Von Mises stresses on Mushroom-loop archwires for incisor retraction: a numerical study

ABSTRACT Objective: To perform a numerical simulation using FEM to study the von Mises stresses on Mushroom archwires. Methods: Mushroom archwires made of titanium-molybdenum alloy with 0.017 x 0.025-in cross-section were used in this study. A YS of 1240 MPa and a Young's modulus of 69 GPa were adopted. The archwire was modeled in Autodesk Inventor software and its behavior was simulated using the finite element code Ansys Workbench (Swanson Analysis Systems, Houston, Pennsylvania, USA). A large displacement simulation was used for non-linear analysis. The archwires were deformed in their extremities with 0° and 45°, and activated by their vertical extremities separated at 4.0 or 5.0 mm. Results: Tensions revealed a maximum of 1158 MPa at the whole part of the loop at 5.0mm of activation, except in a very small area situated at the top of the loop, in which a maximum of 1324 Mpa was found. Conclusions: Mushroom loops are capable to produce tension levels in an elastic range and could be safely activated up to 5.0mm.

RESUMO Objetivo: Realizar uma simulação numérica, por meio do Método dos Elementos Finitos (MEF), para obter as tensões de von Mises em arcos Mushroom. Métodos: Foram usados arcos com geometria Mushroom de titânio-molibdênio, com secção transversal 0,017" x 0,025". Adotou-se valores de tensão de escoamento (σesc) de 1.240 MPa e módulo de elasticidade (E) de 69 GPa. O arco foi modelado por meio do software Autodesk Inventor, e seu desempenho foi simulado utilizando-se o software de elementos finitos Ansys Workbench (Swanson Analysis System, Houston, Pennsylvania, EUA). Para a simulação, foi considerada a análise para grandes deslocamentos. O arco foi conformado em suas extremidades considerando-se planos de 0° e 45°, pré-ativado em 2,5mm e ativado por meio de suas extremidades verticais, separadas 4,0 mm ou 5,0 mm. Resultados: As tensões revelaram um valor máximo de 1.158 MPa na maior parte da alça, aos 5,0 mm de ativação, com exceção de uma área muito pequena, com valor de 1.324 MPa, situada no topo da alça. Conclusões: Os arcos Mushroom são capazes de produzir níveis de tensão situados dentro da região elástica e poderiam ser ativados com segurança até os 5,0 mm de ativação.

Three-dimensional analysis of an orthodontic delta spring

INTRODUCTION: The purpose of this study was to analyze the force system, moment-force ratios (M/F) and von Mises stresses in an orthodontic delta spring using a 3D finite element model. The M/F ratio produced by an orthodontic spring is related to the different types of tooth movement that are likely to occur in the sagittal and occlusal planes. METHODS: Analyses were performed using a 3D finite element model, and a data acquisition system was used to validate the numerical results. RESULTS: Reactive forces between 0.0 and 2.0 N were observed along the x-axis, while null values were observed along the y- and z-axes. The maximum activation that ensured geometric stability and mechanical stresses below the elastic limit of the material was 10.0 mm. CONCLUSION: The results indicate that a delta spring can provide (i) uncontrolled tipping for activation of less than 1.0 mm; (ii) controlled counterclockwise tipping for activation between 1.0 and 4.5 mm; (iii) translation for activation between 4.5 and 5.0 mm; and (iv) controlled clockwise tipping in the sagittal plane for activation between 5.0 and 10.0 mm. No tooth movement was observed in the occlusal plane for the M/F ratios observed.