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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Athanasios Tzavaras
Title: The problem of shear band formation: a study of a parabolic regularization of an elliptic initial-value problem

Abstract: This talk is devoted to the explanation of the onset of localization and the formation of shear bands in high strain-rate plasticity of metals. The phenomenon of shear strain localization appears in several instances of material instability in mechanics. It is associated with ill-posedness of an underlying initial value problem, what has coined the term Hadamard-instability for its description in the mechanics literature. It should however be noted that while Hadamard instability indicates the catastrophic growth of oscillations around a mean state, it does not by itself explain the formation of coherent structures typically observed in localization. The latter is a nonlinear effect that is the subject of this talk. For a class of models proposed for explaining the phenomenon of shear band formation: (i) we use an asymptotic procedure to derive an effective equation for the evolution of the strain rate. The latter is a backward parabolic with a small stabilizing fourth order correction. (ii) We conduct a careful analysis of the linearized problem and show that the effect of rate-dependence induces some form of Turing instability. (iii) We construct a class of self- similar solutions that describe the self-organization into a localized solution starting from well prepared data. (joint works with Min-Gi Lee and Th. Katsaounis, KAUST)

Date: Tuesday, December 5, 2017
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice