Concurrent coupling of bond-Based peridynamics and the navier equation of classical elasticity by blending

The peridynamics theory of solid mechanics has been proposed as a suitable framework for material failure and damage simulation. As a nonlocal model, based upon integro-differential equations, peridynamics is computationally expensive. Concurrent multiscale methods are thus of interest for efficient and accurate solutions of peridynamic problems. The goal is to restrict the use of peridynamic models to regions where discontinuities are present or may be generated, while employing classical local models in domains characterized by smooth displacement fields. In this article, we derive a blending scheme to concurrently couple bond-based peridynamic models and the Navier equation of classical elasticity. We extend the work for one-dimensional linear peridynamic models presented by Seleson et al. (2013a), to general bond-based peridynamic models in higher dimensions, and we provide an error estimate for the coupling scheme. We show analytically and numerically that the blended model does not exhibit ghost forces and is also patch-test consistent. Numerical results demonstrate the accuracy and efficiency of the blended model proposed, suggesting an alternative framework for cases where peridynamic models are too expensive, whereas classical local models are not accurate enough.