Problems with ultrasonic measurements of shear modules of structured media

The elastic constants of linearly elastic, isotropic or anisotropic bone material are required for many numerical simulations. These constants are often measured ultrasonically, but this can lead to mistakes, especially if shear modules of spongiosa are considered. The reason is that spongiosa is a structure composed of trabeculae, each of which acts as a kind of beam which allows longitudinal, shear and also bending waves to propagate; the bending waves are as fast as the longitudinal waves and are indistinguishable from the shear waves. Furthermore, mistakes in measuring Young's modulus cannot be avoided in every case. Several numerical simulations of wave propagations in homogeneous media, and especially in periodically and irregularly structured media, were carried out via the application of explicit finite element codes. Results showing the above-mentioned effects are presented and discussed. These can help to explain in detail why mistakes may occur during ultrasonic measurements.