, whilst the parameter du determines the

residual value σu. For the FE analysis it is not good practice to reduce the material stresses

directly to zero at material fracture, as this may lead to numerical instabilities. Thus under

tensile stresses typically du ≅ 0.9, indicating that the element is nearly fully damaged, whilst in

compression du ≅ 0.5 to model the residual compression crushing stress. Materials rate

dependence is not included in the modelling presented here.



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3. Crash response of helicopter subfloor beams

A helicopter design concept which meets the structural and crashworthiness requirements

should provide a protective shell for the occupants, with energy absorbing elementsincorporated in the landing gear, the subfloor and the seats. The subfloor typically consists of a

framework of longitudinal beams and lateral bulkheads covered by the outer skin and cabin

floor. The total structural height is often only about 200 mm. The design of intersections

(cruciforms) of beams and bulkheads, the beam webs, outer skins, and floor sections (boxes)

all contribute to the overall crash response of a helicopter subfloor assemblage. A versatile FE

model has been developed which allows different beam and cruciform elements to be used

within a subfloor box, so that both the static structural integrity and the dynamic crush response

of a range of different boxes may be simulated. In this section the dynamic crush response of

some typical composite subfloor elements are simulated with PAM-CRASH as part of the

design validation process using the degenerate bi-phase model outlined above.

Fig. 2 Cruciform element: comparison of FE simulation with impacted element

The FE model of the cruciform intersection element contained about 5200 4-node orthotropic

layered shell elements to simulate the hybrid composite laminates, together with 22 rigid body

elements which simulated the rivets in the structure. A rivet failure model was not used, since

in tests rivet failures never occurred. Structural tests on the cruciforms are carried out in a drop

weight tower where the upper edges are embedded in an aluminium plate, which is impacted at

about 10 m/s by a 100 kg mass. In the model the nodes of the upper edges form a rigid bodywith an added mass of 100 kg at the centre of gravity, and the base plate was modelled as a

rigid wall. The cruciform element is designed to absorb energy under vertical impact loads,

thus the composite materials selected are hybrid laminates of carbon and aramid fabric/epoxy.

The laminate construction varied between different plate elements in the cruciform, for

example in the transverse floor beam direction the laminate construction is a symmetric hybrid

8 ply layup [A45 /A45 /C45 /C0]S, where A and C refer to aramid and carbon fabric prepregs and

the subscript is the fabric angle relative to the vertical direction.

The results of the dynamic simulations of vertical impacts on the cruciform elements showed

excellent agreement between the predicted modes of failure and those observed in tests. In tests



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the element fails by regular folding of the vertical webs in contact with the base plate, initiated

by the J-trigger at this position. This is clearly seen in Fig. 2 in the FE simulation after 12 ms.

Folding failures occur because of the hybrid laminate chosen, in which the more ductile aramid

fabric plies are on the outer faces where the bending stresses are higher, which seems to inhibitbrittle failures associated with carbon fibre composites.

As a further example of the design procedure, a helicopter subfloor box was simulated

dynamically. The box consisted of 4 cruciform elements, connected by 4 sikken stiffened web

elements and fabricated from hybrid carbon/aramid fabric laminates. The simulation conditions

of vertical impact at 10 m/s and the materials modelling were as described above for the

cruciform element. Simulation results for the quarter deformed box after 8 ms are shown in

Fig. 3. It is seen that the cruciform element fails again in the local progressive folding mode,

whilst the stiffened beam elements fail in single fold with some local crushing of the stiffeners.

Simulations of helicopter subfloor boxes with other beam configurations showed differentfailure modes, such as local crushing in sine-wave webs, with higher EA properties. PAM-

CRASH simulations could thus be used as a design tool for the selection of suitable elements

in the subfloor structure.

kN

0

100

200

300

400

500

600

700

mm

0 15 30 45 60 75 90 105 120 135

Test dlr_r1: Z-Load/ DeformationSimul. dlr_r1_v3a: Z_load/ Deformation

Fig. 3 Subfloor box: simulated deformation with predicted and measured load-deflections

Fig. 3 also compares the predicted load-deflection response under impact compared with test

data on the rib-stiffened boxes. After decay of the initial numerical peak, there is general

agreement in the shape of the load-deflection curves between test and simulation. However, the

load levels, and hence the total energy absorbed in the simulations, are well below the test

results, which shows that further improvements are required in the dynamic modelling of thesehybrid laminates. Similar results are found in [8] where high velocity impact simulations are

carried out on a quasi-isotropic UD shell structure using the same default bi-phase model. Here

the energy absorbed at impact was seriously underestimated. In ongoing work these crash and

impact simulations will be repeated with the improved damage mechanics models outlined in

Section 2, and more extensive materials tests are being carried out to determine appropriate

materials parameters. However, it is clear from the observed failure modes in the subfloor

structure tests that the approach being adopted with layered shell elements is limited. Fig. 2

shows that the failure process includes progressive folding of the laminate, delamination

between aramid and carbon plies and crushing of interior carbon plies. The crush stress can be

included in the shell model by suitable choice of the residual compression strength, but not



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delamination. Thus attention is being turned in the next section to new approaches for

delamination modelling in shell structures.

