Determination of material constants and hydraulic strengthening of trabecular bone through an orthotropic structural model

Abstract

A statistical mathematical model is used to describe the viscoelastic behavior of trabecular bone from the description of its microstructure. Trabecular bone is regarded as an orthotropic composite material consisting of two phases: The trabeculae, modelled as a non-linear elastic material, and the marrow, modelled as a Maxwell element. The macroscopic constitutive equation contains, as parameters, the constants of the material phases’ constitutive equations, the respective volume fractions and parameters descriptive of the geometry of trabecular bone. With this model, the contribution of the marrow to the mechanical behavior of trabecular bone is determined and it is calculated that, under a step load and at strain rate, 10 min⁻¹, the marrow can bear about 25% of the applied load. The constants of the material phases are also calculated from a series of stress-relaxation curves on trabecular bone specimens. It is concluded that the trabeculae display non-linear elastic behavior.