Peridynamic correspondence model for finite elastic deformation and rupture in Neo-Hookean materials

Abstract

This study considers finite elastic deformation and rupture in rubber-like materials under quasi-static loading conditions by employing the bond-associated weak form of peridynamics with nonuniform horizon. The weak form of peridynamic equilibrium equation is derived based on the Neo-Hookean material model with slight compressibility. The nonlocal deformation gradient tensor is computed in a bond-associated domain of interaction using the PD differential operator. This approach is free of oscillations and spurious zero energy modes that are commonly observed in the PD correspondence models. Also, it permits the direct imposition of natural and essential boundary conditions. Its fidelity for predicting large deformation is established by comparison with those of finite element analysis of a rubber sheet with a hole under stretch. Also, its validity for predicting damage is demonstrated through simulations of experiments concerning progressive damage growth and final rupture in polymers undergoing large elastic deformation.