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An asymptotic model of a nonlinear adaptive orthotropic elastic rod
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Robert J. Ronkese
Veröffentlicht/Copyright:
29. Februar 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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Artikel in diesem Heft
- Masthead
- Stability estimates for the multidimensional elliptic obstacle problem
- On the two-point boundary value problems for linear impulsive systems with singularities
- Explicit solutions of the boundary value problems of the theory of consolidation with double porosity for the half-plane
- Convergence of modification of the Durrmeyer type -Baskakov operators
- Backward stochastic differential equations with a convex generator
- On some ideal defined by density topology in the Cantor set
- Maximal operator of the Fejér means of triangular partial sums of two-dimensional Walsh–Fourier series
- Fixed point theorems for hybrid mappings satisfying an integral type contractive condition
- On the nonexistence of blowing-up solutions to a fractional functional-differential equation
- Two-weight inequalities for multilinear maximal operators
- An asymptotic model of a nonlinear adaptive orthotropic elastic rod
- Approximation of functions on locally compact abelian groups
