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Numerical Analysis of a Bone Remodelling Contact Problem

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Recent Advances in Contact Mechanics

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 56))

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Abstract

In this work, a frictionless quasistatic contact problem between an elastic body and a rigid obstacle is numerically studied. The bone remodelling of the elastic material is also taken into account and the well-known Signorini contact conditions are employed to model the contact. The variational formulation is written as an elliptic variational inequality of the first kind for the displacement field coupled with a first-order ordinary differential equation for the bone remodelling function. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced, based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are provided, from which the linear convergence of the algorithm is derived under suitable regularity conditions. Finally, a one-dimensional numerical example is described to show the numerical convergence of the algorithm, and two two-dimensional problems are presented to demonstrate the behaviour of the solution.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada I, Universidade de Vigo, ETSE de Telecounicacion, Campus As Lagoas Marcosende s/n, 36310, Vigo, Spain

    José R. Fernández & Rebeca Martínez

  2. Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Univ. Sur s/n, 15782, Santiago de Compostela, Spain

    Rebeca Martínez

Authors
  1. José R. Fernández
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  2. Rebeca Martínez
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Corresponding author

Correspondence to José R. Fernández .

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Editors and Affiliations

  1. Dept. Production Engineering &, Management, Technical University of Crete, Crete, 731 00, Greece

    Georgios E. Stavroulakis

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Fernández, J.R., Martínez, R. (2013). Numerical Analysis of a Bone Remodelling Contact Problem. In: Stavroulakis, G. (eds) Recent Advances in Contact Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33968-4_11

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  • DOI: https://doi.org/10.1007/978-3-642-33968-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33967-7

  • Online ISBN: 978-3-642-33968-4

  • eBook Packages: EngineeringEngineering (R0)

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