Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in Three Dimensions

Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled energy whose minimizers are free from uncontrollable errors on the atomistic/continuum interface. In this paper a consistent coupling in three dimensions is proposed. The main challenge in three dimensions was to identify and efficiently treat the modified Cauchy-Born continuum model which can be coupled to the exact atomistic model. The convergence and stability of the method is confirmed with numerical tests.