Load displacement behavior

Using matrix algebra, a mathematical model is formulated for a particular type of external fixator with wires (system developed by Ilizarov) for the treatment of bone fractures. The mathematical model is used to give a linear estimate of the stiffness under lateral and axial loads in a representative number of practical conditions. Relative displacements of the bone ends at the fracture site are calculated not only in the common case of a gap, but also for various angles of inclined sliding contact; in this case, a realistic load is applied and nonlinear stiffening of the wires under transversal loads is iteratively taken into account.
The biomecanical stability of a fixator is analyzed and a set of coefficients and formulae is formulated to evaluate the stiffness of certain wire fixators. A mathematical model is developed and applied to provide a linear estimate of the stiffness of the fixator under lateral and axial stress. The formulae developed permits the simulation of any fixation geometry with the least computational efforts and shows the correlation between some variables and mechaniical properties of the fixator.