Theoretical investigation of elastic flexural properties for multistranded orthodontic archwires

The bending and torsional stresses during flexure were detailed and simplified for a single twisted strand, which emulates a spring. General expressions were derived to evaluate the elastic properties (i.e., strength, stiffness, and range) of multistranded wires by combining the effects of a number of outer twisted strands, with or without an inner strand. Specific expressions were solved for single-stranded, twisted, and coaxial wires. Initially, we considered the following multistranded wire configurations: two- (twin), three- (triple), four-strand (quad) twisted, and coaxial wires. The elastic properties of the twin and quad wires were essentially subsets of the triple wire. For a given overall wire diameter (D) and helix angle (alpha), the ranges of multistranded wires were independent of wire configurations. By varying the alpha from 45 to 85 degrees, the D from 0.394 to 0.546 mm (15.5 to 21.5 mil), and the stress at the proportional limit from 1.03 to 3.28 GPa (150 to 475 ksi), the theoretical elastic properties of triple and coaxial stainless steel wires matched many of the properties of conventional nickel titanium leveling wires.