The notion of a critical stress, at which a perfect crystal under uniform loading would become structurally unstable, was extended to non-uniform loading. A position-dependent defect nucleation criterion was derived and was used in molecular dynamics and finite-element simulations of dislocation emission in single-crystal nano-indentations. The resultant measure had the physical meaning of a local stiffness. It provided a rigorous basis for modeling the incipient plasticity of thin-film material. A close connection was shown to exist between the initial unstable elastic wave and the final atomistic defect.

Elastic Criterion for Dislocation Nucleation. J.Li, T.Zhu, S.Yip, K.J.Van Vliet, S.Suresh: Materials Science and Engineering A, 2004, 365[1-2], 25-30