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Numerical analysis of a quasistatic piezoelectric problem with damage

Stavroulakis Georgios, José R. Fernández, Rebeca Martínez

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URI: http://purl.tuc.gr/dl/dias/910B48DE-177E-45E7-84A6-5D40317CB7C0
Year 2008
Type of Item Peer-Reviewed Journal Publication
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Bibliographic Citation J. R. Fernándeza, R. Martínez, G. E. Stavroulakis ,"Numerical analysis of a quasistatic piezoelectric problem with damage ," Com. Rendus Méc. vol. 336, no.7, pp. 559–564, Jul.2008.doi: 10.1016/j.crme.2008.05.002 https://doi.org/10.1016/j.crme.2008.05.002
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Summary

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

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