An implicit stabilized peridynamic model for swelling-induced fracture in nearly incompressible hyperelastic materials

Abstract

This study presents a stabilized chemo-mechanical peridynamic model solved implicitly (ISCMPD) to address swelling and fracture in nearly incompressible hyperelastic materials. Utilizing the multiplicative decomposition of the deformation gradient, the total deformation is decomposed into a free swelling component induced by solvent diffusion and an elastic component accounting for the geometric constraint response. To describe the transient swelling process, the classical solvent diffusion equation in continuum mechanics is reformulated into a nonlocal form within the peridynamic framework. Subsequently, a stiffness-scaled penalty term based on dilatation micromodulus is introduced to mitigate numerical oscillations arising from the non-uniform chemical potential scalar state. Additionally, an incremental iterative numerical scheme integrating the Newton-Raphson algorithm with the backward Euler method is proposed to address the system’s nonlinear behavior. The stability and robustness of the proposed ISCMPD model are demonstrated through representative numerical examples. Finally, numerical results from both tensile fracture tests on pre-swollen plates and deswelling-driven fracture tests under fixed displacement validate the reliability and applicability of the proposed method for predicting complex fracture behaviors in chemo-mechanical coupled systems.