Modeling via peridynamics for large deformation and progressive fracture of hyperelastic materials

Hyperelastic materials are frequently observed in the natural world and engineering applications such as rubbers and animal soft tissues. Modeling large deformation and progressive fracture of these materials is challenging for grid-based methods due to the severe mesh distortions at crack tips. To address this problem, we proposed a novel meshfree framework using bond-based peridynamics (PD) based on finite deformation theory. The proposed modeling framework has the following novelties: (1) An original bond strain, derived from the spectrum representation of hyperelastic models is used to describe the nonlinear bond force-stretch relationship, which gives more concise and robust solutions to large deformation problems; (2) A numerical damping parameter inspired by the mass–dashpot–spring system is developed to endow the proposed framework with numerical advantages in terms of enhancing the stability of explicit time integration in modeling quasi-static problems; (3) It outperforms grid-based methods in capturing notable features like non-smooth crack surfaces, secondary damages, and materials fragmentations. The capability of our framework was successfully validated via several examples, including large deformation, crack initiation and propagation tests of specimens with various notches and eccentric holes. Besides, the numerical performance of our model to capture the crack deflection in laminate rubber specimens was also tested, with results showing good consistency with experimental observations. This framework is compatible with diverse hyperelastic models and sheds new light on modeling of elastomer-hydrogel composites and soft tissues.