On the effective anisotropic elastic properties of porous hydroxyapatite,porous collagen,and cortical bone: A homogenization scheme with percolation threshold concept

Abstract

The objective of this study is to model the effective anisotropic elastic properties of porous hydroxyapatite, wet collagen, and cortical bone by an advanced homogenization scheme with a percolation threshold concept. The theoretical basis of the anisotropic homogenization theory is first presented. A homogenization scheme with a percolation threshold concept is then introduced and validated against experimental data for porous hydroxyapatite as well as bone after decollagenization. It is also validated on a porous collagen that is a result of the demineralization of bone. Even though aligned collagen fibers are considered, similar values of the elastic stiffnesses $C_{11}$ and $C_{33}$ were found for demineralized bone due to its very high porosity. Finally the proposed method is used to model cortical bone as a mixture of hydroxyapatite mineral and soft organic content that is in turn a mixture of collagen fiber and pores filled by water. Good agreement between modeled and measured data is observed. The model presented herein is simpler than existing multi-scale homogenization schemes in the literature, but its results fit very well with the experimented trends.