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Conical differentiability for bone remodeling contact rod models

Published online by Cambridge University Press:  15 July 2005

Isabel N. Figueiredo ,
Carlos F. Leal  and
Cecília S. Pinto
Isabel N. Figueiredo
Affiliation:
Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal; isabel.figueiredo@mat.uc.pt; carlosl@mat.uc.pt
Carlos F. Leal
Affiliation:
Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal; isabel.figueiredo@mat.uc.pt; carlosl@mat.uc.pt
Cecília S. Pinto
Affiliation:
Departamento de Matemática, Escola Superior de Tecnologia de Viseu, Campus Politécnico 3504-510 Viseu, Portugal; cagostinho@mat.estv.ipv.pt
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Abstract

We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified displacement constraint set defined by the obstacle and the differentiability of the two forms associated to the variational inequality.

Keywords

Adaptive elasticityfunctional spacespolyhedric setrod.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 3 , July 2005 , pp. 382 - 400
Copyright
© EDP Sciences, SMAI, 2005

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