title: A method for calculating the compliance of bonded-interfaces under shrinkage: validation for Class I cavities.
abstract: OBJECTIVE
  The compliance for tooth cavity preparations is not yet fully described in the literature. Thus, the objectives were to present a finite element (FE) method for calculating compliance and to apply this to peak shrinkage stress regions in model cavities restored with resin-composite.
  
  
  METHODS
  Three groups of FE-models were created, with all materials considered linear, homogeneous, elastic and isotropic: (a) a pair of butt-joint bonded cubic prisms (dentin/resin-composite), with dentin of known compliance (0.0666 μm/N). Free ends were fixed in the Z-axis direction. A 1% volumetric shrinkage was simulated for the resin-composite. Mean displacements in the Z direction at each node at the dentin-resin interface were calculated and divided by the sum of normal contact forces in Z for each node. (b) A series of more complex restored cavity configurations for which their compliances were calculated. (c) A set of 3D-FE beam models, of 4 mm × 2 mm cross-section with lengths from 2 to 10mm, were also analyzed under both tensile and bending modes.
  
  
  RESULTS
  The compliance calculated by FEM for the butt-joint prisms was 0.0652 μm/N and corresponded well to the analytical value (0.0666 μm/N). For more accurate representations of the phenomenon, such as the compliance of a cavity or any other complex structure, the use of the displacement-magnitude was recommended, as loading by isotropic contraction also produces transversal deformations. For the beam models, the compliance was strongly dependent upon the loading direction and was greater under bending than in tension.
  
  
  CONCLUSIONS
  The method was validated for the compliance calculation of complex structures subjected to shrinkage stress such as Class I 'cavities'. The same FEM parameters could be applied to calculate the real compliance of any interface of complex structures. The compliance concept is improved by considering specific load directions.
authors.affiliation: Department of Dental Materials and Prosthodontics, School of Dentistry, Institute of Science and Technology, UNESP - Univ Estadual Paulista, São José dos Campos, SP, Brazil; Biomaterials Unit, University of Birmingham, School of Dentistry, Birmingham, UK. Electronic address: F.Rodrigues@bham.ac.uk.
authors.forename: Flávia P
authors.initials: FP
authors.lastname: Rodrigues
authors.affiliation: Department of Mechanical Engineering, University of São Paulo, School of Engineering, São Paulo, SP, Brazil.
authors.forename: Raul G
authors.initials: RG
authors.lastname: Lima
authors.affiliation: Department of Biomaterials and Oral Biology, University of São Paulo, School of Dentistry, São Paulo, Brazil.
authors.forename: Antonio
authors.initials: A
authors.lastname: Muench
authors.affiliation: University of Manchester, School of Dentistry and Photon Science Institute, Manchester, UK.
authors.forename: David C
authors.initials: DC
authors.lastname: Watts
authors.affiliation: Department of Biomaterials and Oral Biology, University of São Paulo, School of Dentistry, São Paulo, Brazil.
authors.forename: Rafael Y
authors.initials: RY
authors.lastname: Ballester
mesh_terms: D001840:Dental Bonding; D003731:Dental Caries / Q000628:therapy*; D020342:Finite Element Analysis; D006801:Humans
keywords: Class I cavities; Compliance; Finite element analysis; Interface; Shrinkage