How to compute strain energy density using stress and strain tensor?

Question

I am novice working with FEniCS and FEM method.
Can you guide me how to compute element wise strain energy density knowing strain
\epsilon = 1/2 (F^T + F) - I, where F= grad(u),
Strain energy density U is given as
U = \lambda/2 (tr(\epsilon))^2 + mu tr(\epsilon^2) (Saint Venant–Kirchhoff model)

Answer 1

Project your expression for the strain energy density onto a piecewise constant basis:

DG = FunctionSpace(mesh, "DG", 0)
elementwise_density = project(<your expression>, DG)