A Pressure‐Projection Stabilized Hybrid ES‐FEM/FEM Formulation for Phase‐Field Fracture of Nearly Incompressible Elastomers

Modeling phase‐field fracture in nearly incompressible elastomers is challenging due to volumetric locking and mesh distortion under finite strains. Conventional displacement‐based FEM often exhibits locking‐induced over‐stiff responses and severe mesh distortion, leading to inaccurate stress fields and loss of convergence. To address these issues, we propose a pressure‐projection stabilized hybrid ES‐FEM/FEM framework for large‐deformation phase‐field fracture. The mixed displacement–pressure field is approximated by equal‐order interpolation within an edge‐based smoothed finite element (ES‐FEM) formulation equipped with pressure projection, which alleviates volumetric locking and enhances stability under large deformations through strain smoothing. The phase‐field variable is solved using standard FEM on the same mesh, maintaining computational efficiency comparable to classical implementations. The resulting framework is naturally compatible with adaptive mesh refinement, rendering it well suited for resolving the highly localized gradients inherent to phase‐field formulations. Benchmark tests and comparisons with experimental observations demonstrate improved convergence, accurate load–displacement responses, and physically consistent crack paths in soft, nearly incompressible elastomers.