This FEniCS code is associated with a paper titled "Stabilized formulation for phase-field fracture in nearly incompressible hyperelasticity" published in the International Journal for Numerical Methods in Engineering (IJNME). If using or referencing this code, please cite the associated paper.
This work presents a stabilized formulation for phase-field fracture of hyper- elastic materials near the limit of incompressibility. At this limit, traditional mixed displacement and pressure formulations must satisfy the inf-sup condition for solution stability. The mixed formulation coupled with the damage field can lead to an inhibition of crack opening as volumetric changes are severely penalized effectively creating a pressure-bubble. To overcome this bottleneck, we utilize a mixed formulation with a perturbed Lagrangian formulation which enforces the incompressibility constraint in the undamaged material and reduces the pressure effect in the damaged material. A mesh-dependent stabilization technique based on the residuals of the Euler-Lagrange equations multiplied with a differential operator acting on the weight space is used, allowing for linear interpolation of all field variables of the elastic sub-problem.
Dependencies and versioning can be checked by 'pip3 list' Operating System: Ubuntu 20.04.4 LTS (Focal Fossa) Python: 3.8.10 FEniCS: 2019.2.0.dev0 (type dolfin-version to check) Mshr will be the same version since it is packaged in FEniCS If using the Gmsh files provided: Gmsh: 4.9.5 matplotlib: 3.1.2 numpy: 1.22.3 scipy 1.8.0 sympy 1.5.1