Open AccessAnalysis of two quasistatic history-dependent contact models
Author(s) -
Xiaoliang Cheng,
Stanisław Migórski,
Anna Ochał,
Mircea Sofonea
Publication year - 2014
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2014.19.2425
Subject(s) - quasistatic process , uniqueness , subderivative , mathematics , constitutive equation , viscoelasticity , boundary value problem , mathematical analysis , weak solution , boundary (topology) , physics , geometry , finite element method , thermodynamics , convex optimization , quantum mechanics , regular polygon
International audienceWe consider two mathematical models which describe the evolution of a viscoelastic and viscoplastic body, respectively, in contact with a piston or a device, the so-called obstacle or foundation. In both models the contact process is assumed to be quasistatic and the friction is described with a Clarke subdifferential boundary condition. The novelty of the models consists in the constitutive laws as well as in the contact conditions we use, which involve a memory term. We derive a variational formulation of the problems which is in the form of a system coupling a nonlinear integral equation with a history--dependent hemivariational inequality. Then, we prove the existence of a weak solution and, under additional assumptions, its uniqueness. The proof is based on a result on history--dependent hemivariational inequalities obtained in [18