Phase-field modeling of ductile fracture in polymers: a finite-strain framework with nonlinear hardening effects

Polymers often experience ductile fracture under adverse loading conditions, accompanied by significant visco-elastic-plastic deformation prior to failure. The damage evolution in polymers is strongly influenced by isotropic hardening and nonlinear kinematic hardening, which affect the stress field and energy dissipation characteristics during plastic deformation. A finite-strain phase-field model is developed to simulate ductile fracture in polymers undergoing large deformations. In this model, a finite-strain thermodynamically consistent framework is formulated, where the viscoplastic free energy is decomposed into contributions from isotropic and nonlinear kinematic hardening mechanisms. Furthermore, to prevent unrealistic crack propagation under compressive loading, a spectral decomposition scheme is applied. Subsequently, the mechanics and phase-field governing equations are derived and implemented in an incremental form within finite element software. The proposed model is validated against three benchmark cases. The simulation results show good agreement with experimental data, including load-displacement curves, crack propagation paths, and strain fields. As a result of incorporating the finite-strain thermodynamically consistent framework and kinematic hardening formulation, a significantly improved accuracy in damage evolution prediction is achieved when polymer specimens undergo large deformations, particularly after isotropic hardening saturation is attained.