Modeling Elasticity of HCP Crystals Using a Nonlocal Lattice Particle Method

In this paper, a novel nonlocal lattice particle method is proposed for modeling mechanical behavior of hexagonal closed packing single crystals. LPM is a meshfree method that discretizes material domain with potential crystal lattice structure. Nonlocal interactions between material particles is represented by that material particles interacts with neighboring material particles within certain distances, and deformation state of two material particles depends not only on these two particles but also all the neighbors of them. We derived a top-down approach to determine this non-local interaction based on classical continuum theory. By equalizing potential energy of a material particle in LPM with its counterpart in continuum theory, we can capture mechanical behavior of HCP single crystals. The anisotropy of HCP single crystals is modeled by a lattice rotation scheme which is equivalent to traditional way of coordinates transformation. Several benchmark tests are developed to prove the validity and prediction accuracy of developed LPM model. Good agreements with theoretical solution and FEM solution are found throughout the numerical tests.