Meshed rigid indenter in contact with a hyperelastic body in FEniCSx

variational formulation
1

Dear FEniCSx community,

I would like to simulate a rigid indenter being pushed into a hyperelastic material. The indenter should be represented as a meshed body, so that different indenter geometries can be studied. As a first step, I would like to consider a 2D, frictionless contact formulation.

I have looked at several existing approaches:

  • The “Contact Penalty” demo from comet-fenics uses an analytical indenter and assumes small deformations.
  • The “Coupling PDEs” example by Jørgen S. Dokken shows coupling across a simple interface, but not general contact between meshed bodies.
  • Contact using dolfinx_mpc seems suitable for tied or constrained interfaces, but as far as I understand, it does not allow surfaces to separate.
  • I also found discussions about a “third medium contact” approach. However, in my case the indenter should eventually be able to penetrate the material using a cohesive zone model, which would create new surfaces.
  • I also found the dolfinx-contact / asimov-contact project, which seems to support contact between meshed entities. From a first look at the source code, it appears that the implemented material behavior is mainly linear elastic.

My questions are:

  1. Is dolfinx-contact currently suitable for large-deformation hyperelastic contact problems?
  2. If not, would it be feasible to extend it to finite-strain hyperelasticity?
  3. Are there other recommended approaches in FEniCSx for frictionless contact between a meshed rigid indenter and a hyperelastic body?
  4. Has anyone combined such a contact formulation with damage or cohesive zone models where new surfaces may be created?

Any guidance, references, or examples would be greatly appreciated.

2

Hi @tomkuh,

I recently published some codes here that might be a useful starting point. In my case the indenter is rigid, but it is still possible to vary its geometry from the parametrization.

For deformable-to-deformable contact (which is what you need with a meshed indenter), the most relevant existing work in FEniCSx is asimov-contact. As far as I know it currently targets a small-deformation setting, but its contact detection infrastructure could in principle be extended to large deformations. @dokken would probably be the right person to confirm this and clarify the current capabilities of the library.