Abstract
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.
Highlights
A piezoelectric body is one that produces an electric charge when a mechanical stress is applied
In this work we continue in this line of research, where we extend the result established in [3,20] for contact problem described with the Signorini conditions into contact problem described with the Signorini conditions with adhesion where the obstacle is a perfect insulator and the resistance to tangential motion is generated by the glue, in comparison to which the frictional traction can be neglected
We introduce the set Q = { β ∈ L∞(0, T ; L2( 3)) | 0 ≤ β(t) ≤ 1 ∀ t ∈ [0, T ], a.e. on 3 }
Summary
A piezoelectric body is one that produces an electric charge when a mechanical stress is applied (the body is squeezed or stretched). Different models have been developed to describe the interaction between the electrical and mechanical fields( see, e.g., [2,14,16,17,18,19,29,30,31] and the references therein). General models for elastic materials with piezoelectric effect, called electro-elastic materials, can be found in [2,4,14]. A static frictional contact problem for electricelastic materials was considered in [1,15], under the assumption that the foundation is insulated. Adhesion may take place between parts of the contacting surfaces It may be intentional, when surfaces are bonded with glue, or unintentional, as a seizure between very clean surfaces. 2 we present the electro-viscoelastic contact model with adhesion and provide comments on the contact boundary conditions.
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