Coupling Local and Nonlocal Models

In [46], it was shown that elastic PD models converge to corresponding CCM models in the limit of vanishing nonlocality. Moreover, it can be shown that linear PD models exhibit the same material response as corresponding CCM models in problems characterized by smooth deformations (cf. Section 14.3.1). As a consequence, it may be possible to replace PD governing equations with corresponding CCM equations in domains where the models behave similarly. In that case, PD models are applied in regions where discontinuities may be present, while CCM models are applied far from such regions, where displacement fields are smooth. Simulations based on a coupled PD/CCM model can result in efficient and accurate solutions of PD problems. The main challenge lies in the design of algorithms that properly couple the two models across interfaces.