Deformations of Flexible Rods
An efficient and accurate numerical technique, based on a shooting procedure, is being developed to analyze the problem of flexible rods undergoing large three-dimensional deformations under arbitrary loading conditions. Due to the large deformations that occur, the governing equations are highly nonlinear so that a variety of interesting behaviours can occur, such as the possible existence of multiple equilibrium solutions is currently being investigated.
Analysis and Design of Orthodontic Retraction Appliances
As a practical application of the numerical technique mentioned above, the analysis of orthodontic appliances to determine force systems produced during activation is currently underway. The three-dimensional effects of these appliances, which are usually studied in two-dimensions only, are being investigated with the goal of reducing unwanted clinical side effects and reducing patient treatment times.
Characterization and Modeling of Shape Memory Alloys
Shape memory alloys have unique properties that make them well suited for orthodontic applications. More information about the constitutive response of shape memory alloy wires, particularly due to bending and torsion, is required to design with these materials effectively. This project will involve the characterization of the response of shape memory alloy wires to bending and torsion. The resulting constitutive information will be used to investigate applications for shape memory alloys as retraction appliances.
Key words: biomechanics, orthodontics, shape memory alloys, stability, continuum mechanics
Raboud, D., Faulkner, M.G. and Lipsett, A.W., "A Segmental Approach for Large Three-Dimensional Rod Deformations", International Journal of Solids and Structures, Vol. 33, No. 8, 1996, pp. 1137-1156.
Raboud, D., Faulkner, M.G. and Lipsett, A.W., "Multiple Three-Dimensional Equilibrium Solutions for Cantilever Beams Loaded by Dead Tip and Uniform Distributed Loads", Journal of Nonlinear Mechanics, Vol. 31, No. 3, 1996, pp. 297-311.
Raboud, D., Faulkner, M.G., Lipsett A.W. and Haberstock, D.L., "Three Dimensional Effects in Retraction Appliance Design", American Journal of Orthodontics, Vol. 112, 1997, pp. 378-392.
Raboud D., "Simulation of the Superelastic Response of SMA Orthodontic Wires", ASME Journal of Biomechanical Engineering, Vol. 120, 1998, pp. 675-685.