Analysis for unilateral contact problem with Coulomb’s friction in thermo-electro-visco-elasticity

Bouallala, Mustapha; Essoufi, El Hassan

doi:10.2298/fil2213443b

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…In the literature, there are some mathematical results concerning the variational analysis for this kind of problems; see, for instance, [1,3,4] for static models that consider the effects of mechanical, electrical, and thermal interactions in frictional contacts. The mathematical models that describe quasistatic frictional contact with thermo-piezoelectric effects are already addressed in [5,6,7,11,12], and more recently in [8]. Numerical schemes and their error estimates for the aforementioned models were also discussed for both static and quasistatic cases in [1,5,6,8].…”

Section: Introductionmentioning

confidence: 99%

On the dynamic frictionless contact problem with normal compliance in thermo-piezoelectricity

Alaoui,

EL-Hassan,

Ouaanabi

et al. 2024

EJMCA

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In this work, we study, from a variational and numerical point of view, a dynamic contact problem between a thermo-electro-viscoelastic body and an electrically and thermally conductive foundation. The normal compliance condition and a nonlinear regularized electrical and thermal conditions are employed to model the contact. We provide existence and uniqueness results of a weak solution to the model using adequate auxiliary problems, Gronwall’s lemma, and Banach fixed point theorem. Finally, we introduce a fully discrete approximation using the finite element method and an Euler scheme. Then we derive some error estimates, leading to the linear convergence result under suitable additional regularity conditions.

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Section: Introductionmentioning

confidence: 99%

On the dynamic frictionless contact problem with normal compliance in thermo-piezoelectricity

Alaoui,

EL-Hassan,

Ouaanabi

et al. 2024

EJMCA

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“…The mathematical models, which describes the quasistatic frictional contact with thermo-piezoelectric effect, are already addressed in Refs. [7][8][9][10][11]. Numerical schemes and their error estimates for the previous models were also addressed for static and quasistatic cases in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Numerical schemes and their error estimates for the previous models were also addressed for static and quasistatic cases in Refs. [7,9,[11][12][13]. Moreover, the literature concerning the contact problems with such kind of materials in a dynamic case is very poor, we refer to Refs.…”

Section: Introductionmentioning

confidence: 99%

On the dynamic Coulomb's frictional contact problem for thermo‐piezoelectric materials

Alaoui,

Essoufi,

Ouaanabi

et al. 2024

Z Angew Math Mech

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In this work, we study, from a variational point of view, a dynamic contact problem between a thermo‐piezoelectric body and a thermally conductive foundation. The normal compliance contact condition and Coulomb's friction law are employed to model the contact. We provide existence and uniqueness results of a weak solution to the model using adequate auxiliary problems, an abstract result on nonlinear first‐order evolution inequalities and Banach fixed point argument. Finally, the continuous dependence of the solution on the surface traction force and the surface electrical charge is studied.

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Analysis of a quasistatic thermo‐electro‐viscoelastic contact problem modeled by variational‐hemivariational and hemivariational inequalities

Alaoui,

Bouallala,

Hassan Essoufi

et al. 2024

Math Methods in App Sciences

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We study, from both variational and numerical perspectives, a quasistatic contact problem involving a thermo‐electro‐viscoelastic body and an electrically and thermally conductive rigid foundation. The contact is modeled by the Signorini's unilateral contact condition for the velocity field. Both the electrical and thermal conductivity conditions on the contact surface are described using the Clarke subdifferential boundary. We derive the weak formulation of the problem as a system coupling a variational‐hemivariational inequality and two hemivariational inequalities. We utilize recent results from the theory of variational‐hemivariational inequalities to establish the existence and uniqueness of the weak solution of the model. Finally, we study a fully discrete scheme for the problem using the Euler scheme and the finite element method. Under additional solution regularity assumptions, we derive error estimates for the approximate solutions.

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Analysis for unilateral contact problem with Coulomb’s friction in thermo-electro-visco-elasticity

Cited by 4 publications

References 10 publications

On the dynamic frictionless contact problem with normal compliance in thermo-piezoelectricity

On the dynamic frictionless contact problem with normal compliance in thermo-piezoelectricity

On the dynamic Coulomb's frictional contact problem for thermo‐piezoelectric materials

Analysis of a quasistatic thermo‐electro‐viscoelastic contact problem modeled by variational‐hemivariational and hemivariational inequalities

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