Hencky(Logarithm) strain

variational formulation
1

Hi everyone

I just wonder if there is any way to compute the 3D Hencky strain. I know if the left stretch tensor V is a diagonal tensor, then we can use

E_h = diag(elem_op(ln,diag_vector(V)))

But for the general case, we need to calculate the eigenvalues and eigenvectors of V, which is very difficult in FEniCS especially for the 3D case.

And I also noticed that, in the finite elastoplasticity example of MFont, the logarithm strain is used. But it seems I couldn’t only take the strain calculation part out.

So, my question is, is there any way to use logarithm strain feasibly in FEinCS?

2

Hi, no the eigenvalue decomposition for evaluating the Hencky strain is done within MFront. It cannot be easily done with UFL operators apart from implementing the complex expressions for 3D eigenvalues.

3

Do you mean eigenvalue decomposition is not used within MFront?

4

Yes it is. The deformation gradient F is passed to MFront which internally performs the eigendecomposition of the stretch tensor, computes the Hencky strain then evaluates the constitutive law and gives back the PK stress and tangent stiffness.

5

Thank you for your answers.