d e n t a l m a t e r i a l s 3 0 ( 2 0 1 4 ) 936–944 Available online at www.sciencedirect.com ScienceDirect jo ur nal ho me pag e: www.intl.elsevierhealth.com/journals/dema A method for calculating the compliance of bonded-interfaces under shrinkage: Validation for Class I cavities Flávia P. Rodrigues a,b,* , Raul G. Lima c , Antonio Muench d , David C. Watts e , Rafael Y. Ballester d a Department of Dental Materials and Prosthodontics, School of Dentistry, Institute of Science and Technology, UNESP – Univ Estadual Paulista, São José dos Campos, SP, Brazil b Biomaterials Unit, University of Birmingham, School of Dentistry, Birmingham, UK c Department of Mechanical Engineering, University of São Paulo, School of Engineering, São Paulo, SP, Brazil d Department of Biomaterials and Oral Biology, University of São Paulo, School of Dentistry, São Paulo, Brazil e University of Manchester, School of Dentistry and Photon Science Institute, Manchester, UK a r t i c l e i n f o Article history: Received 19 May 2014 Accepted 26 May 2014 Keywords: Compliance Finite element analysis Interface Shrinkage Class I cavities a b s t r a c t Objective. The compliance for tooth cavity preparations is not yet fully described in the lit- erature. 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 lin- ear, homogeneous, elastic and isotropic: (a) a pair of butt-joint bonded cubic prisms (dentin/resin-composite), with dentin of known compliance (0.0666 m/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 cal- culated. (c) A set of 3D-FE beam models, of 4 mm × 2 mm cross-section with lengths from 2 to 10 mm, were also analyzed under both tensile and bending modes. Results. The compliance calculated by FEM for the butt-joint prisms was 0.0652 m/N and corresponded well to the analytical value (0.0666 m/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. ∗ Corresponding author at: Av. Eng. Francisco José Longo, no. 777, Jardim São Dimas, 12245-000 São José dos Campos, SP, Brazil. Tel.: +55 12 3947 9000; fax: +55 12 3947 9010. E-mail addresses: F.Rodrigues@bham.ac.uk, flavia.rodrigues@ict.unesp.br, flapiro@gmail.com (F.P. Rodrigues) . http://dx.doi.org/10.1016/j.dental.2014.05.032 0109-5641/© 2014 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.