Section 12: Mechanics of - Materials

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18 Ιουλ 2012 (πριν από 5 χρόνια και 3 μήνες)

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Section 12: Mechanics of
Materials

Stress / Strain
12-1
BasicBiomechanics
Basic

Biomechanics
Force
Force
Area
ΔΔL
L
Stress =
Force/Area
Strain =
Chan
g
e Hei
g
ht
(
Δ
L
)
 =
12-2From: Le
Force/Area
gg(
)
Original Height(L0)
Stress
Stress


Stress(
σ
)
:i湴敲湡n
却牥獳
=
(
σ
)
:
=
楮瑥牮慬
=
牥獩獴慮捥⁴漠慮r
數瑥牮慬潡e
Axial
–Axial (compressive or
tensile) σ=F/A
Sh
F/A(lll

Sh
ear τ=
F/A

(
para
ll
e
l

or tangential forces)

UnitsPascal(Pa)
=
Shear
Units

Pascal

(Pa)

1Nm
2
Shear
12-3From: Noffal
12-4From: Grimm and Atkinson
12-5From: Seeley
DefinitionofStress
Definition

of

Stress
F
o
A
F
=
σ
F
o
•This is the definition of engineering stress.
•F is the force in Newton
(
N
)
A0
()
•A0 is the initialarea of the specimen in m2.
•The unit of stress is therefore N/m2.
•1 N/m2=1 Pascal or 1 Pa.

1KPa=10
3
Pa;1MPa=10
6
Pa;1GPa=10
9
Pa
F

1

KPa=10
3
Pa;

1

MPa=10
6
Pa;

1

GPa=10
9
Pa
.
•Strengths of metals are usually in MPa; elastic modulus of
metals usually in GPa.
F
12-6From: Wei
Basic Biomechanics
Force, Displacement & Stiffness
F
o
r
ce
Slope
=
Stiffness
=
oce
Slope

Stiffness

Force/Displacement
12-7From: Le
Displacement
Basic Biomechanics
Stress-Strain & Elastic Modulus
Stress
=
Stress

Force/Area
Slope =
Elastic Modulus =
Stress/Strain
Strain =
ChiLth/OiilLth(
Δ

L
)
12-8From: Le
Ch
ange
i
n
L
eng
th/O
r
i
g
i
na
l

L
eng
th

(
Δ

=
L
0
)
12-9From: Grimm and Atkinson
Basic Biomechanics
Common Materials in Orthopaedics
•Elastic Modulus
(GPa)
•Stainless Steel200
•Titanium100
•Cortical Bone7-21
•Bone Cement2.5-3.5
•Cancellous Bone 0.7-
4.9
Stress
•UHMW-PE1.4-4.2
Strain
12-10From: Le
Strain
12-11From: Seeley
12-12From: Seeley