A force-based coupling scheme for peridynamics and classical elasticity

Abstract

In this work, we present a novel methodology to derive blending schemes to concurrently couple local and nonlocal models obtained from a single reference framework based upon the peridynamic theory of solid mechanics. A consistent force-based blended model that couples peridynamics and classical elasticity is presented using nonlocal weights composed of integrals of blending functions. The proposed blended model possesses desired properties of multiscale material models such as satisfying Newton’s third law and passing the patch test. This approach finds useful applications in material failure for which the peridynamics theory can be used to describe regions where fracture is expected, whereas classical elasticity could be efficiently used elsewhere. Numerical experiments demonstrating the accuracy and efficiency of the blended model are presented as well as qualitative studies of the error sensitivity on different model and problem parameters. We also generalize this approach to the coupling of peridynamics and higher-order gradient models of any order.