For plane strain, the deformation occurs in the xy-plane and it is fully characterized by the in-plane displacement components
u(
X,
Y) and
v(
X,
Y). There is no out-of-plane displacement,
w = 0, and there are only in-plane strains. In this case, the displacement gradient reads
For the 1D plane strain representation, only the x-component of the displacement field is computed, and only gradients with respect to the
x-direction are considered, this is,
u =
u(
X),
, and
.