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Numerical analysis of a piezoelectric bone remodelling problem

Published online by Cambridge University Press:  25 May 2012

J. R. FERNÁNDEZ ,
J. M. GARCÍA-AZNAR  and
R. MARTÍNEZ
J. R. FERNÁNDEZ
Affiliation:
Departamento de Matemática Aplicada I, Universidade de Vigo, ETSI Telecomunicación, Campus As Lagoas Marcosende s/n, 36310 Vigo, Spain email: jose.fernandez@uvigo.es
J. M. GARCÍA-AZNAR
Affiliation:
Aragon Institute of Engineering Research (I3A), Universidad de Zaragoza, María de Luna, 3, E-50018, Zaragoza, Spain email: jmgaraz@unizar.es
R. MARTÍNEZ
Affiliation:
Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Sur s/n, 15782 Santiago de Compostela, Spain email: rebeca.martinez@usc.es
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Abstract

Although in recent years bone piezoelectricity has been normally neglected, lately a new interest has appeared to show the importance of bone piezoelectricity in wet bone's complex response to loading. Here we numerically study a problem, including a strain-adaptive bone remodelling and the piezoelectricity. Its variational formulation leads to a coupled system composed of two linear variational equations for displacements and electric potential, and a parabolic variational inequality for the apparent density. Fully discrete approximations are now introduced by using the finite element method to approximate spatial variable and the explicit Euler scheme to discretise time derivatives. Some a priori error estimates are proved and the linear convergence of the algorithm is deduced under additional regularity conditions. Finally, some one- and two-dimensional numerical simulations are described to show the accuracy of the proposed algorithm and the behaviour of the solution.

Keywords

65M1565M6074B2074F99
Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 5 , October 2012 , pp. 635 - 657
Copyright
Copyright © Cambridge University Press 2012

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