Relaxation of the Non-Convex, Incremental Energy-Minimization Problem in Single-Slip Strain-Gradient Plasticity

We consider a variational formulation of gradient elasto-plasticity, as they arise in the incremental formulation of the plastic evolution problem, subject to a class of single-slip side conditions. Such side conditions typically render the associated boundary-value problems non-convex. We first sho...

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Bibliographic Details
Published inKey Engineering Materials Vol. 651-653; pp. 963 - 968
Main Authors Dondl, Patrick W., Anguige, Keith
Format Journal Article
LanguageEnglish
Published Zurich Trans Tech Publications Ltd 10.07.2015
Subjects
Boundary conditions
Deformation
Elastoplasticity
Energy
Evolution
Mathematical analysis
Mathematical models
Microstructure
Plasticity
Slip planes
Specifications
Vectors (mathematics)
Relaxation
Non-Convex Energies
Single Slip
Strain-Gradient Plasticity
Calculus of Variations
Microstructure
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Summary:We consider a variational formulation of gradient elasto-plasticity, as they arise in the incremental formulation of the plastic evolution problem, subject to a class of single-slip side conditions. Such side conditions typically render the associated boundary-value problems non-convex. We first show that, for a large class of plastic deformations, a given single-slip condition (specification of Burgers' vectors and slip planes) can be relaxed by introducing a lamination microstructure. This yields a relaxed side condition which allows for arbitrary slip in a prescribed family of slip planes. This relaxed model can be thought of as an aid to simulating macroscopic plastic behavior without the need to resolve arbitrarily fine spatial scales. We also discuss issues of existence of solutions for the relaxed model.
Bibliography:Selected, peer reviewed papers from the 18th International ESAFORM Conference on Material Forming (ESAFORM 2015), April 15-17, 2015, Graz, Austria
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ISBN:3038354716
9783038354710
ISSN:1013-9826
1662-9795
1662-9795
DOI:10.4028/www.scientific.net/KEM.651-653.963