A quasistatic electro-viscoelastic contact problem with adhesion. (English) Zbl 1358.35186
Summary: The aim of this paper is to study the process of contact with adhesion between a piezoelectric body and an obstacle, the so-called foundation. The material’s behavior is assumed to be electro-viscoelastic; the process is quasistatic, the contact is modeled by the Signorini condition. The adhesion process is modeled by a bonding field on the contact surface. We derive a variational formulation for the problem and then we prove the existence of a unique weak solution to the model. The proof is based on a general result on evolution equations with maximal monotone operators and fixed-point arguments.
MSC:
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 74M10 | Friction in solid mechanics |
| 74M15 | Contact in solid mechanics |
| 49J40 | Variational inequalities |
| 74D05 | Linear constitutive equations for materials with memory |
| 74F15 | Electromagnetic effects in solid mechanics |
Keywords:
electro-viscoelastic material; Signorini’s condition; adhesion; quasi-variational inequality; maximal monotone operator; weak solution; fixed pointReferences:
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