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

Migórski, Stanisław; Szafraniec, Paweł

doi:10.1016/j.nonrwa.2013.07.002

Cited by 26 publications

(24 citation statements)

References 31 publications

(62 reference statements)

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“…The present paper is a continuation of Migórski and Szafraniec [23] which provided a result on the existence and uniqueness of a weak solution for dynamic frictional contact problems governed by a system of hemivariational inequalities in thermoviscoelasticity without damage. Our goal is to extend the results of Migórski and Szafraniec [23] to dynamic problems with damage which appear in the theory of thermoviscoelasticity. We assume nonmonotone relations between the normal stress and the normal displacement, and between the tangential force and the tangential displacement.…”

Section: Introductionmentioning

confidence: 89%

Dynamic nonsmooth frictional contact problems with damage in thermoviscoelasticity

Szafraniec

2014

Mathematics and Mechanics of Solids

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In this paper we prove the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem describing contact problem between the body and foundation. The process is dynamic, the material behaviour is described by nonlinear viscoelastic law, strongly coupled with the thermal effects. The contact is modelled by nonmonotone subdifferential boundary conditions. The mechanical damage of the material is described by a parabolic equation. We use recent results from the theory of hemivariational inequailities and fixed point theorems.

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Section: Introductionmentioning

confidence: 89%

Dynamic nonsmooth frictional contact problems with damage in thermoviscoelasticity

Szafraniec

2014

Mathematics and Mechanics of Solids

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“…Finally, assumption guarantees

|\partial φ_{α} (t, x, \cdot) (v)| \leq C_{μ} (1 + (||, v) + (|| α (t, x))) {\overset{σ}{true}}_{normaln} + C .

While [, Thm. 8] requires to hold without dependence on t or x , a look at the proof reveals that we are free to add any term from

L^{2} false(0, T, X false)

, and thus we can allow for arbitrary

α \in C (0, T, X)

, see also [].

□

…”

Section: Analysis Of the Rate Problem (The Mechanical Problem For U)mentioning

confidence: 99%

Existence of long‐time solutions to dynamic problems of viscoelasticity with rate‐and‐state friction

Pipping

2019

Z Angew Math Mech

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We establish existence of global solutions to a dynamic problem of bilateral contact between a rigid surface and a viscoelastic body, subject to rate-and-state friction. The term rate-and-state friction describes friction laws where the friction is rate-dependent and depends on an additional internal state variable defined on the contact surface. Our mathematical conditions rule out certain slip laws, but do cover the ageing law, and thus at least one of the rate-and-state friction laws commonly used in the geoscience. K E Y W O R D Sageing law, quasivariational evolutionary inequality, rate-and-state friction, surface friction, viscoelasticity M S C ( 2 0 1 0 ) 74L10, 74M10, 35Q74This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

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

Cited by 26 publications

References 31 publications

Dynamic nonsmooth frictional contact problems with damage in thermoviscoelasticity

Dynamic nonsmooth frictional contact problems with damage in thermoviscoelasticity

Existence of long‐time solutions to dynamic problems of viscoelasticity with rate‐and‐state friction

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

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