Construction and Sharp Consistency Estimates for Atomistic/Continuum Coupling Methods with General Interfaces: A Two-Dimensional Model Problem

Abstract

We present a new variant of the geometry reconstruction approach for the formulation of atomistic/continuum coupling methods (a/c methods). For many-body nearest-neighbor interactions on the two-dimensional triangular lattice, we show that patch test consistent a/c methods can be constructed for arbitrary interface geometries. Moreover, we prove that all methods within this class are first-order consistent at the atomistic/continuum interface and second-order consistent in the interior of the continuum region.