On the existence of minimisers for strain-gradient single-crystal plasticity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00481468" target="_blank" >RIV/67985556:_____/18:00481468 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1002/zamm.201700032" target="_blank" >http://dx.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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the existence of minimisers for strain-gradient single-crystal plasticity

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the existence of minimisers for strain-gradient single-crystal plasticity

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik

ISSN

0044-2267

e-ISSN

—

Svazek periodika

98

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

17

Strana od-do

431-447

Kód UT WoS článku

000427147300005

EID výsledku v databázi Scopus

2-s2.0-85043467628