Local continuum consistent peridynamics with bond‐associated modeling and dynamic fracture

Abstract

This paper explores the theoretical foundations and practical challenges of peridynamics as a nonlocal continuum mechanics method. We establish connections between classical continuum mechanics principles and peridynamics formulations, with a particular focus on understanding how the pairwise force function in peridynamics relates to stress concepts in local theories. The work addresses persistent numerical challenges in peridynamic simulations, including zero‐energy modes and instabilities in correspondence‐based formulations. We present bond‐associated modeling approaches that enhance stability while maintaining computational accuracy. The theoretical discussions are supplemented with discretization methods for spatial and temporal domains. Through illustrative examples of complex fracture phenomena, we demonstrate how these theoretical insights translate to practical applications, providing guidance on selecting appropriate peridynamic formulations for computational mechanics problems. The numerical comparison identifies the bond‐associated quadrature point formulation as the most accurate correspondence‐class approach in the elastic regime. Under progressive bond deletion, however, the shape tensor, on which this formulation relies, becomes ill‐conditioned, and the model loses stability. This necessitates the development of refined damage formulations within the correspondence framework.