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ON THE EXISTENCE OF MINIMISERS FOR STRAIN-GRADIENT SINGLE-CRYSTAL PLASTICITY
Type of publication: Misc
Citation:
Year: 2017
Abstract: We prove the existence of minimisers for a family of models related to the singleslip- to-single-plane relaxation of single-crystal, strain-gradient elastoplasticity with Lp-hardening penalty. In these relaxed models, where only one slip-plane normal can be activated at each material point, the main challenge is to show that the energy of geometrically necessary dislocations is lower-semicontinuous along bounded-energy sequences which satisfy the single-plane condition, meaning precisely that this side condition should be preserved in the weak Lp-limit. This is done with the aid of an `exclusion' lemma of Conti & Ortiz, which essentially allows one to put a lower bound on the dislocation energy at interfaces of (single-plane) slip patches, thus precluding ne phase-mixing in the limit. Furthermore, using div-curl techniques in the spirit of Mielke & Muller, we are able to show that the usual multiplicative decomposition of the deformation gradient into plastic and elastic parts interacts with weak convergence and the single-plane constraint in such a way as to guarantee lower-semicontinuity of the (polyconvex) elastic energy, and hence the total elasto-plastic energy, given sucient (p > 2) hardening, thus delivering the desired result.
Preprint project: NCMM
Preprint year: 2017
Preprint number: 01
Preprint ID: NCMM/2017/01
Keywords:
Authors Anguige, K.
Dondl, P.
Kružík, Martin
Added by: [JP]
Total mark: 0
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  • 20170306101339.pdf
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