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An asymptotic model of a nonlinear adaptive orthotropic elastic rod
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Robert J. Ronkese
Published/Copyright:
February 29, 2012
Abstract.
Cancellous bone can be regarded as a lattice of asymptotically small rods and plates. In this paper, a thin rod of an orthotropic elastic material with a cross-section 
where 
is considered. This thin cross-section leads to asymptotic expansions of the displacement vector, stress and strain tensors, and of the temporal change in the volumetric fraction of solid bone in the bone matrix. A rate equation describing this change in the volumetric fraction governs the remodeling process of bone deposition and reabsorption. It has linear and quadratic terms of strain tensors and thus, its own asymptotic expansion. This expansion's leading term is used in some simple numerical simulations.
Received: 2010-12-21
Revised: 2011-07-26
Published Online: 2012-02-29
Published in Print: 2012-March
© 2012 by Walter de Gruyter Berlin Boston
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