Enriched space–time finite element method: a new paradigm for multiscaling from elastodynamics to molecular dynamics

Abstract

SUMMARYThe main objective of this paper is to present an enriched version of the space–time FEM method to incorporate multiple temporal scale features with a focus on dynamics problems. The method is established by integrating the basic framework of the space–time discontinuous Galerkin method with the extended finite element method. Two versions of the method have been developed: one at the continuum scale (elastodynamics) and the other focuses on the dynamics at the molecular level. After an initial outline of the formulation, we explore the incorporation of different types of enrichments based on the length scale of interest. The effects of both continuous and discontinuous enrichments are demonstrated through numerical examples involving wave propagations and dynamic fracture in harmonic lattice. The robustness of the method is evaluated in terms of convergence and the ability to capture the fine scale features. It is shown that the enriched space–time FEM leads to an improvement in the convergence properties over the traditional space–time FEM for problems with multiple temporal features. It is also highly effective in integrating atomistic with continuum representations with a coupled framework. Copyright © 2012 John Wiley & Sons, Ltd.