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SUMMARY:Hadamard instability and the emergence of localized states in dyna
 mic plasticity - Athanasios E. Tzavaras (University of Crete\, Heraklion\,
  Greece)
DTSTART:20121126T150000Z
DTEND:20121126T160000Z
UID:TALK41446@talks.cam.ac.uk
CONTACT:Prof. Clément Mouhot
DESCRIPTION:This talk is devoted to the phenomenon of localization and for
 mation of shear bands in high strain-rate plasticity of metals. Shear stra
 in localization appears in several instances of material instability in me
 chanics\, always associated with ill-posedness of an underlying initial va
 lue problem\, what has coined the term Hadamard-instability for its descri
 ption in the mechanics literature. It should however be noted that while H
 adamard instability indicates the catastrophic growth of oscillations arou
 nd a mean state\, it does not by itself explain the formation of coherent 
 structures typically observed in localization. The latter is a nonlinear e
 ffect 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 mecha
 nisms affecting the prob- lem: thermal softening\, momentum diffusion and 
 thermal diffusion mechanisms. Then\, we employ a nonlinear model\, and con
 struct localized states - in the form of appropriate similarity solutions 
 - that emerge as coherent structures in the localization process.
LOCATION:CMS\, MR11
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