A peridynamics-based finite element method for quasi-static fracture analysis

TL;DR

This paper introduces a novel peridynamics-based finite element method (Peri-FEM) for quasi-static fracture analysis, integrating peridynamics with classical FEM to model crack propagation through property degradation.

Contribution

It develops a new computational framework combining peridynamics with finite element method, defining peridynamic elements that do not interfere with classical elements.

Findings

Method accurately models crack propagation.

Numerical examples validate the approach.

Framework is consistent with classical FEM.

Abstract

In this paper, a peridynamics-based finite element method (Peri-FEM) is proposed for the quasi-static fracture analysis, which is of the consistent computational framework with the classical finite element method (FEM). First, the integral domain of the peridynamics is reconstructed, and a new type of element called peridynamic element (PE) is defined. Although PEs are generated by the continuous elements (CEs) of classical FEM, they do not affect each other. Then the spatial discretization is performed based on PEs and CEs, and the linear equations about the nodal displacement are established according to the principle of minimum potential energy. Besides, the cracks are characterized as the degradation of the mechanical properties of PEs. Finally, the validity of the proposed method is demonstrated through numerical examples.