On the existence of minimisers for strain-gradient single-crystal plasticity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F18%3A00381733" target="_blank" >RIV/68407700:21110/18:00381733 - isvavai.cz</a>
Alternative codes found
RIV/67985556:_____/18:00481468
Result on the web
<a href="https://doi.org/10.1002/zamm.201700032" target="_blank" >https://doi.org/10.1002/zamm.201700032</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/zamm.201700032" target="_blank" >10.1002/zamm.201700032</a>
Alternative languages
Result language
angličtina
Original language name
On the existence of minimisers for strain-gradient single-crystal plasticity
Original language description
We prove the existence of minimisers for a family of models related to the single-slip-to-single-plane relaxation of single-crystal, strain-gradient elastoplasticity with L-p-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 L-p-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 fine 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 sufficient (p > 2) hardening, thus delivering the desired result. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Zeitschrift für angewandte Mathematik und Mechanik
ISSN
0044-2267
e-ISSN
1521-4001
Volume of the periodical
98
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
17
Pages from-to
431-447
UT code for WoS article
000427147300005
EID of the result in the Scopus database
2-s2.0-85043467628