A variational-hemivariational inequality in contact problem for locking materials and nonmonotone slip dependent friction

We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferen...

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Bibliographic Details
Published in:Acta mathematica scientia 2017-11, Vol.37 (6), p.1639-1652
Main Authors: MIGÓRSKI, Stanisław, OGORZAŁY, Justyna
Format: Article
Language:English
Subjects:
47J20
47J22
49J53
74M10
74M15
Clarke subdifferential
locking material
nonmonotone friction
unilateral constraint
variational-hemivariational inequality
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Summary:We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(17)30097-8