Elasticity/Sample quiz 3

Given the displacement vector

$𝐮=X_1^2{X}_2{\widehat{𝐞}}_1+X_3{\widehat{𝐞}}_2+X_3^2{\widehat{𝐞}}_3$

1. Find the strain tensor $\mathit{\epsilon }$ and the rotation tensor $𝐖$.
2. Write down the compatibility equation in the ${\widehat{𝐞}}_1$- ${\widehat{𝐞}}_2$ plane. Use index notation with commas representing partial derivatives with respect to Lagrangian material co-orinates.