State of dolfinx for multiscale simulations with computational homogenization

[JStorm]

Hi,
I’m considering using dolfinx for an FE2 problem, where the microscale is a periodic material loaded based on the strain of the macroscale structure. I want to know to which extent this is already possible using existing dolfinx extensions.

What I’ve found:

• Micmacsfenicsx could be an all-in-one solution but is under construction to port to dolfinx. It does support legacy fenics.
• dolfinx_materials supports arbitrary material models, and can thus be combined with another library that supports generic PBCs
• dolfinx_mpc implements PBCs. But from what I can tell from this discussion it does not out of the box support dirichlet+PBCs
  • See this further discussion: Periodic Boundary Condition + Constant · jorgensd/dolfinx_mpc · Discussion #76 · GitHub, the extension should in principle not be difficult.

Based on this I think it would likely be best to combine dolfinx_materials with dolfinx_mpc, and implement defining the PBC with an imposed displacement as in the linked discussion.

Since some of these discussions are >1.5 years old, I was wondering if there is something I am missing, and this is already possible in some other way?

Thank you,
Joep

[dokken]

Periodic conditions can be achieved within native DOLFINx with the code from:

https://gist.github.com/jorgensd/e0e610fd17f73337178bc12788fa17ba

as shown in:

Periodic BCs in parallel not working

This is due to the fact that the mesh is actually periodic and you have to use a different method for visualization (and setting initial conditions). Here is an mwe that is adjusted to illustrate that it works: # Import Libraries from mpi4py import MPI from dolfinx import mesh, fem, io, la import dolfinx.fem.petsc import numpy as np from pathlib import Path from script import create_periodic_mesh # Create mesh domain = mesh.create_unit_square( MPI.COMM_WORLD, 100, 100, cell_t…