MULTISCALE MODELING FOR AMORPHOUS MATERIALS — MAPPING ATOMISTIC DISPLACEMENTS TO MACROSCOPIC DEFORMATION

Abstract

A method to relate the displacements of atoms within a representative volume element (RVE) of amorphous material to the deformation of the RVE is presented. The displacement relationship is expressed as a mapping matrix, T, which operates on the displacements of representative points in the RVE to return the atom displacements within it. While the mapping operation has the same mathematical form as an interpolation operation, the T matrix is not an interpolant. It is derived taking into account atom displacements in amorphous materials which cannot be simplified as a continuous, much less homogenous, field. It is shown that the computational domain of a material can be partitioned into nonintersecting sub-domains comprising representative cells — pseudo-amorphous cells (PAC) — and sub-domains of atoms for concurrent multiscale simulations of amorphous materials through the T matrix. Multiscale simulations of nanoindentation on a polymer substrate using the T matrix show good agreement with pure molecular mechanics simulations. When homogenization techniques commonly used for crystalline materials were employed for the same simulations, they gave much less accurate predictions.