title: An analytical mechanical model to describe the response of NiTi rotary endodontic files in a curved root canal.
abstract: OBJECTIVE
  To build a mathematical model describing the mechanical behavior of NiTi rotary files while they are rotating in a root canal.
  
  
  METHODS
  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.
authors.affiliation: Department of Metallurgical and Materials Engineering, School of Engineering, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, Brazil; Department of Mechanical and Materials Engineering, École des Ponts Paristech (ENPC), Champs-sur-Marne, France.
authors.forename: Agnès Marie Françoise
authors.initials: AM
authors.lastname: Leroy
authors.affiliation: Department of Restorative Dentistry, Faculty of Dentistry, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, Brazil.
authors.forename: Maria Guiomar de Azevedo
authors.initials: MG
authors.lastname: Bahia
authors.affiliation: Department of Mechanical and Materials Engineering, École des Ponts Paristech (ENPC), Champs-sur-Marne, France.
authors.forename: Alain
authors.initials: A
authors.lastname: Ehrlacher
authors.affiliation: Department of Metallurgical and Materials Engineering, School of Engineering, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, Brazil.
authors.forename: Vicente Tadeu Lopes
authors.initials: VT
authors.lastname: Buono
mesh_terms: D003786:Dental Pulp Cavity / Q000187:drug effects*; D008422:Materials Testing; D055595:Mechanical Phenomena; D009532:Nickel / Q000008:administration & dosage* / Q000737:chemistry*; D012399:Rotation; D013314:Stress, Mechanical; D014025:Titanium / Q000008:administration & dosage* / Q000737:chemistry*; D019553:Tooth, Nonvital / Q000628:therapy*
chemical_list: D009532:Nickel; D014025:Titanium