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