Numerical analysis of a bone remodelling contact problem
Lecture Notes in Applied and Computational Mechanics, ISSN: 1613-7736, Vol: 56 LNACM, Page: 173-188
2013
- 2Captures
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Metrics Details
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Conference Paper Description
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. © 2013 Springer-Verlag.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84870740490&origin=inward; http://dx.doi.org/10.1007/978-3-642-33968-4_11; https://link.springer.com/10.1007/978-3-642-33968-4_11; http://www.springerlink.com/index/10.1007/978-3-642-33968-4_11; http://www.springerlink.com/index/pdf/10.1007/978-3-642-33968-4_11; https://dx.doi.org/10.1007/978-3-642-33968-4_11; https://link.springer.com/chapter/10.1007/978-3-642-33968-4_11
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