2 three dimensional stress and strain
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Three Dimensional Stress and Strain
In order to more fully understand this reality, we must take into account other dimensions of a broader reality. ~ John Archibald Wheeler
BIOE 3200 - Fall 2014
Learning ObjectiveIdentify constitutive equations
(relating stress to strain)
BIOE 3200 - Fall 2014
How do we measure strain?Strain gauge:
BIOE 3200 - Fall 2014
Images from https://www.biomedtown.org/biomed_town/LHDL/Reception/collection/StrainGauges
As the material of interest deforms, the wires in the strain gauge are stretched and electrical conductivity decreases (resistance increases as wires stretch)
From https://ueidaq.wordpress.com/2013/08/02/the-twists-of-strain-gauge-measurements-part-1/
Hooke’s Law by SuperpositionStrain
x y z xy xz yzAppliedStress
x
y
z
xy= yx
xz= zx
yz= zy
x
E x
E x
E
y
E
y
E
y
E
z
E z
E z
E
xy
G
xz
G
yz
G
0 0 0
0 0 0
0 0 00 0 0 0 00 0 0 0 00 0 0 0 0
Constitutive Equations: 3D Stress and Strain
BIOE 3200 - Fall 2014
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