Bridging scale simulation of lattice fracture using enriched space-time Finite Element Method

A multiscale method that couples the space-time Finite Element Method with molecular dynamics is developed for the simulation of dynamic fracture problems. A coarse scale description based on finite element discretization is established in the entire domain. This representation overlaps with a detailed atomistic description employed in the region immediately surrounding the crack tip with the goal to capture the initiation and propagation of the fracture. On the basis of the crack evolution informed by the atomistic simulation, an enrichment function is introduced to represent the fracture path. The space-time framework further enables flexible choice of time steps in different regions of interest. Coupling between the fine and coarse scale simulation is achieved with the introduction of a projection operator and bridging scale treatment. The main feature of the work is that the evolution of the crack is adaptively tracked and the enrichment in the coarse scale simulation evolves along with it. As a result, we have a moving atomistic region in the concurrent simulation scheme. The robustness of the method is illustrated through examples involving crack propagation in hexagonal lattices with different orientations and loading conditions. Copyright (c) 2013 John Wiley & Sons, Ltd.