# Homework #6

Feel free to use http://www.continuummechanics.org/interactivecalcs.html when applicable.

Use the following deformation gradient for the problems.

${\bf F} = \left[ \matrix{ \;\;\; 1.5 & \;\;\; 0.3 & -0.2 \\ -0.1 & \;\;\;1.2 & \;\;\; 0.1 \\ \;\;\; 0.3 & -0.2 & \;\;\; 1.1 } \right]$
1. Determine $${\bf R}$$ and $${\bf U}$$ in $${\bf F} = {\bf R} \cdot {\bf U}$$.
Do it the hard way by multiplying all the matrices out yourself (but not by hand! use software).
3. Now that you have $${\bf R}$$ and $${\bf U}$$ from #2, calculate $${\bf V}$$ and use http://www.continuummechanics.org/techforms/VRDecomposition.html to check that you got it right.