A structural mathematical model for the viscoelastic anisotropic behaviour of trabecular bone

The presented paper is based on the conclusions of the preceding paper (1). On the basis of a general theoretical approach to the mechanics of heterogeneous materials published earlier / (2) , (3) , (4) / macroscopic constitutive equation of trabecular bone is deduced from the description of its microstructure. For the behaviour in physiological limits trabeculae are described as elastic and the remaining material constituent as a Maxwell body. The resulting macroscopic constitutive equation comprehends tensorial internal variables and the parameters appearing in it are the constants of the material constituents constitutive equations, the respective volume fractions and special structural parameters descriptive of the geometry of composition. The system of the trabeculae as well as the system of the remaining constituent of the composite are considered to be interconnected - continuous. Explicite formulae are given for the case of transverse isotropy, but the extension to more general cases of anisotropy is well possible. The procedure of identification of the model parameters is shown and a numerical example calculated.