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Anisotropic density growth of bone-A computational micro-sphere approach

Waffenschmidt, Tobias; Menzel, Andreas LU and Kuhl, Ellen (2012) In International Journal of Solids and Structures 49(14). p.1928-1946
Abstract
Bones are able to adapt their local density when exposed to mechanical loading. Such growth processes result in densification of the bone in regions of high loading levels and in resorption of the material in regions of low loading levels. This evolution and optimisation process generates heterogeneous distributions of bone density accompanied by pronounced anisotropic mechanical properties. While several constitutive models reported in the literature assume the growth process to be purely isotropic, only few studies focus on the modelling and simulation of anisotropic functional adaptation we can observe in vivo. Some of these few computational models for anisotropic growth characterise the evolution of anisotropy by analogy to... (More)
Bones are able to adapt their local density when exposed to mechanical loading. Such growth processes result in densification of the bone in regions of high loading levels and in resorption of the material in regions of low loading levels. This evolution and optimisation process generates heterogeneous distributions of bone density accompanied by pronounced anisotropic mechanical properties. While several constitutive models reported in the literature assume the growth process to be purely isotropic, only few studies focus on the modelling and simulation of anisotropic functional adaptation we can observe in vivo. Some of these few computational models for anisotropic growth characterise the evolution of anisotropy by analogy to anisotropic continuum damage mechanics while others include anisotropic growth but assume isotropic elastic properties. The objective of this work is to generalise a well-established framework of energy-driven isotropic functional adaptation to anisotropic microstructural growth and density evolution. We adopt the so-called micro-sphere concept, which proves to be extremely versatile and flexible to extend sophisticated one-dimensional constitutive relations to the three-dimensional case. In this work we apply this framework to the modelling and simulation of anisotropic functional adaptation by means of a directional density distribution, which evolves in time and in response to the mechanical loading condition. Several numerical studies highlight the characteristics and properties of the anisotropic growth model we establish. The formulation is embedded into an iterative finite element algorithm to solve complex boundary value problems. In particular, we consider the finite-element-simulation of a subject-specific proximal tibia bone and a comparison to experimental measurements. The proposed model is able to appropriately represent the heterogeneous bone density distribution. As an advantage over several other computational growth models proposed in the literature, a pronounced local anisotropy evolution is identified and illustrated by means of orientation-distribution-type density plots. (C) 2012 Elsevier Ltd. All rights reserved. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Adaptation, Remodelling, Anisotropic growth, Micro-sphere, Finite, element method
in
International Journal of Solids and Structures
volume
49
issue
14
pages
1928 - 1946
publisher
Elsevier
external identifiers
  • wos:000305441600002
  • scopus:84861532381
ISSN
0020-7683
DOI
10.1016/j.ijsolstr.2012.03.035
language
English
LU publication?
yes
id
d6cc36c2-33e6-4d05-9e41-606aff31aca0 (old id 2883899)
date added to LUP
2012-07-25 10:41:31
date last changed
2017-10-01 04:17:35
@article{d6cc36c2-33e6-4d05-9e41-606aff31aca0,
  abstract     = {Bones are able to adapt their local density when exposed to mechanical loading. Such growth processes result in densification of the bone in regions of high loading levels and in resorption of the material in regions of low loading levels. This evolution and optimisation process generates heterogeneous distributions of bone density accompanied by pronounced anisotropic mechanical properties. While several constitutive models reported in the literature assume the growth process to be purely isotropic, only few studies focus on the modelling and simulation of anisotropic functional adaptation we can observe in vivo. Some of these few computational models for anisotropic growth characterise the evolution of anisotropy by analogy to anisotropic continuum damage mechanics while others include anisotropic growth but assume isotropic elastic properties. The objective of this work is to generalise a well-established framework of energy-driven isotropic functional adaptation to anisotropic microstructural growth and density evolution. We adopt the so-called micro-sphere concept, which proves to be extremely versatile and flexible to extend sophisticated one-dimensional constitutive relations to the three-dimensional case. In this work we apply this framework to the modelling and simulation of anisotropic functional adaptation by means of a directional density distribution, which evolves in time and in response to the mechanical loading condition. Several numerical studies highlight the characteristics and properties of the anisotropic growth model we establish. The formulation is embedded into an iterative finite element algorithm to solve complex boundary value problems. In particular, we consider the finite-element-simulation of a subject-specific proximal tibia bone and a comparison to experimental measurements. The proposed model is able to appropriately represent the heterogeneous bone density distribution. As an advantage over several other computational growth models proposed in the literature, a pronounced local anisotropy evolution is identified and illustrated by means of orientation-distribution-type density plots. (C) 2012 Elsevier Ltd. All rights reserved.},
  author       = {Waffenschmidt, Tobias and Menzel, Andreas and Kuhl, Ellen},
  issn         = {0020-7683},
  keyword      = {Adaptation,Remodelling,Anisotropic growth,Micro-sphere,Finite,element method},
  language     = {eng},
  number       = {14},
  pages        = {1928--1946},
  publisher    = {Elsevier},
  series       = {International Journal of Solids and Structures},
  title        = {Anisotropic density growth of bone-A computational micro-sphere approach},
  url          = {http://dx.doi.org/10.1016/j.ijsolstr.2012.03.035},
  volume       = {49},
  year         = {2012},
}