Geodesic
Conical differentiability for bone remodeling contact rod models
Figueiredo, Isabel N. ; Leal, Carlos F. ; Pinto, Cecília S.1
1 Departamento de Matemática, Escola Superior de Tecnologia de Viseu, Campus Politécnico 3504-510 Viseu, Portugal;
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 382-400

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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.

DOI : 10.1051/cocv:2005011
Classification : 49J15, 49J20, 74B20, 74K10, 74L15, 90C31
Keywords: adaptive elasticity, functional spaces, polyhedric set, rod

Figueiredo, Isabel N.  ; Leal, Carlos F.  ; Pinto, Cecília S. 1

1 Departamento de Matemática, Escola Superior de Tecnologia de Viseu, Campus Politécnico 3504-510 Viseu, Portugal; 
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     title = {Conical differentiability for bone remodeling contact rod models},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {382--400},
     publisher = {EDP-Sciences},
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Figueiredo, Isabel N.; Leal, Carlos F.; Pinto, Cecília S. Conical differentiability for bone remodeling contact rod models. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 382-400. doi: 10.1051/cocv:2005011

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