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University of Cambridge > Talks.cam > Partial Differential Equations seminar > Hadamard instability and the emergence of localized states in dynamic plasticity
Hadamard instability and the emergence of localized states in dynamic plasticityAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact Prof. ClĂ©ment 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 Partial Differential Equations seminar series. This talk is included in these lists:
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