A priori error analysis of two force-based atomistic/continuum models of a periodic chain

The force-based quasicontinuum (QCF) approximation is a nonconservative atomistic/continuum hybrid model for the simulation of defects in crystals. We present an a priori error analysis of the QCF method, applied to a one-dimensional periodic chain, that is valid for an arbitrary interaction range, large deformations, and takes coarse-graining into account. Our main tool in this analysis is a new concept of atomistic stress. Moreover, we formulate a new atomistic/continuum coupling mechanism based on coupling stresses instead of forces and extend the a priori analysis to this new method. We show that the new method has several theoretical advantages over the original QCF method. This work was supported by the EPSRC Critical Mass Programme “New Frontiers in the Mathematics of Solids” (OxMOS). CM wishes to acknowledge the hospitality of OxMOS while visiting the Oxford Mathematical Institute. The research of CM was partially supported by the FP7-REGPOT project “Archimedes Centre for Modeling, Analysis and Computations.” The research of CO was partially supported by the EPSRC grant “Analysis of atomistic-to-continuum coupling methods.” C. Makridakis Department of Applied Mathematics, University of Crete, GR 714 09 Heraklion-Crete Tel.: +3