CMU Campus
Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact
CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Athanasios Tzavaras
KAUST
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