Using Cauchy Stress as Target Value in Homogenization System

[hugary1995]

Discussed in https://github.com/idaholab/moose/discussions/23275

^{Originally posted by **grld** January 30, 2023} Dear community, I would like to use the MOOSE tensor mechanics module to run stress-controlled RVE calculations. I read about the `homogenization system` and that it can be used in combination with periodic boundary conditions to impose cell-average stress or strain conditions. The documentation states that in the finite strain framework, either the deformation gradient **F** or the first Piola-Kirchhoff **PK1** can be used as target quantities. For the calculations that I would like to run, I am interested in targeting the Cauchy stress tensor **and** use the finite strain formulation. The reason is that I don't know the deformation gradient F _before_ I run the simulation so I can not define the **PK1** beforehand as boundary condition but only the cauchy. I know that this is theoretically possible in Abaqus as explained in this [work](https://hss-opus.ub.ruhr-uni-bochum.de/opus4/frontdoor/index/index/docId/5082). The author implements periodic boundary conditions by coupling edge and face nodes at opposite sides of the RVE. Either Neumann or Dirichlet boundary conditions are applied on so-called reference nodes at the corners of the RVE (see page 27). Defining Neumann boundary conditions on the reference nodes is then equivalent to defining an average Cauchy stress (see page 80) I was wondering if this can be also done in MOOSE. Has someone experience with this or any recommendations? Thank you very much for your support already:)

[grld]

Hello community, any progress on this topic?

[hugary1995]

We hope to get to this next fiscal year.