Simplified evaluation of mechanical instability in large-scale atomic structures

For the investigation of mechanical instability in a large-scale atomic structure, a simplified method is presented that can describe unstable deformation with reduced degrees of freedom by introducing linear elements. The proposed method is applied to a cracked atomic structure under tension, and it can successfully reproduce the minimum eigenvalue of the Hessian matrix of the potential energy before the dislocation emission and its deformation mode near the crack-tip. The computational load is considerably reduced in comparison with the original precise method, and this enables us to address the mechanical instability in a large-scale atomic system. Moreover, the critical area that mainly dominates unstable deformation can be determined using the proposed method.