A hybrid static-dynamic continuum approach for concurrent atomistic-to-continuum methods

Concurrent atomistic-to-continuum methods commonly employ either a dynamic or a quasi-static continuum model. Both of these approaches have advantages and drawbacks which render their applicability problem-specific. We present a new hybrid static–dynamic continuum model, which combines the advantages of both approaches while potentially removing the drawbacks. This numerical approach is an innovative superposition of a dynamic and a quasi-static subproblem and, thus, is limited to linear elastic continua. We apply the approach to a prototypical representative of the concurrent atomistic-to-continuum methods and namely, the coupled atomistic and discrete dislocation method. We present three numerical examples to compare the performance of the dynamic, quasi-static and hybrid continuum model.