Coarse-grained free-energy-functional treatment of quasistatic multiscale processes in heterogeneous materials

Hybrid atomistic-coarse-grained treatment of multiscale processes in heterogeneous materials: A self-consistent-field approach

A treatment of multiscale quasistatic processes that combines an atomistic description of microscopic heterogeneous ("near") regions of a material with a coarse-grained (quasicontinuum) description of macroscopic homogeneous ("far") regions is presented. The hybrid description yields a reduced system consisting of the original atoms of the near regions plus pseudoatoms (nodes of the coarse-graining mesh) of the far regions, which interact through an effective many-body potential energy V(eff) that depends on the thermodynamic state. The approximate nature of V(eff) gives rise to "ghost forces," which are reflected in spurious heterogeneities close to interfaces between near and far regions. The impact of ghost forces, which afflict all previous hybrid schemes, is greatly diminished by a self-consistent-field hybrid atomistic-coarse-grained (SCF-HACG) methodology. Tests of the SCF-HACG technique on a fully three-dimensional prototypal model [Lennard-Jones (12,6) crystal] yield thermomechanical properties (e.g., local stress) in good agreement with "exact" properties computed in the fully atomistic limit. The SCF-HACG method is also successfully used to characterize the grain boundary in a Lennard-Jones bicrystal.