A coupled molecular dynamics and extended finite element method for dynamic crack propagation

A multiscale method is presented which couples a molecular dynamics approach for describing fracture at the crack tip with an extended finite element method for discretizing the remainder of the domain. After recalling the basic equations of molecular dynamics and continuum mechanics, the discretization is discussed for the continuum subdomain where the partition-of-unity property of finite element shape functions is used, since in this fashion the crack in the wake of its tip is naturally modelled as a traction-free discontinuity. Next, the zonal coupling method between the atomistic and continuum models is recapitulated. Finally, it is discussed how the stress has been computed in the atomic subdomain, and a two-dimensional computation is presented of dynamic fracture using the coupled model. The result shows multiple branching, which is reminiscent of recent results from simulations on dynamic fracture using cohesive-zone models