The use of porous scaffolds for repairing the damaged bone tissues has been increased in recent years. As exploration of the mechanical properties of the scaffolds on the basis of experiments is time consuming and uneconomic, mathematical models are increasingly being introduced into the field, but most of them rely on finite element method and theoretical studies are rarely found in the literature. In this paper, different micromechanical models are presented for obtaining the effective elastic properties of bone scaffolds. Using these models, the mechanical properties of different scaffolds, including ceramic and composite bone scaffolds, are investigated. Single scale and multi-scale modeling approaches are used to simulate the ceramic and composite scaffolds, respectively. Furthermore, because of the wide application of hydroxyapatite in fabrication of bone scaffolds, the mechanical properties of hydroxyapatite scaffolds in different porosities are obtained in the current study by means of the presented methods. Results show that Dewey, self-consistent and differential schemes are the best methods in calculation of the value of Young’s modulus of these scaffolds in porosity ranges of less than 30 %, 30 to 60 % and more than 60 %, respectively. Moreover, self-consistent scheme gives good estimation of the value of Poisson’s ratio of hydroxyapatite scaffolds in different porosities. By obtaining the values of the mechanical properties of the scaffolds in different porosities by these models and using the statistical analysis, the mathematical relationship between the porosity and the mechanical properties of this kind of scaffolds (Young’s modulus and Poisson’s ratio) is obtained.

Keywords: Bone Tissue Engineering, Bone scaffold, Micromechanical Modeling, Multi-scale Modeling, Effective Elastic Properties

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