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.
 Figure out the corresponding Green strain tensor.

If a stress tensor is
\[
\boldsymbol{\sigma} =
\left[ \matrix{
10 & 20 & 30 \\
20 & 40 & 10 \\
30 & 10 & 50 }
\right]
\]
then calculate the traction vector on a plane with
unit normal \({\bf n} = (0.100, \; 0.700, \; 0.707)\).