Finite element implementation of a gradient-damage theory for fracture in elastomeric materials

We present a finite element implementation procedure for a phase-field framework for fracture in elastomeric materials based on the gradient-damage theory. Governing equations of macroscopic and microscopic force balances, and constitutive theories for large elastic deformation and damage are summarized, and the computational implementation is described in significant detail. To facilitate the computational implementation of the gradient-damage theory for elastomeric materials in a widely available finite element program, the source codes are provided as online Supplemental Materials to this paper. Furthermore, we provide a comparative study of the gradient-damage models with two distinct driving forces for damage: (1) entropy-driven and (2) internal energy-driven. We then show that the internal energy-driven damage model presents more realistic descriptions of the failure that accompanies extreme stretching and scission in elastomeric networks.