2018
DOI: 10.1155/2018/8346891
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Variational and Numerical Analysis of a Static Thermo-Electro-Elastic Problem with Friction

Abstract: We consider a mathematical model which describes a static frictional contact between a piezoelectric body and a thermally conductive obstacle. The constitutive law is supposed to be thermo-electro-elastic and the contact is modeled with normal compliance and a version of Coulomb's friction law. We derive a variational formulation of the problem and we prove the existence and uniqueness of its solution. The proof is based on some results of elliptic variational inequalities and fixed point arguments. Furthermor… Show more

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Cited by 4 publications
(4 citation statements)
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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].…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…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].…”
Section: Introductionmentioning
confidence: 99%
“…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%
“…Several models of fully coupled thermo-piezoelectricity has been developed for determining static responses under combined thermal, electric and mechanical excitations, see (Liu et al, 2014;Shang et al, 2002;Sládek et al, 2010;Tiersten, 1971). Recently, contact problems involving thermo-piezoelectric materials (Baiz et al, 2018;Benaissa et al, 2015Benaissa et al, , 2016 have been studied.…”
Section: Introductionmentioning
confidence: 99%
“…Assume the hypothesis of Theorem 3.1 and, in addition, assume that u ∈ H2 (Ω) d , u | Γ 3 ∈ H 2 (Γ 3 ) d , ϕ ∈ H 2 (Ω), θ ∈ H 2 (Ω) and σν ∈ L 2 (Γ 3 ) d .Then there exists a constant c, independent of h, such that…”
mentioning
confidence: 99%