For two-dimensional problems, there are tree possible approximations: plane strain, Generalized Plane Strain, and Plane Stress. The selection is made in the settings for the Solid Mechanics node.

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

and the strain tensor εij = εij (X, Y) only has in-plane components:

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), ∂u/∂Y = ∂u/∂Z = 0, and εxy = εy = 0.