Interrelationships among the viscoelastic functions for anisotropic solids: Application to calcified tissues and related systems

Abstract

The Boltzmann superposition integral is applied to the anisotropic solid in order to derive relationships between various viscoelastic functions for orthotropic solids with special emphasis on describing biological systems such as calcified and connective tissues. These relations show that the results of uniaxial tension or compression experiments are rather complicated functions of the stiffness modulus tensor elements; as such the data could not be readily treated in a theoretical manner. On the other hand, torsional type experiments can be used to directly yield the appropriate shear elements of the tensor. Applying these derived relationships, the experimental results on cortical bone in uniaxial compression were transformed by means of computer techniques into a common representation (the complex dynamic modulus). The lack of agreement among these transformed results, based on the data from several different experimenters, as well as the failure of data from individual experiments to satisfy internal consistency tests, lead to the conclusion that the Boltzmann integral fails to describe properly the viscoelastic properties of cortical bone in compression. This implies that linear viscoelasticity theory, invariably assumed for bone, does not apply to bone in compression over the entire frequency range studied. For the purpose of comparison, dynamic moduli for synthetic (PMMA and high density linear polyethylene) and other natural (dentin and cancellous bone) materials are also presented. Fourier analytic techniques similar to those used for the above have been applied to the time-dependence of knee-joint forces obtained from gaiting studies.