Displaying similar documents to “The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory”

A quasistatic contact problem with adhesion and friction for viscoelastic materials

Arezki Touzaline (2010)

Applicationes Mathematicae

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We consider a mathematical model which describes the contact between a deformable body and a foundation. The contact is frictional and is modelled by a version of normal compliance condition and the associated Coulomb's law of dry friction in which adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behaviour is modelled by a nonlinear viscoelastic constitutive law. We derive a variational...

Conical differentiability for bone remodeling contact rod models

Isabel N. Figueiredo, Carlos F. Leal, Cecília S. Pinto (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified...

A General Linear Theory of Elastic Plates and its Variational Validation

Danilo Percivale, Paolo Podio-Guidugli (2009)

Bollettino dell'Unione Matematica Italiana

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We provide a variational justification for shearable-plate models that generalize the classic Reissner-Mindlin model. Firstly, we give an argument leading to choose a fairly general linearly elastic monoclinic material response. Secondly, we prove that, for materials in such constitutive class, the variational limit of certain suitably scaled 3D energies is a functional whose minimum over a maximal subspace of admissible functions coincides with the minimum of the generalized Reissner-Mindlin...

Analysis of a contact adhesive problem with normal compliance and nonlocal friction

Arezki Touzaline (2012)

Annales Polonici Mathematici

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The paper deals with the problem of a quasistatic frictional contact between a nonlinear elastic body and a deformable foundation. The contact is modelled by a normal compliance condition in such a way that the penetration is restricted with a unilateral constraint and associated to the nonlocal friction law with adhesion. The evolution of the bonding field is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove...

A quasistatic contact problem with unilateral constraint and slip-dependent friction

Arezki Touzaline (2015)

Applicationes Mathematicae

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We consider a mathematical model of a quasistatic contact between an elastic body and an obstacle. The contact is modelled with unilateral constraint and normal compliance, associated to a version of Coulomb's law of dry friction where the coefficient of friction depends on the slip displacement. We present a weak formulation of the problem and establish an existence result. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments.

A study of a unilateral and adhesive contact problem with normal compliance

Arezki Touzaline (2014)

Applicationes Mathematicae

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The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational...

Frictionless contact problem with adhesion and finite penetration for elastic materials

Arezki Touzaline (2010)

Annales Polonici Mathematici

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The paper deals with the problem of quasistatic frictionless contact between an elastic body and a foundation. The elasticity operator is assumed to vanish for zero strain, to be Lipschitz continuous and strictly monotone with respect to the strain as well as Lebesgue measurable on the domain occupied by the body. The contact is modelled by normal compliance in such a way that the penetration is limited and restricted to unilateral contraints. In this problem we take into account adhesion...

A Remark on Variational Principles of Choban, Kenderov and Revalski

Adrian Królak (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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We consider some variational principles in the spaces C*(X) of bounded continuous functions on metrizable spaces X, introduced by M. M. Choban, P. S. Kenderov and J. P. Revalski. In particular we give an answer (consistent with ZFC) to a question stated by these authors.