Data from the book "Introduction
to Biomechanical Engineering (inJapanese)“: published by Corona
Publishing Co., Ltd. Tokyo, Japan.
Author: Shigehiro Hashimoto
Kogakuin University,
Department of Mechanical Engineering,
Biomedical Engineering
shashimoto@cc.kogakuin.ac.jp© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.1: Spring

Dilation

Dilation

Dilation

Dilation

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

Fig. 3.2: Mode of deformation
Extension
Bending

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

Fig. 3.3: Orientation of cells andmatrices
Longitudinal direction of cell

Orientation of cells

Orientation of extracellular matrices(Endothelium)
Longitudinal direction of extracellular matrix© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.4: Direction of forces at tube
wall
Longitudinal

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

Fig. 3.5: Transmission of force?

(A)

ForceCell
Scaffold
Slip at attachment part

Flow(B)

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

Fig. 3.6: Fixation(a)(b)(c)

TensionFixation
PressureMark
Measurement
PressureMark
Compliance

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

Fig. 3.7: Origin
compositematerialForce

Origin?
Linear part

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

Fig. 3.8: Stress
Surface

Normal stress

Surface

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

Fig. 3.9: Poisson’s ratio
Forcex＋ΔxxDeformationｙForcey－Δy© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.10: Strains in tension
TensionTensile strain

Compressive strain

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

Fig. 3.11: Strain gauge
Strain gauge

StrainStrain gauge

TensionWire
thick &shortWire
small &longResistance change© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.12: Stress-strain diagram
Plastic
Stress τ

Yield point

Elastic
Elastic modulus E

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

Fig. 3.13: True stress
F0x0

F1x1A0Deformation

ｙ0F0
τ0＝F0 / A0

A1y1F1
τ1＝F1 / A1: True stress
τ＝F1 / A0: Nominal stress© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.14: Balance of forces inhemisphere

rrγ

ΔP

ΔPπr2＝2πr γ
ΔP＝2γ／r(3.10)(3.11)

Equation of Young-Laplace© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.15: Tensile force at membrane oferythrocyte
γP1

r2r1
P2

Capillary
P3

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

Fig. 3.16: Bending(a)Fx
F/ 2a/ 2a/ 2

F／2＋F／2－F ＝0(3.12)－(a／2)F＋a(F／2)＝0(3.13)

(b)
x

F/ 2

Positive
Shearing force

M=xF/ 2F/ 2F/ 2

Positive

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

Fig. 3.17: Simple & rigid support(a) Simple support
Simple supportxFSimple support

F/ 2a/ 2(b) One side rigid support
Rigid support

F/ 2a/ 2Fx
aMF© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.18 Three-point bending test
(a)

F1x

a/ 2a

F1 / 2(b) F0

F1 / 2F1 / 2a/ 2
Shearing force diagram(c) M
F1a/ 40a/ 2Bending moment diagramax

F1 / 2a© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japanx

Fig. 3.19: Four-point bending test
(a)

F1x

a/ 3F1(b) F0F12a/ 3aF1aa/ 3M
0aF1a/ 3a/ 3x

F1

Shearing force diagram(c)

F12a/ 3Bending moment diagram© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japanx

Fig. 3.20: Center line and strain
ydA

yxz
Cross
sectionCross-sectional area:
Center lineA

Moment of inertia: Iz

Iz＝∫y2 dA(3.15)© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.21: Yield and fracture
StressStrengthFracture

Yield point

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

Fig. 3.22: Repetitive load(a) Extension
Stress(b) Compression

Amplitude

StressTime0Period0Time(c) Extension & Compression
Stress0Time© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.23 Fracture surface
DimpleStriation
Fracturesurface© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.24: Stress amplitude vs.
number of cycles

Stressamplitude

Destructive
area
Nondestructivearea

Destruction
Nondestruction

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

Fig. 3.25: Erythrocyte fatigue in flow
TensileCompression

Compression
TensileShearstress

Hemolysis ratio＞
0.01
Hemolysis ratio ＜0.01(Shear rate)×(Exposure time)© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.26: Erythrocyte destruction

Hemolysis

Periodicaldeformation(Ellipsoid)0.01 mm© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.27: Close-packed lattice
Facecenteredcubic lattice

Close-packed
hexagonallattice

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

Fig. 3.28: Surface
Interaction
SurfaceInside© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.29: Poly-crystal
Crystal grain© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.30: Lattice defectVacancy

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

Fig. 3.31: Stress concentration
Force

Stressconcentration

Notch

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

Fig. 3.32(a): Orientation ofendothelial cells

Flow

Orientation

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

Fig. 3.32(b): Orientation of C2C12Flow

Orientation

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

Fig. 3.33: Electrodes

Cell culture

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

Fig. 3.34: Force applied on laryngoscope

TongueLaryngoscope

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

Fig. 3.35: Phantom(a) Copper sulfate
aqueous solution(b) MRI (magneticresonance image)© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan

Fig. 3.36: Penetration of phenol-red
into agar

Phenol red

Agar© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, JapanQ. 3.3 Fig. 3.37: Face-centeredcubic unit latticerrr© Shigehiro Hashimoto 2013, Published by Corona Publishing Co., Ltd. Tokyo, Japan