On renormalised solutions for thermomechanical problem in perfect-plasticity with damping forces

Leszek Bartczak , Sebastian Owczarek

Abstract

We consider the quasi-static evolution of the thermo-plasticity model in which the evolution equation law for the inelastic strain is given by the Prandtl–Reuss flow rule. The thermal part of the Cauchy stress tensor is not linearized in the neighbourhood of a reference temperature. This nonlinear thermal part is imposed to add a damping term to the balance of the momentum, which can be interpreted as external forces acting on the material. In general, the dissipation term occurring in the heat equation is an integrable function only and the standard methods can not be applied. Combining truncation techniques and Boccardo-Gallouët approach with monotone methods, we prove an existence of renormalized solutions.
Author Leszek Bartczak (FMIS / DPDE)
Leszek Bartczak,,
- Department of Partial Differential Equations
, Sebastian Owczarek (FMIS / DPDE)
Sebastian Owczarek,,
- Department of Partial Differential Equations
Journal seriesMathematics and Mechanics of Solids, ISSN 1081-2865, e-ISSN 1741-3028, (A 25 pkt)
Issue year2019
Vol24
No4
Pages1030-1053
Publication size in sheets1.15
Keywords in Polishidealna plastyczność, rozwiązania zrenormalizowane, termo-plastyczność, metoda Boccardo-Gallouët
Keywords in Englishcontinuum mechanics, perfect plasticity, heat conduction, thermoplasticity, Boccardo-Gallouët approach, renormalised solutions
ASJC Classification2211 Mechanics of Materials; 2500 General Materials Science; 2600 General Mathematics
Abstract in PolishUdowadniamy istnienie rozwiązań zrenormalizowanych dla quasistatycznego modelu termo-plastyczności, w którym niesprężysty związek konstytutywny jest zadany regułą Prandtla-Reussa. Metody użyte w dowodzie to: Aproksymacja Yosidy, metody punktu stałego, oszacowania energetyczne na pochodne czasowe rozwiązań przybliżonych, metody Boccardo-Gallouët.
DOIDOI:10.1177/1081286518768673
URL https://journals.sagepub.com/doi/abs/10.1177/1081286518768673?journalCode=mmsa
Languageen angielski
Score (nominal)25
ScoreMinisterial score = 25.0, 01-08-2019, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2017 = 0.989; WoS Impact Factor: 2017 = 2.545 (2) - 2017=1.971 (5)
Citation count*
Cite
Share Share

Get link to the record


* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Back