An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions

TL;DR

This paper introduces an optimization-based method for coupling peridynamic and finite element models, enabling accurate, efficient simulations of complex geometries with nonlocal boundary conditions in solid mechanics.

Contribution

The paper presents a novel control-based coupling strategy that minimizes mismatch between models, improving accuracy and computational efficiency in nonlocal elasticity simulations.

Findings

Method achieves consistent and accurate coupling in 3D geometries.

Numerical convergence demonstrated through tests.

Applicable to realistic engineering problems.

Abstract

We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the solutions of the PD and classical equations, the objective is to minimize their mismatch on an overlap of the PD and classical domains, and the controls are virtual volume constraints and boundary conditions applied at the local-nonlocal interface. Our numerical tests performed on three-dimensional geometries illustrate the consistency and accuracy of our method, its numerical convergence, and its applicability to realistic engineering geometries. We demonstrate the coupling strategy as a means to reduce computational expense by confining the nonlocal model to a subdomain of interest, and as a means to transmit local (e.g., traction) boundary conditions applied at a surface to a nonlocal model in the bulk of the domain.