On numerically predicting the onset and mode of instability in atomistic systems

We present an accurate and efficient method based on the Lanczos algorithm for predicting the onset and mode of instability in atomistic systems. Specifically, we develop a framework that is identically applicable to all flavors of atomistic simulations, including ab-initio calculations. Notably, we do not make any apriori assumptions regarding the nature of the instability or its location. We verify the accuracy of the proposed approach by studying defect nucleation during the nanoindentation of a triangular lattice and hydrostatic tension test of an aluminum crystal. We demonstrate that the computational cost in practical calculations scales linearly with system size, and is accompanied by a small prefactor. Overall, the proposed method is attractive because it enables the stability analysis of atomistic systems at the mesoscale.