Nonlinear plastic modes in disordered solids

Original · EN

We propose a framework within which a robust mechanical definition of precursors to plastic instabilities, often termed `soft-spots', naturally emerges. They are shown to be collective displacements (modes) z₀ that correspond to local minima of the `barrier function' b(z). The latter is derived from the cubic approximation of the variation δUz(s) of the potential energy upon displacing particles a distance s along z. We show that modes z₀ corresponding to low-lying minima of b(z) lead to transitions over energy barriers in the glass, and are therefore associated with highly asymmetric variations δUz(s) with s. We further demonstrate how a heuristic search for local minima of b(z) can a-priori detect the locus and geometry of imminent plastic instabilities with remarkable accuracy, at strains as large as γc-γ 10⁻² away from the instability strain γc, where the non-affine displacements under shear are still largely delocalized. Our findings suggest that the a-priori detection of plastic instabilities can be effectively carried out by the investigation of the landscape of b(z).