Modeling elasticity of cubic crystals using a novel nonlocal lattice particle method

A novel nonlocal lattice particle method for modeling elastic deformation of cubic crystals was proposed and verified in this paper. Different from all other numerical models, the lattice particle method decomposes the grain domain into regularly packed discrete material particles according to the internal crystal lattice. Two most common Bravais cubic lattices, i.e., the body-centered cubic lattice and the face-center cubic lattice, were studied in this work. Model parameters were derived in terms of the three elastic material constants based on energy equivalency and theory of hyper-elasticity. Different from coordinates transformation used in the classical continuum mechanics theory, rotation of the discretization lattice is employed to equivalently represent the material anisotropy while capturing the underlying microstructure in the proposed model. The validity and prediction accuracy of the proposed model were established by comparing the predicted directional Young’s modulus and the resolved shear stress of different slip systems against analytical solutions.