0481468 20240103214945.020171116235959.9 85043467628 000427147300005 10.1002/zamm.201700032 17 s. P cav_un_epca*02577150044-2267983 (2018)431-447Wiley existence of minimizers plasticity cav_un_auth*0353451 33 Anguige K. DE K cav_un_auth*0353452 33 Dondl P. DE cav_un_auth*0101142 Kružík Martin Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2017/MTR/kruzik-0481468.pdf cav_un_auth*0304434 GA14-15264S GA ČR cav_un_auth*0331681 GF16-34894L GA ČR CZ 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 & Müller, 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-semicontinuityo fthe(polyconvex)elasticenergy,andhencethetotalelasto-plasticenergy, givensufficient(p > 2) hardening, thus delivering the desired result. BA 10000 10100 10101 2019 3 RVO:67985556 http://hdl.handle.net/11104/0277042 1 S 3+4 Article Mathematics Applied|Mechanics MECHANICS|MATHEMATICS.APPLIED 1.351 0.467 23.1 0.0028 0.469 2940 0.590 1.379 120 Q2 29.762 49.7 Q3 Q2 0.74 Q2 69.094 2018 85043467628 SCOPUS PUBMED 000427147300005 WOS cav_un_epca*0257715 ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik 0044-2267 1521-4001 Roč. 98 č. 3 2018 431 447 Wiley