4. Interlaminar failure modelling

A review of the literature shows that extensive research work has investigated the numerical

analysis of interlaminar failure in composite laminates. Most of this work has used finite

element techniques to model the plies and ply interfaces giving an accurate description of

local stress distribution; the propagation of a delamination crack can then be described using

various techniques. In general failure criteria and damage mechanics (stress degradation)

methods have been preferred for problems involving multiple delamination fronts, whereas

fracture mechanics approaches have mostly been used to predict the propagation of a single

crack emanating from an initial flaw.

An example of delamination modelling using damage mechanics is shown in Fig. 4 for the

crushing of a laminated composite tube. A fine mesh of solid elements represent both the plies

and inter-ply resin. The ‘bi-phase’ orthotropic elastic damage model is used for the

unidirectional plies and an elasto-plastic damage model for the resin rich interface layers. This

approach can capture both ply and inter-ply failure but has the obvious disadvantage that a

large number of elements are needed limiting the method to small scale structures.

Fig 4 Composite tube crushing: Simulation model and example results

The application of fracture mechanics approaches to practical structures has so far been

limited due to computational difficulties of handling a 'softening' structural response [9] andpredicting the growth of multiple fracture cracks. However, these difficulties may be

overcome using an ‘explicit’ finite element formulation in which an element-by-element

scheme and explicit integration solution is used to solve the structural dynamic equations.

These codes are generally preferred for dynamic impact and crashworthiness analysis. A new

technique for laminate and delamination modelling is proposed here that is specifically suited

for explicit FE codes.

The laminate is modelled using one shell element per ply and the ply elements are then

mechanically tied together via contact interfaces and nodal constraints. Failure at the interface

is imposed by monitoring and degrading stresses using damage mechanics once a critical

15mm

5mm

Rigid

wall

Interlaminar

Matrix – 0° and

90° plies



9

value of strain is reached. Fracture mechanics concepts are indirectly introduced by relating

the energy absorbed in the damaging process to the material fracture energy (Gc). One

advantage of this modelling approach, compared to that used in Fig. 4, is that far fewer

elements are needed and the computationally expensive interface solids are eliminated.

The contact interface first identifies adjacent elements and then imposes traction forces

between corresponding slave nodes (upper ply nodes) and master segments (lower ply

elements) using a constitutive law, Fig. 5. The first requirement of this modelling approach is

to ensure that the simplified stacked shell representation has the same kinematic behaviour as

the laminate. This has been verified by comparing results with equivalent solid finite element

models of a laminate for a number of loading cases. Example results are given in Fig. 6 for the

case where the upper and lower plies are loaded to impose high interply shear forces. The

overall deformations, force-deflections response and deformations within the plies all show a

good agreement.

Fig. 5 Main features of the interface contact and interface constitutive law

For the interply failure the interface energy (nodal force * displacement) is monitored and, if

this is found to exceed the limiting value GC, then the crack is advanced. More correctly

mixed mode loading exists and both mode 1 (GC) and mode II (GII) must be monitored with

fracture depending on an interaction criteria [10] of the form:

D

n

IIC

II

m

IC

I eG

G

G

G=

+

(6)

where GI and GII are the monitored interface strain energy in modes 1 and 2 respectively, GIC

and GIIC are the corresponding critical fracture energies and constants m and n are chosen to

fit

the test data. Delamination is assumed to extend if eD ≥ 1.

Mastersegment

Slave node

Slave segment

δIδII

σσ I = EI * δδI / LO

ττ II = GS *

δδII / LO

EI is the equivalent ply and resin tensile modulus (mode I)

GS is the equivalent ply and resin shear modulus (mode II)

EI GIIUndeformed position

Deformed position

L O



10

Fig. 6 Comparison of the stacked shell and solid approaches to modelling composite laminates

Crisfield [9] has proposed a delamination model for interface elements within an implicit

finite element code. These ideas are used here for the explicit FE code with contact interface

treatment. Briefly a softening traction/relative displacement relationship is assumed as shown

in Fig. 7. This curve is typical of damage mechanics methods, however fracture mechanics is

indirectly introduced by relating the energy absorption (area under the stress-strain curve) to

Gc. As in damage mechanics any unloading in the failure zone uses the partially damaged

modulus and is therefore directed toward the origin.

