Lower semi-continuity and existence of minimizers in incremental finite-strain elastoplasticity

Alexander Mielke and Stefan Müller

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Submission date: 09. Feb. 2005
Pages: 27
published in: Zeitschrift für angewandte Mathematik und Mechanik, 86 (2006) 3, p. 233-250 
DOI number (of the published article): 10.1002/zamm.200510245
Bibtex
MSC-Numbers: 74C15, 74B20
Keywords and phrases: elastoplasticity, finite strain, existence
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Abstract:
We study incremental problems in geometrically nonlinear elastoplasticity. Using the multiplicative decomposition we consider general energy functionals of the form

which occur as the sum of the stored energy and the dissipation in one time step. Here is the dislocation tensor which takes the form in dimension d=3.

Imposing the usual constraint and suitable growth and polyconvexity conditions on U we show that the minimum of is attained in the natural Sobolev spaces. Moreover, we are able to treat multiple time steps by controlling the stored and dissipated energies. We also address the relation of the incremental problem to the time-continuous energetic formulation of elastoplasticity.