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Issue ESAIM: COCV
Volume 11, Number 3, July 2005
Page(s) 382 - 400
DOI 10.1051/cocv:2005011

ESAIM: COCV, July 2005, Vol. 11, pp. 382-400
DOI: 10.1051/cocv:2005011

Conical differentiability for bone remodeling contact rod models

Isabel N. Figueiredo1, Carlos F. Leal1 and Cecília S. Pinto2

1  Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal; isabel.figueiredo@mat.uc.pt; carlosl@mat.uc.pt
2  Departamento de Matemática, Escola Superior de Tecnologia de Viseu, Campus Politécnico 3504-510 Viseu, Portugal; cagostinho@mat.estv.ipv.pt


(Received June 29, 2004.)

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.


Mathematics Subject Classification. 49J15, 49J20, 74B20, 74K10, 74L15, 90C31

Key words: Adaptive elasticity, functional spaces, polyhedric set, rod.


© EDP Sciences, SMAI 2005


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