Problem 4: The local deformation of the material is described in
Cartesian coordinates by the displacement vector
u=U_(x)i+U_(y)j+U_(z)k
, where
U_(x)=x²+y²-z,U_(y)=3xz
, and
U_(z)=2z³
. Calculate the infinitesimal strain tensor(cf. last slides of lecture 4).