A micropolar anisotropic constitutive model of cancellous bone from discrete homogenization.

Cosserat models of cancellous bone are constructed, relying on micromechanical approaches in order to investigate microstructure-related scale effects on the macroscopic properties of bone. The derivation of the effective mechanical properties of cancellous bone considered as a cellular solid modeled as two-dimensional lattices of articulated beams is presently investigated. The cell walls of the bone microstructure are modeled as Timoshenko thick beams. The asymptotic homogenization technique is involved to get closed form expressions of the equivalent properties versus the geometrical and mechanical microparameters, accounting for the effects of bending, axial, and transverse shear deformations. Considering lattice microrotations as additional degrees of freedom at both the microscopic and macroscopic scales, an anisotropic micropolar equivalent continuum model is constructed, the effective mechanical properties of which are identified. The effective elastic moduli of various periodic cell structures are computed in situations of low and high effective densities to assess the impact of the transverse shear deformation. The stress distribution in a cracked bone sample is computed based on the effective micropolar model, highlighting the regularizing effect of the Cosserat continuum in comparison to a classical elasticity continuum model.
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