Simplified Analysis of Mechanical Instability in Three-dimensional Atomic Components and Its Application to Nanoscale Crack

Abstract

For the investigation of nature of mechanical instability in a large-scale atomic system, we propose a simplified analytical method that can describe unstable deformation with reduced degrees of freedom by introducing linear elements. The approach is applied to a three-dimensional atomic structure with a crack under tension, and it successfully reproduce the minimum eigenvalue of the Hessian matrix of the potential energy before the dislocation emission, namely instability criterion, as well as its deformation mode at the junction of the crack tip and surface. The computational load is considerably reduced in comparison with the original method, enabling us to address the mechanical instability issues in a large-scale atomic system. Moreover, the critical area that mainly dominates unstable deformation can be determined using the proposed method.