A mathematical analysis of a dynamical frictional contact model in thermoviscoelasticity

Chau, Oanh; Oujja, Rachid; Rochdi, M.

doi:10.3934/dcdss.2008.1.61

Cited by 8 publications

(11 citation statements)

References 2 publications

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“…are the components of the tensor of thermal expansion was considered in [1,5]. The behavior of the material is described by the nonlinear thermoviscoelastic constitutive law of Kelvin-Voigt type with a long-term memory of the form…”

Section: Physical Setting and Classical Formulationmentioning

confidence: 99%

“…Recently dynamic viscoelastic frictional contact problems with or without thermal effects have been investigated in a large number of papers, see e.g. Adly et al [1] Amassad et al [2], Andrews et al [3,4], Chau et al [5], Han and Sofonea [14], Jarusek [16], Kuttler and Shillor [20], Migorski [25], Migorski and Ochal [27], Migorski et al [28,29], Rochdi and Shillor [33] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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A class of dynamic frictional contact problems governed by a system of hemivariational inequalities in thermoviscoelasticity

Migórski

Szafraniec

2014

Nonlinear Analysis: Real World Applications

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In this paper we prove the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation. We employ the nonlinear constitutive viscoelastic law with a long-term memory, which include the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions for the contact, friction and heat flux. The model consists of the system of the hemivariational inequality of hyperbolic type for the displacement and the parabolic hemivariational inequality for the temperature. The existence of solutions is proved by using recent results from the theory of hemivariational inequalities and a fixed point argument.

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Section: Physical Setting and Classical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A class of dynamic frictional contact problems governed by a system of hemivariational inequalities in thermoviscoelasticity

Migórski

Szafraniec

2014

Nonlinear Analysis: Real World Applications

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“…There are numerous publications concerning mathematical analysis of contact processes with thermal effect, that essentially deal with existence and uniqueness of solution for the stated problems. We recommend [1,2,3,4,16,21,29] as the exemplary references in this field.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

Bartosz¹,

Jureczka²,

Szafraniec³

2019

Preprint

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In this work we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a nonmonotone relation between the tangential stress and the tangential velocity. This leads to a system of hyperbolic inclusion for displacement and parabolic equation for temperature. We provide a fully discrete approximation of studied problem and find optimal error estimates without any smallness assumption on the data. The theoretical result is illustrated numerically.

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“…Dynamic contact problems involving porous thermoelastic or thermoviscoelastic materials have received an increasing interest during the last twenty years, because of the application of this type of materials in the modelling of rocks, soils, wood, manufactured porous materials like ceramics and pressed powders or biological systems as bones (see, for instance, [] and the numerous references cited therein).…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of a contact problem in poro‐thermoelasticity with microtemperatures

Bazarra

2018

Z Angew Math Mech

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A dynamic contact problem, between a thermoelastic rod with voids and microtemperatures and a deformable obstacle, is numerically investigated in this work. The contact is modelled with a modification of the classical normal compliance contact condition. The mechanical problem consists of a coupled system of two hyperbolic partial differential equations and two parabolic ones. An existence and uniqueness result, and an energy decay property, are stated. Then, fully discrete approximations are introduced to approximate this nonlinear problem by using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximation and the behaviour of the solution.

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A mathematical analysis of a dynamical frictional contact model in thermoviscoelasticity

Cited by 8 publications

References 2 publications

A class of dynamic frictional contact problems governed by a system of hemivariational inequalities in thermoviscoelasticity

A class of dynamic frictional contact problems governed by a system of hemivariational inequalities in thermoviscoelasticity

Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

Numerical analysis of a contact problem in poro‐thermoelasticity with microtemperatures

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