A VARIATIONAL FORMULATION GOVERNED BY TWO BIPOTENTIALS FOR A FRICTIONLESS CONTACT MODEL-Reference-Cited by-同舟云学术

A VARIATIONAL FORMULATION GOVERNED BY TWO BIPOTENTIALS FOR A FRICTIONLESS CONTACT MODEL

Published:2024-02-23 Issue:1 Volume:29 Page:109-124
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Matei Andaluzia¹^ORCID,Osiceanu Madalina²^ORCID

Affiliation:

1. Department of Mathematics, University of Craiova, A.I.Cuza 13, 200585 Craiova, Romania

2. Doctoral School of Sciences, University of Craiova, A.I.Cuza 13, 200585 Craiova, Romania

Abstract

We consider a frictionless contact model whose constitutive law and contact condition are described by means of subdifferential inclusions. For this model, we deliver a variational formulation based on two bipotentials. Our formulation envisages the computation of a three-field unknown consisting of the displacement vector, the stress tensor and the normal stress on the contact zone, the contact being described by a generalized Winkler condition. Subsequently, we obtain existence and uniqueness results. Some properties of the solution are also discussed, focusing on the data dependence.

Publisher

Vilnius Gediminas Technical University

Reference30 articles.

1. W. Arendt and M. Kreuter. Mapping theorems for Sobolev-spaces of vector-valued functions. Studia Math., 240(3):275-299, 2018. https://doi.org/10.4064/sm8757-4-2017

2. V. Barbu and T. Precupanu. Convexity and Optimization in Banach Spaces. Springer, New York, 2012. https://doi.org/10.1007/978-94-007-2247-7

3. H. Bauschke and Y. Lucet. What is... a Fenchel conjugate. Notices of the American Mathematical Society, 59(1):44-46, 2012. https://doi.org/10.1090/noti788

4. G. Bodovillé and G. de Saxcé. Plasticity with non-linear kinematic hardening: modelling and shakedown analysis by the bipotential approach. Eur. J. Mech. A Solids, 20(1):99-112, 2001. https://doi.org/10.1016/S0997-7538(00)01109-8

5. M. Buliga, G. de Saxcé and C. Vallée. Existence and construction of bipotentials for graphs of multivalued laws. J. Convex Anal., 15(1):87-104, 2008. https://doi.org/10.48550/arXiv.math/0608424