Homework #10
Reminder - you're going to need these webpages:
http://www.continuummechanics.org/interactivecalcs.html
to do this homework.... unless you prefer to use Matlab, Mathematica, etc.
Take advantage of software programs to do all the matrix multiplication
and other procedures when you have a chance.
Use the following true strain tensor for the first three problems.
\[
\boldsymbol{\epsilon}_{\text{True}} =
\left[ \matrix{
\;\;\; 0.758 & -0.237 & \;\;\;0.012 \\
-0.237 & -0.546 & \;\;\;0.067 \\
\;\;\; 0.012 & \;\;\; 0.067 & -0.212 \\
} \right]
\]
- This true strain tensor is for an incompressible material.
Demonstrate that this is indeed the case.
- Calculate \(\epsilon_{\text{Hyd}}\), \(\gamma_{\text{Max}}\), and
\(\gamma_{\text{Sec}}\), and determine whether the strain tensor represents
a state closer to uniaxial tension, shear, or equibiaxial tension(compression).
- Figure out the corresponding engineering strain tensor.
- Figure out the corresponding Green strain tensor.