Necessary and sufficient conditions for global stability and uniqueness in finite element simulations of adaptive bone remodeling
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for global stability and uniqueness in finite element simulations of adaptive bone remodeling
zbMATH Open document ID: 0811.73051
DOI: 10.1016/0020-7683(94)90178-3
author: Timothy P. Harrigan
author: James J. Hamilton
published in: International Journal of Solids and Structures
publication date: 1994-08-02T00:00:00Z
review text: Using a finite element method, the authors studied the necessary and sufficient conditions for global stability and uniqueness of adaptive bone remodeling. For that, they modeled the bone tissue as isotropic with a constant Poisson ratio and with the elastic modulus proportional to volumetric density of calcified tissue raised to the power \(n\). Their remodeling rate equation took the rate of change of volumetric hard tissue density as proportional to the difference between a stimulus and a set point. In one of their previous studies they defined state variables which are conjugate to the remodeling stimulus, and the function which acts as a variational indicator for the remodeling stimulus. Using this variational indicator properties, they studied the stability and uniqueness of the solution to the remodeling rate equations for all possible density distributions. They showed that the solution is the global minimum of a weighted sum of the total strain energy and the integral of density to the power \(m\) over the remodeling elements. In the reviewer's opinion this work is quite interesting and may find readers working in the field of biomechanics.
reviewed by: Hilmi Demiray
Mathematics Subject Classification ID: 74L15
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 92C10
zbMATH DE Number: 612085
zbMATH Keywords: conjugate state variables
zbMATH Keywords: constant Poisson ratio
zbMATH Keywords: volumetric density of calcified tissue
zbMATH Keywords: remodeling stimulus
zbMATH Keywords: variational indicator
zbMATH Keywords: global minimum
MaRDI profile type: Publication
full work available at URL: 0020-7683(94)90178-3
OpenAlex ID: W2031148182
description: scientific article; zbMATH DE number 612085