Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling

Abstract

Motivated by recent development on nonlocal mechanical models like peridynamics, we consider nonlocal integral models with a spatially varying horizon that allows the finite range of nonlocal interactions to be position-dependent. In particular, we focus on linear variational problems of such nonlocal models with heterogeneous localization on co-dimension one interfaces. The well-posedness is established for several classes of variational problems involving homogeneous and inhomogeneous Neumann- and Dirichlet-type constraints. We also study their seamless coupling with local models. In addition, we present numerical studies of the nonlocal models and local-nonlocal coupled models based on the asymptotically compatible Galerkin finite element discretizations.