Frictional contact problem for elastic-viscoplastic materials with thermal effect

A dynamic contact problem is considered in the paper. The material behavior is described by electrovisco-elastic constitutive law with piezoelectric effects. The body is in contact with a rigide obstacle. Contact is described with the Signorini condition, a version of Coulomb's law of dry friction, and with a regularized electrical conductivity condition. A variational formulation of the problem is derived. Under the assumption that coefficient of friction is small, existence and uniqueness of a weak solution of the problem is proved. The proof is based on evolutionary variational inequalities and fixed points of operators.

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“…Proof. The proof based on the first order nonlinear evolutionary inequalities is given in ( [6,15]).…”

Section: Existence and Uniquenessmentioning

confidence: 99%

Variational Analysis of a Dynamic Electroviscoelastic Problem with Friction

Boutechebak¹,

Serrar²,

Bachmar³

et al. 2019

J. Sib. Fed. Univ., Math. phys.

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“…Moreover, the contacting surfaces exchange heat and energy is lost to the surroundings. Models taking into account thermal effects can be found in [3], [15] and [16] .…”

Section: Introductionmentioning

confidence: 99%

“…15) and(5.16) yieldsS ρ w ρ (t) − Sw (t) Y ≤ h n t 0 w ρ (s) − w (s) V ds + max r∈[0,n] B ρ (r) − B (r) Q∞ t 0 u (s) V ds,(5 17). …”

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A History-Dependent Frictional Contact Problem With Wear for Thermoviscoelastic Materials

Chouchane

Selmani

2019

Mathematical Modelling and Analysis

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In this manuscript we study a contact problem between a deformable viscoelastic body and a rigid foundation. Thermal effects, wear and friction between surfaces are taken into account. A variational formulation of the problem is supplied and an existence and uniqueness result is proved. The idea of the proof rested on a recent result on history-dependent quasivariational inequalities. Finally, a perturbation of the data is initiated and a convergence result is demonstrated when the perturbation parameter converges to zero.

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“…We need to mention that, in the framework of variational inequality, the continuous dependence result of viscoplastic or elastic-viscoplastic contact can be found in [1,2,26,27,29] for quasistatic process, and [24] for dynamic process. It is proved in these papers that, the strong convergence of data leads to the strong convergence of solution.…”

mentioning

confidence: 99%

“…What's more, the Clarke subdifferential term arising in hemivariational inequality is included in the model in this paper. Due to these differences, we use another approach than that in [24] to prove the continuous dependence result of a dynamic elastic-viscoplastic contact problem.…”

mentioning

confidence: 99%

Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

Wang

Cheng

2022

EECT

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<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.</p>

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Frictional contact problem for elastic-viscoplastic materials with thermal effect

Cited by 6 publications

References 12 publications

Variational Analysis of a Dynamic Electroviscoelastic Problem with Friction

Variational Analysis of a Dynamic Electroviscoelastic Problem with Friction

A History-Dependent Frictional Contact Problem With Wear for Thermoviscoelastic Materials

Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

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