Relaxing strong compatibility at atomistic-continuum interface: Consistent linear coupling method

Abstract

In this paper, we develop a brand-new coupling method called consistent linear coupling (CLC) with a view to resolving the difficulty of scaling down of the interface elements in the strong compatibility coupling (SCC), employed in the most accurate multiscale methods such as quasicontinuum. To this end, the CLC determines some conditions required to be satisfied to reproduce the SCC rigorously, regardless of the size of the interface elements. Therefore, it can produce a solution as accurate as the SCC with two additional features: significantly less computational cost and easier implementation. The CLC-based schemes are compared with well-known coupling methods including the SCC in terms of solving quasi-static 3D nanoscale contact and a 2D crystal under uniaxial tension. Numerical results demonstrate the superiority of the CLC with regard to the accuracy and computational efficiency.