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Hadamard instability and the emergence of localized states in dynamic plasticity

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If you have a question about this talk, please contact Prof. Clément Mouhot.

This talk is devoted to the phenomenon of localization and formation of shear bands in high strain-rate plasticity of metals. Shear strain localization appears in several instances of material instability in mechanics, always 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 will be the subject of this talk. In this talk, we first carry out a linearized analysis that indicates the effects of the various mechanisms affecting the prob- lem: thermal softening, momentum diffusion and thermal diffusion mechanisms. Then, we employ a nonlinear model, and construct localized states – in the form of appropriate similarity solutions – that emerge as coherent structures in the localization process.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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