Is Hooke's law applicable to an orthodontic cantilever?

Introduction: This study aimed to analyze the load-deflection characteristics of an orthodontic cantilever by using the large deflection elastic model.

Methods: We experimentally measured the vertical deflections of a cantilever with round or rectangular cross-sections, with lengths of 20 mm and 30 mm, and made of either stainless steel or titanium molybdenum alloy. The measurements were obtained under clinically relevant loading ranges (20-60 g of force for round and 20-140 g of force for rectangular wires) and compared with theoretical predictions derived from small and large deflection elastic models. Load-deflection and tangent stiffness curves were subsequently plotted.

Results: The impact of a permanent deformation was clinically insignificant. The stiffness of the cantilever increased with the load or deflection rather than remaining constant. Within the clinical loading range, we identified stiffness reversal loading values at which the stiffness of titanium molybdenum alloy surpassed that of stainless steel. The textbook guidelines on cantilevers can apply only when the vertical deflection remains within 16% of its length.

Conclusions: Within the typical clinical loading range, the load-deflection relationship of a cantilever deviates from Hooke's law because of the prominent deflection trait. The conventional model remains effective when the vertical deflection is within 16% of the cantilever length. Otherwise, it is advisable to determine the load and stiffness on the basis of actual measurements rather than relying on theoretical predictions.