A proper orthogonal decomposition for parametric study of the mechanical behavior of nanowires

Molecular dynamics (MD) simulation is frequently used in exploring the mechanical behaviors of nanowires, which have strong dependency on parameters such as size, strain-rate, temperature, and so on. However, the MD simulations require heavy computation power. For efficient parametric study on the mechanical behaviors, the use of a snapshot-based proper orthogonal decomposition (POD) is proposed. Per-atom virial stress and atom arrangement, which are chosen as the snapshots in this study, are expressed by the linear combinations of POD basis. As a next step, the moving least square method approximates the corresponding POD coefficients. The mechanical behaviors are then predicted by these POD expressions in the parametric ranges of interest. It is demonstrated from the parametric study that the proposed method not only obtains the snapshots but also predicts the abrupt drop-down of stress at the onset of inelastic deformation more efficiently than the original tedious repeated MD simulations.