The Fracture Simulation of Hyperelastic Materials in PhasefieldX

[Mr-ZhangQiang]

Dear PhaseFieldX Development Team,
Thank you for sharing the codes on phase-field fracture. My operating system is Ubuntu (24.04.3), and I could successfully run example cases from phasefieldx in VS Code software. I am currently trying to adapt your codes for phase-field fracture analysis of hyperelastic materials (rubber). After adjusting several files in the phasefieldx package, the code still ran normally. However, unfortunately, the phase-field damage parameter φ could only be calculated up to 0.63, eventually leading to non-convergence (Solver did not converge，got -6). Below are the version numbers of some key packages I used: phasefieldx—0.3.0, fenics-dolfinx—0.10.0, python—3.11.4, petsc4py/petsc—3.24.3, scifem—0.16.1, numpy—2.4.1, mpi4py—4.1.1. My operating system is Ubuntu (24.04.3).
The code I used can be found in the attachment. It would be greatly appreciated if you could provide some advice on how to solve this issue.
Best regards，

test.zip

[CastillonMiguel]

Dear @Mr-ZhangQiang ,

Thank you for your message and for your interest in PhaseFieldX. I’m glad to hear that you were able to successfully run the example cases on your system.

Based on the information you provided, it is unfortunately difficult to precisely identify the source of the non-convergence issue. The fact that the phase-field damage variable φ saturates around 0.63 and eventually leads to a solver failure (PETSc error -6) may be related to several factors, such as the constitutive formulation, the coupling strategy, or the nonlinear solver settings.

At the moment, PhaseFieldX contains a module dedicated to elasticity, (linear elasticity). In my opinion, the most robust way forward would be the following approach:
1. First implement a simple hyperelasticity model within the PhaseFieldX framework, without any phase-field fracture coupling. This allows you to verify that the hyperelastic formulation, boundary conditions, and nonlinear solver settings are working correctly and converge reliably.
2. Once the hyperelastic problem works as expected in PhaseFieldX, the extension to the phase-field fracture formulation becomes straightforward, since the phase-field machinery is already in place.

For reference, you may find the following DOLFINx hyperelasticity example useful as a starting point for implementing a simple hyperelastic model: [https://jsdokken.com/dolfinx-tutorial/chapter2/hyperelasticity.html]

Additionally, I plan to create a dedicated branch in PhaseFieldX for implementing hyperelasticity, allowing this functionality to be developed and tested independently before integrating it with the phase-field fracture solver.

Best regards,
Miguel