Elasticity/Sample quiz 3

Given the displacement vector

$\mathbf {u} =X_{1}^{2}X_{2}{\widehat {\mathbf {e} }}_{1}+X_{3}{\widehat {\mathbf {e} }}_{2}+X_{3}^{2}{\widehat {\mathbf {e} }}_{3}$

1. Find the strain tensor ${\boldsymbol {\varepsilon }}$ and the rotation tensor $\mathbf {W} \,$.
2. Write down the compatibility equation in the ${\widehat {\mathbf {e} }}_{1}$- ${\widehat {\mathbf {e} }}_{2}$ plane. Use index notation with commas representing partial derivatives with respect to Lagrangian material co-orinates.

Elasticity