Numerical analysis of a quasistatic piezoelectric problem with damage |
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Authors: | Jos R Fernndez Rebeca Martínez Georgios E Stavroulakis |
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Institution: | aDepartamento de Matemática Aplicada, Universidade de Santiago de Compostela, Escola Politécnica Superior, Campus Universitario, 27002 Lugo, Spain;bDepartment of Production Engineering and Management, Technical University of Crete, GR-73100 Chania, Greece |
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Abstract: | The quasistatic evolution of the mechanical state of a piezoelectric body with damage is numerically studied in this paper. Both damage and piezoelectric effects are included into the model. The variational formulation leads to a coupled system composed of two linear variational equations for the displacement field and the electric potential, and a nonlinear parabolic variational equation for the damage field. The existence of a unique weak solution is stated. Then, a fully discrete scheme is introduced by using a finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, a two-dimensional example is presented to demonstrate the behaviour of the solution. To cite this article: J.R. Fernández et al., C. R. Mecanique 336 (2008). |
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Keywords: | Computational solid mechanics Damage Piezoelectricity Error estimates Numerical simulationsMots-clé s: Mé canique des solides numé rique Endommagement Pié zoé lectricité Estimations d'erreur Simulations numé riques |
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