A Review of Local-to-Nonlocal Coupling Methods in Nonlocal Diffusion and Nonlocal Mechanics

Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. This allows to consolidate the accuracy of nonlocal models with the computational expediency of their local counterparts, while often simultaneously removing nonlocal modeling issues such as surface effects. The number and variety of proposed LtN coupling approaches have significantly grown in recent years, yet the field of LtN coupling continues to grow and still has open challenges. This review provides an overview of the state of the art of LtN coupling in the context of nonlocal diffusion and nonlocal mechanics, specifically peridynamics. We present a classification of LtN coupling methods and discuss common features and challenges. The goal of this review is not to provide a preferred way to address LtN coupling but to present a broad perspective of the field, which would serve as guidance for practitioners in the selection of appropriate LtN coupling methods based on the characteristics and needs of the problem under consideration.