Application of the reiterated homogenization to determination of effective moduli of a compact bone. (English) Zbl 0963.74037

Summary: The aim of the paper is twofold. First, we survey available results on determining effective macroscopic elastic moduli of a compact bone by using homogenization. Secondly, it is shown that the proper framework for studying such organic materials with hierarchical microstructure is that of reiterated homogenization. \(\Gamma\)-convergence theory is applied to obtain the general formulae for effective elastic moduli of a material with three structural levels.


74L15 Biomechanical solid mechanics
74Q15 Effective constitutive equations in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
92C10 Biomechanics