Thermo-visco-elasticity for Norton-Hoff-type models

被引：15

作者：

Gwiazda, Piotr ^{[1
]}

Klawe, Filip Z. ^{[1
]}

Swierczewska-Gwiazda, Agnieszka ^{[1
]}

机构：

[1] Univ Warsaw, Inst Appl Math & Mech, PL-02097 Warsaw, Poland

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2015年 / 26卷

关键词：

Thermodynamical consistency; Visco-elasticity; Thermal effects; Galerkin approximation; Monotonicity method; Renormalizations; BODNER-PARTOM; MROZ MODEL; EXPANSION; ZERO; PLASTICITY; EXISTENCE; EQUATIONS; FRAMEWORK; COERCIVE; LAW;

D O I：

10.1016/j.nonrwa.2015.05.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our research is directed to a quasi-static evolution of the thermo-visco-elastic model. We assume that the material is subject to two kinds of mechanical deformations: elastic and inelastic, Moreover, our analysis captures the influence of the temperature on the visco-elastic properties of the body. The novelty of the paper is the consideration of the thermodynamically consistent model to describe this kind of phenomena related with a hardening rule of Norton-Hoff type. We provide the proof of existence of solutions to thermo-visco-elastic model in a simplified setting, namely the thermal expansion effects are neglected. Consequently, the coupling between the temperature and the displacement occurs only in the constitutive function for the evolution of the visco-elastic strain. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：199 / 228

页数：30

共 57 条

[1] Quasistatic problems in viscoplasticity theory II: Models with nonlinear hardening [J].

Alber, Hans-Dieter ;

Chelminski, Krzysztof .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2007, 17 (02) :189-213

[2]

Alt H. W., 2006, Lineare Funktionalanalysis: Eine Anwendungsorien Tierte Einfuhrung, V5

[3]

[Anonymous], 1998, LECT NOTES MATH

[4]

[Anonymous], 1998, PARTIAL DIFFERENTIAL

[5]

[Anonymous], 2013, MECH THERMODYNAMICS

[6]

Barbu V., 1976, Nonlinear semigroups and differential equations in Banach spaces

[7] Mathematical analysis of a thermo-visco-plastic model with Bodner-Partom constitutive equations [J].

Bartczak, Leszek .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 385 (02) :961-974

[8] THERMO-VISCO-ELASTICITY WITH RATE-INDEPENDENT PLASTICITY IN ISOTROPIC MATERIALS UNDERGOING THERMAL EXPANSION [J].

Bartels, Soeren ;

Roubicek, Tomas .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2011, 45 (03) :477-504

[9] TRUNCATIONS AND MONOTONICITY METHODS FOR PARABOLIC EQUATIONS [J].

BLANCHARD, D .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1993, 21 (10) :725-743

[10] Renormalised solutions of nonlinear parabolic problems with L1 data:: existence and uniqueness [J].

Blanchard, D ;

Murat, F .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1997, 127 :1137-1152

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