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Published online: 2006-09-30
Mini-Workshop: Analysis and Computation of Microstructures in Finite PlasticityKlaus Hackl, Sergio Conti and Michael Ortiz (1) Ruhr-Universität Bochum, Germany
(2) Universität Bonn, Germany
(3) California Institute of Technology, Pasadena, United States
The miniworkshop was attended by fourteen participants of whom twelve gave
presentations. Additionally Kolumban Hutter from the University of Darmstadt,
then at the research institute as a research-in-pairs fellow, agreed to give a
talk on ``Granular flows and avalanches''.
There was one discussion session chaired by Stefan M\"uller, during which the
most important problems of the field which have to be addressed in the near
future were identified. The individual talks lasted for one and a half hours in
the average and were interlaced with lively discussions.
The main theme in the workshop was the variational formulation of crystal plasticity, in a rate-independent setting. For small time-intervals, this leads to a single variational problem, which is often referred to as the ``first time step''. One substantial difficulty arises from the fact that the resulting functional is not lower semicontinuous, leading to non-existence of minimizers. The corresponding theory of relaxation has some analogies to the one developed in nonlinear elasticity. A second issue is the formulation of a theory that goes beyond small time intervals. In a framework where time is discretized, the functional at each time step depends on the minimizer at the previous one (assuming it exists). This leads to a sequence of coupled variational problems, and even the precise definition of the time-continuous limit is not yet completely understood.
The subjects treated ranged from the mathematical formulation of the variational problems and existence results for those, to analytical and numerical methods to determine their relaxation, and applications to various problems in mechanics and physics. Research in progress and sometimes of speculative nature was presented rather then established results. Specifically, the main questions treated were the following:
During the miniworkshop progress could be made concerning some of these questions and interesting ideas where developed for the rest of them.
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Hackl Klaus, Conti Sergio, Ortiz Michael: Mini-Workshop: Analysis and Computation of Microstructures in Finite Plasticity. Oberwolfach Rep. 2 (2005), 2979-3018. doi: 10.4171/OWR/2005/52