Rodrigo Guerra Peixoto

Non-local constitutive modelling by the boundary element method

Rodrigo G. Peixoto Samuel S. Penna Gabriel O. Ribeiro Roque L. S. Pitangueira rodrigo.peixoto@dees.ufmg.br spenna@dees.ufmg.br gabriel@dees.ufmg.br roque@dees.ufmg.br Dep. de Eng. de Estruturas, Escola de Engenharia, Universidade Federal de Minas Gerais Avenida Antônio Carlos, 6627, CEP: 31270-901, Belo Horizonte, Minas Gerais, Brazil Abstract. The conventional (local) constitutive modelling of materials exhibiting strain softening behaviour is suceptive to a spurious mesh dependence caused by numerically induced strain localization. Also, for very refined meshes, numerical instabilities may be verified, mainly if the simulations are performed by the boundary element method. An alternative to overcome such difficulties is the adoption of the so called non-local constitutive models. In this approach, some internal variables of the constitutive model in a single point are averaged considering its values of the neighbouring points. In this paper, the implicit formulation of the boundary element method for physically non linear problems is used with non-local isotropic damage models. It is shown that the analysis become more stable in comparison to the case of a local application of the same models and that the results recover the desired objectiveness to mesh refinement.

The dependence of step size in the continuum strong discontinuity approach using the boundary element method

Abstract. The failure analysis in structures is extremely important since it allows to evaluate the safety degree and the integrity of structural systems. However, despite the increasing use of numerical methods in the study of material failures in the last years, the boundary element method is still little used when compared to domain methods. Thus, in this work it is analyzed the failure mechanics in some classical problems through the continuum strong discontinuity approach. In this way, it is used the implicit formulation of the boundary element method for nonlinear problems to shown the dependence of the step size when the cells with embedded discontinuity are generated only after step convergence or during any iteration, respectively, in the incremental-iterative process. For this purpose, the same problem was analyzed considering these two cases and also different numbers of steps. It was verified that the results are coincident for all numbers of steps considered in the simulations when cells are generated during any iteration, showing step size independence in this case, while the same is not true for the case of cells generated only after convergence, in which a large numbers of steps is required for well accuracy.

Residual Stresses and Cracking in Dental Restorations due to Resin Contraction Considering In-Depth Young's Modulus Variation

Composite resins have been increasingly used as restorative material, both in anterior and posterior teeth, where they replace metal restorations. Its aesthetic characteristics, coupled with improved physical properties have made their use extend from just anterior teeth to also include posterior teeth. The use of such material in oral regions subjected to higher loading makes it important to account for the effect of residual stresses arising during polymerization, induced by resin contraction (Ausiello, Apicilla and Davidson 2002). Different reports can be found in the literature focused in this aspect and using different approaches, such as X-ray micro-computed tomography (Sun, Eidelman and Gibson 2009), 3D evaluation of the marginal adaptation (Kakaboura et al 2007) and 3 D deformation analysis from MCT images (Chiang et al 2010). These authors agree in the critical role played by resin contraction in restoration success. The Finite Element Method can therefore be a useful tool to investigate the cracking of interfaces, stress concentrations in the internal angles and effects of variations in the mechanical properties in the overall behavior of the resin-based dental restorations.