A General Framework of Linear Elasticity Enhanced Multiscale Coupling Methods for Crystalline Defects

TL;DR

This paper introduces an enhanced multiscale coupling method for crystalline defects that combines linear elasticity with atomistic-to-continuum models, significantly improving computational efficiency while maintaining accuracy.

Contribution

It advances the quasinonlocal coupling method by integrating a linearized Cauchy-Born model, reducing computational costs without sacrificing convergence properties.

Findings

The QNLL method achieves similar convergence as the nonlinear QNL method.

Numerical results show substantial reduction in CPU time.

Theoretical analysis confirms the method's accuracy and efficiency.

Abstract

The atomistic-to-continuum (a/c) coupling methods, also known as the quasicontinuum (QC) methods, are a important class of concurrent multisacle methods for modeling and simulating materials with defects. The a/c methods aim to balance the accuracy and efficiency by coupling a molecular mechanics model (also termed as the atomistic model) in the vicinity of localized defects with the Cauchy-Born approximation of the atomistic model in the elastic far field. However, since both the molecular mechanics model and its Cauchy-Born approximation are usually a nonlinear, it potentially leads to a high computational cost for large-scale simulations. In this work, we propose an advancement of the classic quasinonlocal (QNL) a/c coupling method by incorporating a linearized Cauchy-Born model to reduce the computational cost. We present a rigorous a priori error analysis for this QNL method with linear elasticity enhancement (QNLL method), and show both analytically and numerically that it achieves the same convergence behavior as the classic (nonlinear) QNL method by proper determination of certain parameters relating to domain decomposition and finite element discretization. More importantly, our numerical experiments demonstrate that the QNLL method perform an substantial improvement of the computational efficiency in term of CPU times.