2 three dimensional stress and strain
-
Upload
lisa-benson -
Category
Engineering
-
view
1.245 -
download
2
Transcript of 2 three dimensional stress and strain
![Page 1: 2 three dimensional stress and strain](https://reader037.fdocuments.net/reader037/viewer/2022110108/587761fd1a28ab4e4f8b6ebf/html5/thumbnails/1.jpg)
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
![Page 2: 2 three dimensional stress and strain](https://reader037.fdocuments.net/reader037/viewer/2022110108/587761fd1a28ab4e4f8b6ebf/html5/thumbnails/2.jpg)
Learning ObjectiveIdentify constitutive equations
(relating stress to strain)
BIOE 3200 - Fall 2014
![Page 3: 2 three dimensional stress and strain](https://reader037.fdocuments.net/reader037/viewer/2022110108/587761fd1a28ab4e4f8b6ebf/html5/thumbnails/3.jpg)
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/
![Page 4: 2 three dimensional stress and strain](https://reader037.fdocuments.net/reader037/viewer/2022110108/587761fd1a28ab4e4f8b6ebf/html5/thumbnails/4.jpg)
![Page 5: 2 three dimensional stress and strain](https://reader037.fdocuments.net/reader037/viewer/2022110108/587761fd1a28ab4e4f8b6ebf/html5/thumbnails/5.jpg)
![Page 6: 2 three dimensional stress and strain](https://reader037.fdocuments.net/reader037/viewer/2022110108/587761fd1a28ab4e4f8b6ebf/html5/thumbnails/6.jpg)
![Page 7: 2 three dimensional stress and strain](https://reader037.fdocuments.net/reader037/viewer/2022110108/587761fd1a28ab4e4f8b6ebf/html5/thumbnails/7.jpg)
![Page 8: 2 three dimensional stress and strain](https://reader037.fdocuments.net/reader037/viewer/2022110108/587761fd1a28ab4e4f8b6ebf/html5/thumbnails/8.jpg)
![Page 9: 2 three dimensional stress and strain](https://reader037.fdocuments.net/reader037/viewer/2022110108/587761fd1a28ab4e4f8b6ebf/html5/thumbnails/9.jpg)
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
![Page 10: 2 three dimensional stress and strain](https://reader037.fdocuments.net/reader037/viewer/2022110108/587761fd1a28ab4e4f8b6ebf/html5/thumbnails/10.jpg)
Constitutive Equations: 3D Stress and Strain
BIOE 3200 - Fall 2014