Mixed displacement–pressure-phase field framework for finite strain fracture of nearly incompressible hyperelastic materials

The favored phase field method (PFM) has encountered challenges in the finite strain fracture modeling of nearly or truly incompressible hyperelastic materials. We identified that underlying cause lies innate contradiction between incompressibility and smeared crack opening. Drawing on stiffness-degradation idea PFM, we resolved this through loosening constraint damaged without affecting intact material. By modifying perturbed Lagrangian approach, derived a novel mixed formulation. In numerical aspects, element discretization uses classical Q1/P0 high-order P2/P1 schemes, respectively. To ease mesh distortion at large strains, an adaptive deletion technology is also developed. validity robustness proposed framework are corroborated by four representative examples. comparing performance P2/P1, conclude formulation better choice for cases. Moreover, examples show combination methodology vast potential simulating complex peeling tearing problems.