Stability of a force-based hybrid method with planar sharp interface

Abstract

© 2014 Society for Industrial and Applied Mathematics.We study a force-based hybrid method that couples an atomistic model with a Cauchy-Born elasticity model with sharp transition interface. We identify stability conditions that guarantee the convergence of the hybrid scheme to the solution of the atomistic model with second order accuracy, as the ratio between lattice parameter and the characteristic length scale of the deformation tends to zero. Convergence is established for hybrid schemes with planar sharp interface for systems without defects, with general finite range atomistic potential and simple lattice structure. The key ingredients of the proof are regularity and stability analysis of elliptic systems of difference equations. We apply the results to atomistic-to-continuum scheme for a two-dimensional triangular lattice with planar interface.