Elastic modulus of posts and the risk of root fracture Even though the techniques for restoring endodontically treated teeth were introduced several years ago, the procedure still remains a challenge in Dentistry (1–5). Additional difficulties arise as tooth structure is lost from the crown (6), since a direct restoration is unfeasible in such cases (2, 7), and intra-radicular posts are required to ensure retention of the indirect restoration (8). The worst possible failure in such cases is vertical root fracture (9), which is usually irreparable. A combination of factors can make the structure prone to fracture, and two are noteworthy: (i) the substantially decreased structural integrity of the tooth because of the removal of tooth structure during endodontic access, dowel- preparation, and cavity preparation (10); (ii) stress concentration on the dentin because of the design or high elastic modulus of the post (11, 12). The definition of an optimal elastic modulus for a post material is controversial. Some authors argue that the highest modulus material would be a better (13–17) fit for this situation while others propose the use of materials whose elastic modulus would match that of dentin (18–21). For a given geometry, the higher the modulus, the higher the stiffness. The stiffer post presents higher resistance to bending, therefore will go through less deformation when submitted to transversal loading (22). As a consequence, the root undergoes less strain as well, which reduces the risk of fracture. On the other hand, the stiffer post will have a more pronounced wedge effect (23), which increases the risk of fracture during longitudinal loading. The hypothesis of this study is that the effect of elastic modulus on stress concentration may be dependent on load direction. Therefore, the conflicting results found in the literature may be explained by differences in the set- ups used in each study. The objective of this work was to evaluate the effect of the elastic modulus of the post material on maximum principal stress (r max ) magnitude and direction using different loading directions, through finite element analysis. Method and material Nine three-dimensional models were built (Fig. 1), with 56440 hexahedrical elements (quad 8), in order to represent the root of a central incisor in the bone socket, restored with conical posts built with materials of three different elastic moduli (37, 100 and 200 GPa), sub- mitted to loads of 100 N applied in various directions (0°, 45° and 90°) in relation to the post’s long axis (Figs. 1 and 2). All structures simulated in the model were assumed to be isotropic, homogeneous and linear- elastic (elastic modulus and Poisson’s ratio given in Table 1). Perfectly bonded interfaces were assumed. Total restraining of the degrees of freedom was imposed on the nodes at the upper section. The programs MSC.Marc2005r2 (processing) and MSC/PATRAN2005r2 (pre- and postprocessing) were used. The magnitude of r max on dentin nodes in the A–D and E–H intervals of the plane section represented in Fig. 2 were compared, and the direction of the r max on the same planes were analyzed. Results Figure 3 represents r max values on the dentin as a function of the node position on the intervals A–D and Dental Traumatology 2009; 25: 394–398; doi: 10.1111/j.1600-9657.2009.00772.x 394 Ó 2009 The Authors. Journal compilation Ó 2009 John Wiley & Sons A/S Josete B. C. Meira, Camila O. M. Espo ´ sito, Mayra F. Z. Quitero, Isis A. V. P. Poiate, Carmem Silvia C. Pfeifer, Carina B. Tanaka, Rafael Y. Ballester Department of Dental Materials, School of Dentistry, University of Sa ˜o Paulo, Sa ˜o Paulo, Brazil Correspondence to: Josete Barbosa Cruz Meira, Department of Dental Materials, School of Dentistry, University of Sa ˜o Paulo, Av. Prof. Lineu Prestes, 2227 Sa ˜o Paulo, SP, Brazil, Zip code: 05508 000 Tel./Fax: +055 11 30917840 e-mail: jo@usp.br Accepted 14 November, 2008 Abstract – The definition of an optimal elastic modulus for a post is controversial. This work hypothesized that the influence of the posts’ elastic modulus on dentin stress concentration is dependent on the load direction. The objective was to evaluate, using finite element analysis, the maximum principal stress (r max ) on the root, using posts with different elastic modulus submitted to different loading directions. Nine 3D models were built, representing the dentin root, gutta-percha, a conical post and the cortical bone. The softwares used were: MSC.PATRAN2005r2 (preprocessing) and MSC.Marc2005r2 (process- ing). Load of 100 N was applied, varying the directions (0°, 45° and 90°) in relation to the post’s long axis. The magnitude and direction of the r max were recorded. At the 45° and 90° loading, the highest values of r max were recorded for the lowest modulus posts, on the cervical region, with a direction that suggests debonding of the post. For the 0° loading, the highest values of r max were recorded for higher modulus posts, on the apical region, and the circumferential direction suggests vertical root fracture. The hypothesis was accepted: the effect of the elastic modulus on the magnitude and direction of the r max generated on the root was dependent on the loading direction.