data from the book introduction to biomechanical ... · author: shigehiro hashimoto kogakuin...

Author: Shigehiro Hashimoto

Kogakuin University,

Department of Mechanical Engineering,

Biomedical Engineering

[email protected]

Data from the book "Introduction

to Biomechanical Engineering (in

Japanese)“: published by Corona

Publishing Co., Ltd. Tokyo, Japan.

© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.1: Spring

Dilation Dilation Dilation

Dilation

Weight


Fig. 3.2: Mode of deformation

Extension

Compression

Bending

Twist


Fig. 3.3: Orientation of cells and

matrices

Orientation of extracellular matrices

Orientation of cells

Longitudinal direction of extracellular matrix

Longitudinal direction of cell

(Endothelium)


Fig. 3.4: Direction of forces at tube

wall

Radial

Tangential

Longitudinal


Fig. 3.5: Transmission of force

(A)

(B)

?

Cell Force

Cell

Flow

Shear field

Scaffold

Wall

Slip at attachment part


Fig. 3.6: Fixation

Fixation

Measurement

Mark

Mark

Friction

Pressure

Pressure

Tension

Tension(a) (c)(b)

Compliance


Fig. 3.7: Origin

Deformation

Force

Origin?

Linear part

composite

material


Normal stress

Fig. 3.8: Stress

Shear stress

Surface Surface


Fig. 3.9: Poisson’s ratio

Deformation

x＋Δxx

ｙ y－Δy

Force

Force


Tension

Fig. 3.10: Strains in tension

Compressive strainShear strain

Tensile strain


Fig. 3.11: Strain gauge

Tension

Wire

thick &

short

Wire

small &

long

Resistance change

StrainStrain gaugeStrain gauge


Fig. 3.12: Stress-strain diagram

Strain ε

Stress τYield point

Elastic

Elastic modulus E

Plastic


Fig. 3.13: True stress

Deformation

x1x0

ｙ0 y1

A0 A1

F1

F1

F0

F0

τ0＝F0 / A0 τ1＝F1 / A1: True stress

τ＝F1 / A0: Nominal stress


ΔP

r

γ

r

ΔPπr2＝2πr γ (3.10)

ΔP＝2γ／r (3.11)

Equation of Young-Laplace

Fig. 3.14: Balance of forces in

hemisphere


Fig. 3.15: Tensile force at membrane of

erythrocyte

P1

P2

P3

r1r2

γ

Capillary

Erythrocyte


Fig. 3.16: Bending

F

F/ 2

x

Bending moment

Shearing force

Positive

PositiveM=xF/ 2

x

F/ 2

F/ 2

F/ 2

a/ 2 a/ 2

(a)

(b)

F／2＋F／2－F ＝0 (3.12)

－(a／2)F＋a(F／2)＝0 (3.13)


Fig. 3.17: Simple & rigid support

F

F/ 2

x

F/ 2a/ 2 a/ 2

F

F

x

a

Rigid support

Simple support

M

(a) Simple support

(b) One side rigid support

Simple support


Fig. 3.18 Three-point bending test

F1

F1/ 2 F1/ 2

Shearing force diagram

Bending moment diagram

F

F1/ 2

F1/ 2

a

F1a/ 4

a/ 2

0 x

M

x

a

a

a/ 2

a/ 2

0

x(a)

(b)

(c)


Fig. 3.19: Four-point bending test

F1 F1

F1 F1

Shearing force diagram

Bending moment diagram

a

a/ 3

F1

F1

F1a/ 3

xa

x

a

x

F

M

0

0

a/ 3

2a/ 3a/ 3

2a/ 3

(a)

(b)

(c)


Fig. 3.20: Center line and strain

Center line

y x

Cross-sectional area:

A

dA y

z

Cross

section

Iz＝∫y2 dA (3.15)

Moment of inertia: Iz


Fig. 3.21: Yield and fracture

Strain

Stress

Yield point

Maximum strain

Strength Fracture


Fig. 3.22: Repetitive load

Stress

(b) Compression

(c) Extension & Compression

Time

Stress

(a) Extension

Time

TimeStress

0

0

0

Amplitude

Period


Fig. 3.23 Fracture surface

Fracture

surface

DimpleStriation


Fig. 3.24: Stress amplitude vs.

number of cycles

Destructive

area

Non-

destructive

area

Destruction

Non-

destruction

Number of cycles

Stress

amplitude


Fig. 3.25: Erythrocyte fatigue in flow

Shear

stress

(Shear rate)×(Exposure time)

Hemolysis ratio ＜0.01

Hemolysis ratio＞0.01

Tensile

Compression

Tensile

Compression


Fig. 3.26: Erythrocyte destruction

0.01 mm

Hemolysis

Periodical

deformation

(Ellipsoid)


Fig. 3.27: Close-packed lattice

Close-packed

hexagonal

lattice

Face-

centered

cubic lattice

ABCABC ABABAB

A

B

C


Fig. 3.28: Surface

Inside

Surface

Interaction


Fig. 3.29: Poly-crystal

Crystal grain


Fig. 3.30: Lattice defect

DislocationVacancy


Fig. 3.31: Stress concentration

Curvature

Notch

Stress

concentration

Force

Force


Fig. 3.32(a): Orientation of

endothelial cells

0.1 mm

Flow

Orientation


Fig. 3.32(b): Orientation of C2C12

0.1 mm

Flow

Orientation


Fig. 3.33: Electrodes

10 mmCell culture


Fig. 3.34: Force applied on laryngoscope


Tongue

Superior

incisor

Epiglottis

Laryngoscope

Fig. 3.35: Phantom

(a) Copper sulfate

aqueous solution

(b) MRI (magnetic

resonance image)


Fig. 3.36: Penetration of phenol-red

into agar

Agar

Phenol red


Q. 3.3 Fig. 3.37: Face-centered

cubic unit lattice

r

r

r


data from the book introduction to biomechanical ... · author: shigehiro hashimoto kogakuin...

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