Fig. 6 Assumed interface stress -displacement relation

For material with known delamination stress σt, and critical fracture energy Gc the required

crack opening displacement δmax may be computed. These arguments are applied to determine

the required crack opening for δI,max (mode1) and δII,max (mode 2). Summarising the

expressions derived by Crisfield we have:

[ ]

−=

= II

I

O

II

I E D I ε

ε

σ

σσ

−−=

II

I

O E F I ε

ε

κ

κ

1(7)

GC

δ (crack opening)

δmax max

δO

σt

σ (stress)

unload/

reload



11

Where I is an identity matrix, E O is the diagonal matrix of inter-ply mechanical properties. F

and κ are terms defining the strain and interaction damage model given by,

II I O

II F

,max

max

−

=εε

ε 1

22

−

+

=

n

OII

II

m

OI

I

ε

ε

ε

εκ (8)

where m and n are as defined in Equation 6.

Fig. 8 shows an example analysis for a Double Cantilever Beam (DCB) test under mode 1

loading. A 50mm initial flaw is present in the 125mm long specimen. In this example solid

elements have been used in the study. The model predicts well the crack propagation

emanating from the initial flaw and gives a sensible load-time response consistent with test

data. This is encouraging for the extension of the method to delamination in composite

laminates.

Fig. 8 Example of mode 1 delamination for a composite DCB specimen

5. Conclusions

The paper discusses damage mechanics models for composite shell elements with fibre fabric

reinforcement, as a framework for dynamic simulations on composite structures in explicit FE

codes. A simplified form of the general in-plane model is implemented in PAM-CRASH.



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Simulation of composite helicopter subfloor beam structures under low velocity crash loading

conditions were performed to assess the code and materials models. Structural failure modes

were well modelled in a quasi-isotropic carbon/aramid hybrid laminate but predicted loads and

energy absorption were too low. Thus improvements are required in order to predict accuratelyenergy absorption and peak crushing loads in more complex structures. These should result

from implementation into FE codes of damage mechanics failure models, and improvements in

the measurement of dynamic composites properties at large strains. Both these aspects are

being addressed in ongoing work. There are additional failure situations dominated by

delamination when single shell elements will not be appropriate, and where solid models are

too time consuming. A new numerical approach for modelling composites delamination based

on stacked shell elements with sliding interfaces whose failure properties are consistent with

fracture mechanics principles looks promising in simple test cases and is being extended to full

shell structures. The dynamic properties and failure behaviour of composites are complex and

materials test programmes are very expensive for industry. The challenge for damagemechanics is to develop tractable models, implemented into commercial FE codes, which are

stable to compute and whose parameters may be determined experimentally.

Acknowledgements: Part of the work presented here was developed in the EU project HICAS

[5]. The authors wish to acknowledge the financial contribution of the CEC, and the HICAS

partners for valuable discussions.

References

[1] E. Haug, A. de Rouvray, Crash response of composite structures, Ch. 7 "Structural Crash-

worthiness and Failure" (ed) N. Jones and T. Wierzbicki, Elsevier, London (1993).

[2] P. Ladeveze, E. Le Dantec, Damage modelling of the elementary ply for laminated

composites, Composites Science and Technology, 43, 257-267 (1992).

[3] A.F. Johnson, D. Kohlgrüber, Modelling the crash response of composite aircraft

structures, 8th European Conf. on Composite Materials (ECCM-8), Naples (1998).

[4] A. Matzenmiller, J. Lubliner, R.L. Taylor , A constitutive model for anisotropic damage in

fiber composites , Mech. Materials, Vol. 20, 125-152, 1995.

[5] HICAS High Velocity Impact of Composite Aircraft Structures, CEC DG XII BRITE-

EURAM Project BE 96-4238 (1998).

[6] PAM-CRASH™ FE Code, Engineering Systems International, 20 Rue Saarinen, Silic

270, 94578 Rungis-Cedex, France.[7] A.F. Johnson, Modelling the crash response of a composite aircraft section, ICCM-10, Whistler,

Canada, 1995.

[8] A.F. Johnson, G. Kempe, J. Simon, Design of composite wing access cover under impact

loads, ICCM-12, Paris, 1999.

[9] M.A. Crisfeld, Y. Mi, G.A.O. Davies, H.B. Hellweg, Finite Element Methods and the

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Fundamentals and Applications’, ed DRJ Owen et al., CIMNE Bacelona, Part 1, pp 239-

254, 1997.

[10] Serge Abrate, Impact on Composite Structures, Cambridge University Press, 1998.

impact and crash modelling of composite structures

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