A two$-$dimensional displacement field in the x$,$ y plane is given by u $=\{\backslash$alpha y$,\backslash$alpha x$\},$

where $0<\backslash$alpha $1.$

a$)$ Sketch how a square with corners $($a$,0),(-$a$,0),(0,$ a$)$ and $(0,-$a$)$ is deformed. How to change the area of $$the deformed square?

b$)$ Find the displacement difference $\backslash$geotriangle u between any two points in the field with vector distance $\{\backslash$geotriangle x$,\backslash$geotriangle y$\}.$ Determine the relative displacement difference tensor.

c$)$ Find the tensor for deformations without volume change for the given field.