Theoretical and Finite Element Modeling of Fine Kirschner Wires in Ilizarov External Fixator

The mechanical behavior of the transosseous elements is a defining factor in the overall stiffness, stability, and reliability of an external fixation system. Mechanics involving the application of thin Kirschner wires in Ilizarov apparatus is yet to be fully explained. To address this problem, load-deflection behavior of the pretensioned thin wires laterally loaded by the bone is necessary to be studied. In this paper, the lateral deflections of thin Kirschner wires are studied both theoretically and computationally. Fully three dimensional finite element (FE) modeling and analyses were performed in which the bone was modeled as a hollow cylinder, and the wire-bone interaction was assumed to be frictionless. The mathematical solution resulted in new exact solutions for the deflection as well as final tension in the wires subjected to the lateral loading under a cylinder representing the bone. Results from the FE analyses turned out to be very close to those from the mathematical solution. The results obtained from theory and FE method are comparable to published experimental findings. Some aspects of the pretensioned thin wire behavior in ring fixation systems, e.g., stiffness-tension proportionality, were revealed in the results. The current study adds to the existing knowledge on the general behavior of tensile elements. DOI: 10.1115/1.4001815