Modeling and analysis of the unilateral contact of a piezoelectric body with a conductive support |
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Authors: | Mikael Barboteu Mircea Sofonea |
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Institution: | Laboratoire de Mathématiques, Physique et Systèmes, University of Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan, France |
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Abstract: | We consider a mathematical model which describes the quasistatic process of contact between a piezoelectric body and an electrically conductive support, the so-called foundation. We model the material's behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the Signorini condition and a regularized electrical conductivity condition. 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 arguments of nonlinear equations with multivalued maximal monotone operators and fixed point. Then we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We treat the unilateral contact conditions by using an augmented Lagrangian approach. We implement this scheme in a numerical code then we present numerical simulations in the study of two-dimensional test problems, together with various comments and interpretations. |
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Keywords: | Electro-viscoelastic material Frictionless contact Signorini's condition Conductive foundation Monotone operator Weak solution Augmented Lagrangian method Finite element method Numerical simulations |
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