Strain gradient plasticity with mgis.fenics

[jeanmichelscherer]

Hi,

I am working on a scalar strain gradient plasticity extension of a simple von Mises plasticity behaviour. I would like to use that behaviour in FEniCS through mgis.fenics. The Mfront implementation and FEniCS script are attached.

The behaviour defines 3 Gradients (TotalStrain, CumulatedPlasticStrain, CumulatedPlasticStrainGradient) and 3 Fluxes (Stress, MicroStress, DoubleStress). Based on a Mtest test, that implementation seems to work fine.

In the FEniCS script, the degrees of freedom (u=Displacement, lX=LagrangeMultiplier, pX=CumulatedPlasticStrain) are defined through a mixed function space. Since the model does not fit into the default residual formulation, I updated the residual as follows:

problem.residual = ( inner(voigt2stress(sigma,dim),grad(u_)) + dot(M,grad(pX_)) + S*pX_ + (pX - p)*lX_ )*problem.dx

• If I pass v, the function defined on the mixed function space, to initialize the MFrontNonlinearProblem I get the following UFL error:

This integral is missing an integration domain.
Traceback (most recent call last):
  File "vonMisesStrainGradientPlasticityLagrangeMultiplier.py", line 156, in <module>
    problem.initialize()
  File "/usr/local/lib/python3.8/site-packages/mgis/fenics/nonlinear_problem.py", line 386, in initialize
    self.define_form()
  File "/usr/local/lib/python3.8/site-packages/mgis/fenics/nonlinear_problem.py", line 178, in define_form
    self.residual = (sum([
  File "/home/scherer/Softwares/ANACONDA/anaconda3/envs/fenics/lib/python3.8/site-packages/ufl/measure.py", line 441, in __rmul__
    error("This integral is missing an integration domain.")
  File "/home/scherer/Softwares/ANACONDA/anaconda3/envs/fenics/lib/python3.8/site-packages/ufl/log.py", line 172, in error
    raise self._exception_type(self._format_raw(*message))
ufl.log.UFLException: This integral is missing an integration domain.

• If, however, I pass u, only the displacement part of v, the issue above is not triggered.

• When I pass u to initialize the MFrontNonlinearProblem, the rest of the script runs, but the boundary conditions are not applied.

Do you know how I can pass the boundary conditions correctly?

Thanks,
Jean-Michel

vonMisesStrainGradientPlasticity.tar.gz

[thelfer]

@bleyerj This one is for you !

[jeanmichelscherer]

Hi @bleyerj,

The following links helped to solve the issue:

• https://thelfer.github.io/mgis/web/mgis_fenics_monolithic_transient_thermoelasticity.html
• https://fenicsproject.org/qa/11964/petsc-problem-when-solving-nonlinear-variational-problem/

I was using the wrong split function. The following lines were causing the issue:

v = Function(V, name="DOFs")
u, lX, pX = v.split()

They must be replaced by:

v = Function(V, name="DOFs")
u, lX, pX = split(v)