Numerical analysis of a frictionless viscoelastic piezoelectric contact problem

Mikael Barboteu; Jose Ramon Fernández; Youssef Ouafik

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 4, page 667-682
  • ISSN: 0764-583X

Abstract

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In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximative solutions and, as a consequence, the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, some two-dimensional examples are presented to demonstrate the performance of the algorithm.

How to cite

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Barboteu, Mikael, Fernández, Jose Ramon, and Ouafik, Youssef. "Numerical analysis of a frictionless viscoelastic piezoelectric contact problem." ESAIM: Mathematical Modelling and Numerical Analysis 42.4 (2008): 667-682. <http://eudml.org/doc/250379>.

@article{Barboteu2008,
abstract = { In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximative solutions and, as a consequence, the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, some two-dimensional examples are presented to demonstrate the performance of the algorithm. },
author = {Barboteu, Mikael, Fernández, Jose Ramon, Ouafik, Youssef},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Piezoelectricity; viscoelasticity; normal compliance; error estimates; numerical simulations.; existence; uniqueness; finite element method; Euler scheme},
language = {eng},
month = {6},
number = {4},
pages = {667-682},
publisher = {EDP Sciences},
title = {Numerical analysis of a frictionless viscoelastic piezoelectric contact problem},
url = {http://eudml.org/doc/250379},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Barboteu, Mikael
AU - Fernández, Jose Ramon
AU - Ouafik, Youssef
TI - Numerical analysis of a frictionless viscoelastic piezoelectric contact problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/6//
PB - EDP Sciences
VL - 42
IS - 4
SP - 667
EP - 682
AB - In this work, we consider the quasistatic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle. The linear electro-viscoelastic constitutive law is employed to model the piezoelectric material and the normal compliance condition is used to model the contact. The variational formulation is derived in a form of a coupled system for the displacement and electric potential fields. An existence and uniqueness result is recalled. Then, a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximative solutions and, as a consequence, the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, some two-dimensional examples are presented to demonstrate the performance of the algorithm.
LA - eng
KW - Piezoelectricity; viscoelasticity; normal compliance; error estimates; numerical simulations.; existence; uniqueness; finite element method; Euler scheme
UR - http://eudml.org/doc/250379
ER -

References

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