A quasi-nonlocal coupling method for bond-based peridynamics with classical continuum mechanics

Abstract

Purpose

The purpose of this paper is to propose a novel quasi-nonlocal coupling of the bond-based peridynamic model with the classical continuum mechanics model to fully take advantage of their merits and be free of ghost forces.

Design/methodology/approach

This study reconstructs a total energy functional by introducing a coupling parameter that alters only the nonlocal interactions in the coupling region rather than the whole region and a modified elasticity tensor that affects the local interactions. Then, the consistency of force patch test is enforced in the coupling region to completely eliminate the ghost force in a general energy-based coupling scheme. For a one-dimensional problem, these coupling parameters are further determined through an energy patch test to preserve the energy equivalence or through an l¹-regularization. And, for a two- or three-dimensional problem, depending on the existence of a solution to the discretized force patch test, they are determined through an l¹-minimization or l¹-regularization.

Findings

One- and two-dimensional numerical examples under affine deformation have been conducted to verify the accuracy of the quasi-nonlocal coupling method, which exhibits no ghost force. Moreover, the coupling model can reproduce almost the same deformation behaviors of points near the crack for a cracked plate under tension as that from a pure peridynamic model, the former with a rather low computational cost and an easier application of boundary conditions.

Originality/value

This work is aiming at getting over long-standing ghost force issues in the energy-based coupling scheme. The numerical results from the cracked plate problem are exhibited promising extension to dynamic problems.

Citation

Jiang, F. and Shen, Y. (2022), "A quasi-nonlocal coupling method for bond-based peridynamics with classical continuum mechanics", Engineering Computations, Vol. 39 No. 2, pp. 554-573. https://doi.org/10.1108/EC-05-2020-0246