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

Result code in 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>

Result on the web

<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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Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GX20-11027X" target="_blank" >GX20-11027X: Mathematical analysis of partial differential equations describing far-from-equilibrium open systems in continuum thermodynamics</a><br>

Continuities

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

Publication year

2021

Confidentiality

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

Name of the periodical

Journal of Convex Analysis

ISSN

0944-6532

e-ISSN

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Volume of the periodical

28

Issue of the periodical within the volume

2

Country of publishing house

DE - GERMANY

Number of pages

34

Pages from-to

395-428

UT code for WoS article

000661128900006

EID of the result in the Scopus database

2-s2.0-85099648941