Regularity Results for Two Standard Models in Elasto-Perfect-Plasticity Theory with Hardening

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10435823" target="_blank" >RIV/00216208:11320/21:10435823 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=tLP4hhZKz1" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=tLP4hhZKz1</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Regularity Results for Two Standard Models in Elasto-Perfect-Plasticity Theory with Hardening

Popis výsledku v původním jazyce

We consider two most studied standard models in the theory of elasto-plasticity with hardening in arbitrary dimension d &gt;= 2, namely, the kinematic hardening and the isotropic hardening problem. While the existence and uniqueness of the solution is very well known, the optimal regularity up to the boundary remains an open problem. Here, we show that in the interior we have Sobolev regularity for the stress and hardening while for their time derivatives we have the &quot;half&quot; derivative with the spatial and time variable. This was well known for the limiting problem but we show that these estimates are uniform and independent of the order of approximation. The main novelty consist of estimates near the boundary. We show that for the stress and the hardening parameter, we control tangential derivative in the Lebesgue space L-2, and for time derivative of the stress and the hardening we control the &quot;half&quot; time derivative and also spatial tangential derivative. Last, for the normal derivative, we show that the stress and the hardening have the 3/5 derivative with respect to the normal and for the time derivative of the stress and the hardening we show they have the 1/5 derivative with respect to the normal direction, provided we consider the kinematic hardening or near the Dirichlet boundary. These estimates are independent of the dimension. In case, we consider the isotropic hardening near the Neumann boundary we shall obtain W-alpha,W-2 regularity for the stress and the hardening with some alpha &gt; 1/2 depending on the dimension and W-beta,W-2 with some beta &gt; 1/6 for the time derivative of the stress and the hardening. Finally, in case of kinematic hardening the same regularity estimate holds true also for the velocity gradient.

Název v anglickém jazyce

Regularity Results for Two Standard Models in Elasto-Perfect-Plasticity Theory with Hardening

Popis výsledku anglicky

We consider two most studied standard models in the theory of elasto-plasticity with hardening in arbitrary dimension d &gt;= 2, namely, the kinematic hardening and the isotropic hardening problem. While the existence and uniqueness of the solution is very well known, the optimal regularity up to the boundary remains an open problem. Here, we show that in the interior we have Sobolev regularity for the stress and hardening while for their time derivatives we have the &quot;half&quot; derivative with the spatial and time variable. This was well known for the limiting problem but we show that these estimates are uniform and independent of the order of approximation. The main novelty consist of estimates near the boundary. We show that for the stress and the hardening parameter, we control tangential derivative in the Lebesgue space L-2, and for time derivative of the stress and the hardening we control the &quot;half&quot; time derivative and also spatial tangential derivative. Last, for the normal derivative, we show that the stress and the hardening have the 3/5 derivative with respect to the normal and for the time derivative of the stress and the hardening we show they have the 1/5 derivative with respect to the normal direction, provided we consider the kinematic hardening or near the Dirichlet boundary. These estimates are independent of the dimension. In case, we consider the isotropic hardening near the Neumann boundary we shall obtain W-alpha,W-2 regularity for the stress and the hardening with some alpha &gt; 1/2 depending on the dimension and W-beta,W-2 with some beta &gt; 1/6 for the time derivative of the stress and the hardening. Finally, in case of kinematic hardening the same regularity estimate holds true also for the velocity gradient.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX20-11027X" target="_blank" >GX20-11027X: Matematická analýza parciálních diferenciálních rovnic popisujících silně nerovnovážné stavy v otevřených systémech termodynamiky kontinua</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Journal of Convex Analysis

ISSN

0944-6532

e-ISSN

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Svazek periodika

28

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

34

Strana od-do

395-428

Kód UT WoS článku

000661128900006

EID výsledku v databázi Scopus

2-s2.0-85099648941