| Περίληψη: | Fractures are common at human bones. So, a callus is formed and the procedure
of osteogenesis is initiated. Medical doctors need to have a tool that allows
them to evaluate the healing procedure without taking X-ray photos every week.
Such a variety of tools can be provided by non-destructive inspection techniques.
But rst, one has to create a model for predicting phenomena such as size-e ects
and in particular dispersive acoustic waves propagation.
Before this thesis, there has been made an attempt by (Vavva, 2009), to
predict modal wave propagation with Mindlin's Form-II. Herein, for the rst
time there are presented dynamic solutions of this theory.
To begin with, the bone is considered to be a dampless homogeneous (ortho)
isotropic composite material, with interstitial tissue being the matrix and
the osteons being the bres. So, Mindlin's theory can be applied in this case.
Next, a fundamental solution is obtained for Mindlin's Form-II of his gradient
elasticity theory. In conjunction to an existing integral representation, there can
be obtained solutions using the Boundary Element Method. With the help of a
considered Representative Volume Element, simulations have been conducted and
results are presented for the cases of P, S and Rayleigh waves, as well as guided
waves in plates. The dispersion diagrams as given by Wigner-Ville representations
are compared to the theoretical ones. What is more, the validity and accuracy of
the BEM code have been checked using analytical solutions of one-dimensional
problems.
Furthermore, relaxation functions from viscoelastic theories are considered
and are taken into account using the correspondence principle. So, both viscoelastic
and gradient-visco-elastic models have been considered and the results
of various cases (P, S, Rayleigh and Lamb waves) have been compared to the
above.
Finally, since the present thesis has to do with information extracted from
dispersive wave propagation, some studies have been made and measures have
been proposed for velocities and dispersion.
All in all, this has been a work dealing with the fact that micro-structure
a ects the macro-behavior of a material concerning waves propagation and, in
the framework of Mindlin's Form-II, there have been extracted several conclusions
concerning bone-like materials.
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