# Conical differentiability for bone remodeling contact rod models

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

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 11, Issue: 3, page 382-400
- ISSN: 1292-8119

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topFigueiredo, Isabel N., Leal, Carlos F., and Pinto, Cecília S.. "Conical differentiability for bone remodeling contact rod models." ESAIM: Control, Optimisation and Calculus of Variations 11.3 (2010): 382-400. <http://eudml.org/doc/90769>.

@article{Figueiredo2010,

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.
},

author = {Figueiredo, Isabel N., Leal, Carlos F., Pinto, Cecília S.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Adaptive elasticity; functional spaces; polyhedric set;
rod.; adaptive elasticity; rod; variational inequality},

language = {eng},

month = {3},

number = {3},

pages = {382-400},

publisher = {EDP Sciences},

title = {Conical differentiability for bone remodeling contact rod models},

url = {http://eudml.org/doc/90769},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Figueiredo, Isabel N.

AU - Leal, Carlos F.

AU - Pinto, Cecília S.

TI - Conical differentiability for bone remodeling contact rod models

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 11

IS - 3

SP - 382

EP - 400

AB -
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.

LA - eng

KW - Adaptive elasticity; functional spaces; polyhedric set;
rod.; adaptive elasticity; rod; variational inequality

UR - http://eudml.org/doc/90769

ER -

## References

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- L. Trabucho and J.M. Viaño, Mathematical Modelling of Rods, P.G. Ciarlet and J.L Lions Eds. North-Holland, Amsterdam, Handb. Numer. Anal.4 (1996) 487–974. Zbl0873.73041
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