Relaxing strong compatibility at atomistic-continuum interface: Introduction to consistent linear coupling method

TL;DR

This paper introduces the consistent linear coupling (CLC) method, a flexible atomistic-continuum interface coupling approach that improves accuracy and reduces computational cost compared to traditional strong compatibility coupling (SCC).

Contribution

The paper develops and compares six new coupling schemes based on relaxed compatibility concepts, demonstrating enhanced accuracy and tunability over SCC in multiscale atomistic-continuum simulations.

Findings

CLC schemes are more accurate than surface approximation schemes.

Decreasing interface element size improves CLC accuracy, surpassing SCC.

CLC reduces computational cost while maintaining or improving accuracy.

Abstract

The most essential concept in concurrent multiscale methods involving atomistic-continuum coupling is how to define the relation between atomistic and continuum regions. A well-known coupling method that has been frequently employed in different concurrent multiscale methods such as Quasicontinuum is the strong compatibility coupling (SCC). Although the SCC is a highly accurate coupling method, it constrains the mesh generation and restricts the reduction of computational cost. In this paper, first, we explain the notion of coupling models through the interface in the context of continuum mechanics for quasi-static problems. Then, the SCC is relaxed to overcome the downsides in the following approaches: a surface approximation approach and a force approximation approach. Based on the latter, we develop a brand new coupling method called consistent linear coupling (CLC). Overall, six different coupling schemes are introduced in line with the surface and force approximation approaches. The schemes are compared in terms of solving quasi-static 3D elastic nanoscale contact between an aluminum substrate and a diamond semi-sphere. Numerical results reveal that the CLC-based schemes are more accurate when compared with the surface approximation schemes. Furthermore, we demonstrate that by decreasing the size of interface elements, the accuracy of the CLC converges to and even exceeds the accuracy of SCC, but nevertheless with significantly less computational cost. In other words, in contrast to the SCC, the accuracy of the CLC is tunable, and it can be optimized proportional to the computational cost and accuracy. Finally, we sketch the idea of how the CLC can make the consistency near the atomistic-continuum interface by eliminating ghost forces. The energy of a one-dimensional atomic chain with a finite range of interaction is relaxed to validate the CLC method.