Modeling Thermoelasticity of HCP single crystals using a nonlocal discrete approach

Abstract

This paper presents full-field modeling Thermoelasticity of hexagonal close-packed (HCP) single crystals using reformulations of conventional continuum theories based on a novel nonlocal lattice particle method (LPM). In LPM, grain domain is modeled as an assembly of regularly packed material particles according to the atomic lattice. The interaction between material particles is nonlocal, e.g., for mechanical problems, a material particle interacts with neighboring material particles up to certain distance via bonds and the interaction between two material particles depends on the deformation states of not only the two material particles but also all their neighbors. To determine the nonlocal interaction between material particles, a top-down approach based on the classical continuum theories is developed. Equivalency assumptions of energy, heat transfer rate and thermal strain between LPM and its continuum counterpart are made to consistently determine the material particle interaction for mechanical, thermal, and thermal–mechanical coupling problems, respectively. To capture the crystallographic orientation, a lattice rotation scheme that is equivalent to the coordinate transformation used in the classical continuum theories is adopted. Numerical studies regarding validity of the proposed nonlocal discrete reformulation and accuracy of the model prediction are conducted for all three types of analysis. Good agreements are observed between the results from the developed reformulations and the conventional continuum theories.