Computational study of wave propagation in materials with microstructure effect : bone application

• Κύριος συγγραφέας: Παπαχαραλαμπόπουλος, Αλέξιος
• Άλλοι συγγραφείς: Πολύζος, Δημοσθένης
• Μορφή: Thesis
• Γλώσσα: English
• Έκδοση: 2012
• Θέματα: Fractures; Bones; Mindlin's theory; Κατάγματα; Οστά; Θεωρία του Μίντλιν; Βαθμοελαστική θεωρία; 617.15

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.