A Novel Computational Framework of Peridynamics-Based Finite Element Method for Frictional Contact Problem

Abstract

This paper introduces a novel computational framework for the nonlocal Peridynamics (PD)-based finite element method (PeriFEM) designed to model frictional contact phenomena, including sticking and sliding behaviors, in multi-body systems undergoing finite deformations. The framework integrates classical PD theory with contact mechanics in a semi-Lagrangian description to formulate the weak form description of general contact problems. Contact conditions are enforced through penalty terms based on the constrained variational principle. The mathematical formulation adheres to the laws of momentum conservation and objectivity. To mitigate intrinsic surface effects associated with boundary elements on potential contact surfaces, a hybrid correction strategy combining Monte Carlo integration-based volume correction and energy-based surface correction methods is proposed. An effective local search scheme is proposed to eliminate dead zones for contact searching and reduce spurious fluctuations in the solutions. Validation through numerical tests demonstrates the robustness of the framework in conserving physical laws and modeling frictional interactions with high fidelity. Three numerical examples, including the quasi-static and dynamic impact problems involving coupling schemes and brittle fracture mechanics, are presented to illustrate the adaptability and extensibility of the proposed method. Notably, the framework preserves substantial consistency with the classical FEM, which shows potential for broader applications in future studies.

Keywords: Peridynamics-based finite element method, Frictional contact, fracture, Volume correction, Surface correction, Constrained variational principle