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Nonlinear plastic modes (NPMs) are collective displacements that areindicative of imminent plastic instabilities in elastic solids. In this work weformulate the atomistic theory that describes the reversible evolution of NPMsand their associated stiffnesses under external deformations. Thedeformation-dynamics of NPMs is compared to those of the analogous observablesderived from atomistic linear elastic theory, namely destabilizing eigenmodesof the dynamical matrix and their associated eigenvalues. The key result wepresent and explain is that the dynamics of NPMs and of destabilizingeigenmodes under external deformations follow different scaling laws withrespect to the proximity to imminent instabilities. In particular,destabilizing modes vary with a singular rate, whereas NPMs' exhibit no suchsingularity. As a result, NPMs converge much earlier than destabilizingeigenmodes to their common final form at plastic instabilities. This dynamicaldifference between NPMs and linear destabilizing eigenmodes underlines theusefulness of NPMs for predicting the locus and geometry of plasticinstabilities, compared to their linear-elastic counterparts.

The micromechanics of nonlinear plastic modes