A viscoplastic contact problem with a normal compliance with limited penetration condition and history-dependent stiffness coefficient | Zendy

Mircea Sofonea | Zendy; Meir Shillor | Zendy

Open Access

A viscoplastic contact problem with a normal compliance with limited penetration condition and history-dependent stiffness coefficient

Author(s) -

Mircea Sofonea,

Meir Shillor

Publication year - 2013

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2014.13.371

Subject(s) - quasistatic process , viscoplasticity , mathematical analysis , mathematics , stiffness , mathematical proof , monotonic function , nonlinear system , integral equation , physics , constitutive equation , geometry , finite element method , quantum mechanics , thermodynamics

International audienceWe consider a mathematical model that describes frictionless contact between a viscoplastic body and a deformable obstacle or foundation. The process is quasistatic and contact is modeled with the normal compliance with limited penetration condition, which has been introduced recently. Moreover, the contact stiffness coefficient is allowed to depend on the history of the contact process. We derive a variational formulation of the problem, which is in the form of a strongly nonlinear system coupling an integral equation and a time-dependent variational inequality. Then, we provide the analysis of the problem, which includes its unique weak solvability and the continuous dependence of the solution on the problem data. The proofs are based on results from the theory of history-dependent variational inequalities, on monotonicity and a fixed point argument

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