Lattice dynamical finite-element method

A lattice dynamical finite-element method (LDFEM) is proposed for multiscale analysis of stressed complex crystals. Interatomic potential is embedded into the constitutive relation within the hyperelasticity framework, and two energy-based lattice instability criteria, the Λ criterion and the soft phonon criterion, are incorporated into LDFEM for capturing stress-driven instabilities in a perfect crystal. The simulations of uniaxial loadings and a two-dimensional nanoindentation of B2-NiAl are performed using both LDFEM and molecular dynamics (MD). The good agreement of the simulated mechanical responses between the two methods validates the proposed method. Combination of the two criteria can provide a powerful tool for predicting lattice instabilities in complex crystals under load at zero or low temperatures.