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This paper addresses the problem of consistent energy-based coupling ofatomistic and continuum models of materials, limited to zero-temperaturestatics of simple crystals. It has been widely recognized that the mostpractical coupled methods exhibit large errors on the atomistic/continuuminterface (which are often attributed to spurious forces called "ghostforces"). There are only few existing works that propose a coupling which issufficiently accurate near the interface under certain limitations. In thispaper a novel coupling that is free from "ghost forces" is proposed for atwo-body interaction potential under the assumptions of either (i) one spatialdimension, or (ii) two spatial dimensions and piecewise affine finite elementsfor describing the continuum deformation. The performance of the proposedcoupling is demonstrated with numerical experiments. The coupling strategy isbased on judiciously defining the contributions of the atomistic bonds to thediscrete and the continuum potential energy. The same method in one dimensionhas been independently developed and analyzed in Li and Luskin(arXiv:1007.2336).

Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions