hal-00725899
https://enpc.hal.science/hal-00725899
doi:10.1016/j.msec.2012.04.049
[ENPC] Ecole des Ponts ParisTech
[CNRS] CNRS - Centre national de la recherche scientifique
[UR-NAVIER] Laboratoire Navier
[NAVIER-STRUCTURES] Structures
[PARISTECH] ParisTech
[IFSTTAR] Ifsttar
[UNIV-EIFFEL] Université Gustave Eiffel
[IFSTTAR-UNIVEIFFEL] Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux
An analytical mechanical model to describe the response of NiTi rotary endodontic files in a curved root canal
Leroy, Agnès Marie Françoise
Guiomar de Azevedo Bahia, Maria
Ehrlacher, Alain
Buono, Vicente Tadeu Lopes
ART
Large transformations mechanics
Rotary endodontic files
Nickel-titanium alloys
Superelasticity
Aim To build a mathematical model describing the mechanical behavior of NiTi rotary files while they are rotating in a root canal. Methodology The file was seen as a beam undergoing large transformations. The instrument was assumed to be rotating steadily in the root canal, and the geometry of the canal was considered as a known parameter of the problem. The formulae of large transformations mechanics then allowed the calculation of the Green-Lagrange strain field in the file. The non-linear mechanical behavior of NiTi was modeled as a continuous piecewise linear function, assuming that the material did not reach plastic deformation. Criteria locating the changes of behavior of NiTi were established and the tension field in the file, and the external efforts applied on it were calculated. The unknown variable of torsion was deduced from the equilibrium equation system using a Coulomb contact law which solved the problem on a cycle of rotation. Results In order to verify that the model described well reality, three-point bending experiments were managed on superelastic NiTi wires, whose results were compared to the theoretical ones. It appeared that the model gave a good mentoring of the empirical results in the range of bending angles that interested us. Conclusions Knowing the geometry of the root canal, one is now able to write the equations of the strain and stress fields in the endodontic instrument, and to quantify the impact of each macroscopic parameter of the problem on its response. This should be useful to predict failure of the files under rotating bending fatigue, and to optimize the geometry of the files.
2012
en
Materials Science and Engineering: C
Elsevier