Stabilized formulation for phase?field fracture in nearly incompressible hyperelasticity

This work presents a stabilized formulation for phase-field fracture of hyperelastic materials near the limit incompressibility. At this limit, traditional mixed displacement and pressure formulations must satisfy inf-sup condition solution stability. The coupled with damage field can lead to an inhibition crack opening as volumetric changes are severely penalized effectively creating pressure-bubble. To overcome bottleneck, we utilize perturbed Lagrangian which enforces incompressibility constraint in undamaged material reduces effect damaged material. A mesh-dependent stabilization technique based on residuals Euler–Lagrange equations multiplied differential operator acting weight space is used, allowing linear interpolation all variables elastic subproblem. was validated three examples at finite deformations: plane-stress pure-shear test, two-dimensional geometry plane-stress, three-dimensional notched sample. In last example, incorporate hybrid additive strain energy decomposition account different behaviors tension compression. results show close agreement analytical solutions tip displacements performs well