Finite Temperature Quasi Continuum

Abstract

A generalization of the quasicontinuum (QC) method to finite temperature is presented. The resulting “hotQCâ€‌ formulation is a partitioned domain multiscale method in which atomistic regions modeled via molecular dynamics coexist with surrounding continuum regions. HotQC can be used to study equilibrium properties of systems under constant or quasistatic loading conditions. Two variants of the method are presented which differ in how continuum regions are evolved. In “hotQCstaticâ€‌ the free energy of the continuum is minimized at each step as the atomistic region evolves dynamically. In “hotQCdynamicâ€‌ both the atomistic and continuum regions evolve dynamically in tandem. The latter approach is computationally more efficient, but introduces an anomalous “mesh entropyâ€‌ which must be corrected. Following a brief review of related finitetemperature methods, this review article provides the theoretical background for hotQC (including new results), discusses the implementational details, and demonstrates the utility of the method via example test cases including nanoindentation at finite temperature.