کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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278426 | 1430275 | 2012 | 9 صفحه PDF | دانلود رایگان |
In this paper we revisit a strain-adaptive bone remodelling problem, assuming that the rate of the apparent density at a particular location is described as a local objective function and depending on a particular stimulus at that location. Normally, continuum mathematical descriptions of adaptive bone remodelling can lead to discontinuous solutions on the global apparent density distribution. To improve this numerical solution, in this work, as the main novelty, we include the diffusion of the bone remodelling into the model. The variational problem is written as a coupled system of a nonlinear variational equation for the displacement field and a parabolic elliptic variational inequality for the apparent density. An existence and uniqueness result is stated. Then, a fully discrete problem is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. A priori error estimates are proved from which, under adequate additional regularity conditions, the linear convergence of the algorithm is deduced. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation and the behaviour of the solution.
Journal: International Journal of Solids and Structures - Volume 49, Issues 15–16, August 2012, Pages 2085–2093