Atomistic and continuum length scale coupling in materials using quasicontinuum method

Abstract

We propose coupling atomistic and continuum length scale models in materials to develop a multiscale modeling framework. High fidelity models like Molecular Dynamics and Density Functional Theory exist at atomic scales capable of explaining various small-scale occurrences. However, these models cannot be scaled up efficiently to explain a range of observations occurring at multiple length and time scales. Since continuum properties can be considered emergent from numerous smaller-scale phenomena, models capable of effectively relating multiple length and time scales are needed. Therefore, we propose using existing models at differing yet individual length scales and suitably coupling them for tackling such multiscale problems. This coupling method should facilitate information exchange in real-time and demonstrate rapid convergence without adding significant computational overhead. Together with single-scale models, this coupling could help us relate continuum properties like stiffness, damping, and thermal conductivity to a material's electronic structure and atomic arrangement. As an illustration, we choose a simple one-dimensional problem with a limited region of interest which we wish to study at an atomic scale. We rely upon the Quasicontinuum method to model this limited atomic region, which significantly reduces the degrees of freedom involved for the atomistic subdomain. Preliminary results for this static problem indicate that the displacement error is relevant on the atomic scale. Importance is put on deriving a method capable of effectively coupling atomic and continuum subdomains for solving general static or dynamic structural problems.