A revision of results for standard models in elasto-perfect-plasticity theory

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384152" target="_blank" >RIV/00216208:11320/18:10384152 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00526-018-1322-1" target="_blank" >https://doi.org/10.1007/s00526-018-1322-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00526-018-1322-1" target="_blank" >10.1007/s00526-018-1322-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A revision of results for standard models in elasto-perfect-plasticity theory

Popis výsledku v původním jazyce

We consider two most studied standard models in the theory of elasto-plasticity in arbitrary dimension d &gt;= 2, namely, the Hencky model and the Prandtl-Reuss model subjected to the von Mises condition. There are many available results for these models-from the existence and the regularity theory up to the relatively sharp identification of the plastic strain in the natural function/measure space setting. In this paper we shall proceed further and improve some of known estimates in order to identify sharply the plastic strain. More specifically, we rigorously improve the integrability of the displacement and the velocity (which was known only under a nonnatural assumption that the Cauchy stress is bounded), show the BMO estimates for the stress and finally also the Morrey-like estimates for the plastic strain. In addition, we shall provide the whole theory up to the boundary. As an immediate consequence of such improved estimates, we provide a sharper identification of the plastic strain than that known up to date. In particular, in two dimensional setting, we show that the plastic strain can be point-wisely characterized in terms of the stresses everywhere although the stress is possibly discontinuous and thus the natural duality pairing in the space of measures could be violated.

Název v anglickém jazyce

A revision of results for standard models in elasto-perfect-plasticity theory

Popis výsledku anglicky

We consider two most studied standard models in the theory of elasto-plasticity in arbitrary dimension d &gt;= 2, namely, the Hencky model and the Prandtl-Reuss model subjected to the von Mises condition. There are many available results for these models-from the existence and the regularity theory up to the relatively sharp identification of the plastic strain in the natural function/measure space setting. In this paper we shall proceed further and improve some of known estimates in order to identify sharply the plastic strain. More specifically, we rigorously improve the integrability of the displacement and the velocity (which was known only under a nonnatural assumption that the Cauchy stress is bounded), show the BMO estimates for the stress and finally also the Morrey-like estimates for the plastic strain. In addition, we shall provide the whole theory up to the boundary. As an immediate consequence of such improved estimates, we provide a sharper identification of the plastic strain than that known up to date. In particular, in two dimensional setting, we show that the plastic strain can be point-wisely characterized in terms of the stresses everywhere although the stress is possibly discontinuous and thus the natural duality pairing in the space of measures could be violated.

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

Calculus of Variations and Partial Differential Equations

ISSN

0944-2669

e-ISSN

—

Svazek periodika

57

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

43

Strana od-do

—

Kód UT WoS článku

000431004800021

EID výsledku v databázi Scopus

2-s2.0-85043754677