A computational framework for modeling thermoelastic behavior of cubic crystals

Abstract

In this paper, novel nonlocal reformulations of the conventional continuum-based models for modeling the thermoelastic behavior of cubic crystals based on a recently developed lattice particle method are presented. Like molecular dynamics simulation, the lattice particle method decomposes the grain domain into discrete material particles that are regularly packed according to the underlying atomic lattice. Nonlocal interactions are introduced between material particles and top-down approaches are used to relate model parameters to the material physical constants. Three equivalency assumptions are used in the top-down approach, namely, energy equivalency for the mechanical model, heat transfer rate equivalency for the thermal model, and thermal strain equivalency for the thermal-mechanical coupling model. Different from coordinates transformation used in the conventional continuum-based models, lattice rotation is adopted in the lattice particle method to equivalently represent the material anisotropy while explicitly capturing the crystallographic orientation. Two most common Bravais cubic lattices are studied, i.e., the body-centered cubic lattice and the face-center cubic lattice. The validity and prediction accuracy of the developed models are established by comparing the predicted displacements and temperature results with solutions of conventional continuum theories using the finite element method.