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).
    Then check your result using this page: http://www.continuummechanics.org/techforms/RUDecomposition.html


  2. How many degrees of rigid body rotation are in this deformation gradient, and what is the axis of rotation?


  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.