×

Variational analysis of a thermomechanically coupled quasi-steady rolling problem. (English) Zbl 1299.74140

Summary: In this work, a thermomechanically coupled rolling problem with nonlocal contact, Coulomb’s friction and heat exchange boundary conditions, for incompressible rigid-plastic, temperature-, equivalent strain- and strain-rate-dependent materials, is considered. A coupled variational formulation, consisting of a nonlinear variational inequality for the velocity, a nonlinear variational equation for the temperature and an evolution equation for the equivalent strain, is derived. A variable stiffness parameters method is proposed, its convergence is proved and existence and uniqueness results are obtained.

MSC:

74M15 Contact in solid mechanics
74F05 Thermal effects in solid mechanics
74H20 Existence of solutions of dynamical problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
49J40 Variational inequalities
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hill R, The Mathematical Theory of Plasticity (1950)
[2] Kachanov LM, Fundamentals of the Theory of Plasticity (1971)
[3] Zienkiewicz OC, Intternational Journal for Numerical Methods in Engineering 17 pp 1497– (1981) · Zbl 0462.73053
[4] Kobayashi S, Metal Forming and the Finite Element Method (1989)
[5] Valberg HS, Applied Metal Forming Including FEM Analysis (2010)
[6] Washizu K, Variational Methods in Elasticity and Plasticity (1982)
[7] Korneev VG, Approximate Solution of Plastic Flow Theory Problems (1984)
[8] Lions J-L, Quelques Methodes de Resolution des Problemes aux Limites non Lineares (1969)
[9] Duvaut G, Les Inequations en Mecanique et en Physique (1972)
[10] Nečas J, Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction (1981)
[11] Glowinski R, Numerical Methods for Nonlinear Variational Problems (1984)
[12] Panagiotopoulos PD, Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions (1985)
[13] DOI: 10.1137/1.9781611970845
[14] DOI: 10.1007/978-1-4612-1048-1 · Zbl 0654.73019
[15] Han W, Quasistatic Contact Problems in Viscoelasticity and Visco-plasticity (2002)
[16] Shillor M, Lecture Notes in Physics 655, in: Models and Variational Analysis of Quasistatic Contact (2004) · Zbl 1069.74001
[17] Migorski S, Advances in Mechanics and Mathematics 26, in: Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems (2013) · Zbl 1262.49001
[18] Angelov TA, Mechanics Research Communications 26 pp 287– (1999) · Zbl 1073.74597
[19] Angelov TA, International Journal of Engineering Sciience 42 pp 1779– (2004) · Zbl 1211.74164
[20] Angelov TA, Quarterly Journal of Mechanics and Applied Mathematics 65 pp 361– (2012) · Zbl 1248.74029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.