A local Quantum–Atomistic–Continuum model for mechanical behaviors at micro-nano scale

Abstract

To study non-linear mechanical properties of materials from electronic structure information, we present a physics-based sequential model in this paper. We formulate the ground state strain energy functional to extract continuum description of mechanical quantities from quantum scale. For the large-scale Kohn–Sham density functional calculation, we use linear combination of small-scale interactions to approximate the initial many-body interaction. The expansion is taken to an even-order to keep both the precision and the surface effect. In our deformation framework, the low-frequency deformation part of total displacement is decoupled from the high-frequency thermal vibration. Basic elements are determined based on complex Bravais lattice. Continuum mechanical tensors, such as the Cauchy stress and the elastic constant, are explicitly derived from discrete atomistic system. To confirm the validation of our model, we simulate 3-dimensional single copper nanowires under external tension and bending, along with comparisons against other experimental results.