Peridynamics and Material Interfaces

TL;DR

This paper investigates the behavior of peridynamic models at material interfaces, showing convergence to classical elasticity in homogeneous regions and divergence at interfaces, then proposing nonlocal interface conditions that generalize classical models.

Contribution

It introduces a new peridynamics interface model with nonlocal interface conditions that converges to classical elasticity, addressing divergence issues at material interfaces.

Findings

Peridynamics converges to classical elasticity in homogeneous media.

Divergence occurs at material interfaces with discontinuous properties.

Proposed nonlocal interface conditions generalize classical interface models.

Abstract

The convergence of a peridynamic model for solid mechanics inside heterogeneous media in the limit of vanishing nonlocality is analyzed. It is shown that the operator of linear peridynamics for an isotropic heterogeneous medium converges to the corresponding operator of linear elasticity when the material properties are sufficiently regular. On the other hand, when the material properties are discontinuous, i.e., when material interfaces are present, it is shown that the operator of linear peridynamics diverges, in the limit of vanishing nonlocality, at material interfaces. Nonlocal interface conditions, whose local limit implies the classical interface conditions of elasticity, are then developed and discussed. A peridynamics material interface model is introduced which generalizes the classical interface model of elasticity. The model consists of a new peridynamics operator along with nonlocal interface conditions. The new peridynamics interface model converges to the classical interface model of linear elasticity.