Rogério José Marczak

Three-dimensional FEA of effects of two dowel-and-core approaches and effects of canal flaring on stress distribution in endodontically treated teeth.

PURPOSE The aim of this 3D finite element analysis (FEA) was to assess stress distribution and levels in endodontically treated teeth restored with two dowel-and-core systems with differing root canal configurations. MATERIALS AND METHODS Four 3D finite element models of a laser-digitalized maxillary central incisor embedded in alveolar bone were created. Internal morphology data and mechanical properties of the materials were obtained from the literature. Models included a (1) sound tooth (control) versus an endodontically treated maxillary central incisor with a crown ferrule preparation with two restorative approaches of a ceramic crown over a (2) gold alloy dowel-and-core or (3) glass-fiber dowels with composite cores (4) the latter with a flared root canal. A 100 N static load was applied in the center of the palatal surface at a 45° angle, and the stress distribution pattern was analyzed using ANSYS(®) software. RESULTS In Model 1 (control), maximum stresses occurred at the coronal third of the buccal (2.32 × 10(7) Pa) and palatal aspects of dentin. The stress peak value of the model (2.45 × 10(7) Pa) occurred on the palatal aspect of the enamel at the level of the cementoenamel junction. With the insertion of dowels with thin cement layers (Models 2 and 3), stress concentrations in radicular dentin decreased, while they increased in the dowel/cement/dentin interface. These models exhibited the greatest stress peak values in the incisal margin of the gold alloy core (18.9 × 10(7) Pa) and in the cement layer (4.7 × 10(7) Pa). In Model 4, stress peak value was observed in the porcelain crown (4.62 × 10(7) Pa), and there was no stress concentration inside the cement layer. CONCLUSIONS Within the limits of this study, the results suggest that the use of dowels and cements with mechanical properties similar to those of dentin, and an increased cement layer thickness, results in mechanical behavior similar to the physiological behavior of a sound tooth.

Direct evaluation of singular integrals in boundary element analysis of thick plates

Abstract This work presents the derivation of the asymptotic expansions for two dimensional elasticity and plate bending problems fundamental solutions, applied to the direct evaluation of BEM singular integrals. Interesting conclusions arise from the resulting analytical expressions, regarding the actual order of singularity of the kernel functions. The expansions were tested for a number of plate bending benchmarks, showing good agreement to analytical solutions for thin and thick plates. The convergence behavior for constant, linear and quadratic elements is analyzed and compared with other integration techniques.

Object-oriented numerical integration: a template scheme for FEM and BEM applications

An object-oriented numerical integration template implementation is presented on the basis of the C++ programming language. Aiming its straightforward application in finite and boundary element methods, the design supports integrand objects of scalar, vector or matrix types, so that a single programming statement is able to integrate element matrices and vectors. The integrand can contain singularities like the ones typically found in boundary element methods, allowing the evaluation of both regular and singular integrals under the same programming structure. The use of the proposed design is illustrated through some elementary applications as well as finite element and boundary element code excerpts.

Stresses in implant-supported overdentures with bone resorption: a 3-D finite element analysis

bone resorption of the distal ridge. Acknowledgments Supported by CAPES/Brazilian Ministry of Education. We would like to thank Mr. Maico Thiessen Souza for his technical assistance in the development of all solid models. The geometric models of implants and abutments were mounted at the canine region to build the reference model 1 with absence of bone resorption or bone loss. To build the test models the mandible geometric solid was modified to simulate 2mm vertical bone loss surrounding the implants (model 2) and model 2 + resorption of the distal ridge (model 3).

Effective properties of materials with random micro-cavities using special boundary elements

In this work, a general boundary element procedure is proposed to obtain the effective elastic tensor of solids containing randomly distributed micro-cavities in terms of its primary elastic properties. The average-field theory and a special boundary element formulation are combined to carry out a statistical analysis on the numerical results obtained for a Representative Volume Element (RVE). The two-dimensional isotropic material is simulated as a homogeneous matrix containing cylindrical holes. In the proposed implementation each hole boundary is modeled with a single boundary element. The average variables of the micro-field are evaluated using boundary-only data, which leads to a formulation particularly suitable for Boundary Element Methods. Expressions for effective elastic properties as a function of the micro-fields for both isotropic and transversally isotropic hypothesis are derived. Finally, the methodology is illustrated with some application examples and the results are compared with analytical and experimental results.

Characterization of Constitutive Parameters for Hyperelastic Models Considering the Baker-Ericksen Inequalities

Hyperelastic models are used to simulate the mechanical behavior of rubber-like materials ranging from elastomers, such as natural rubber and silicon, to biologic materials, such as muscles and skin tissue. Once the desired hyperelastic model has its parameters fitted to the available experimental results, these hyperelastic parameters have to fulfill the requirements imposed by the Baker-Ericksen inequalities in order to guarantee a plausible physical behavior to the material, although seldom used. When applied to an incompressible isotropic hyperelastic model, these inequalities state that the first derivative of the strain energy density function with respect to the first strain invariant must be positive and the first derivative of the strain energy density function with respect to the second strain invariant must be non-negative. The aim of this work is to study which improvements the requirement of the Baker-Ericksen inequalities can bring when fitting hyperelastic models to experimental data. This is accomplished through a constrained optimization procedure. Results obtained for natural rubber and silicon samples considering classical and newly developed hyperelastic models are shown and discussed.

Simulating occupant injury in rollover crashes. Part 1: a numerical comparison of design procedures for vehicle roof strength assessment

Among all types of vehicle accidents, rollover crashes are the most complex and least understood. During the last decades, a constant increase in the number of studies involving rollover crashes and injuries associated with it can be observed. The existing experimental standards and procedures to test rollover crashworthiness are still not suitable for direct computer simulation because of the huge computational effort required, and the need of faithful/overly complex representation of the aspects involved in actual crashes. Yet, numerical simulation plays a key role in keeping the design cost low and in delivering reliable structural predictions. The objective of the present work is to show a numerical methodology adapted to simulate three different procedures commonly used to assess vehicle roof strength. The models refer to commercial versions of a compact car and a sport utility vehicle. Results for roof crushing, normal ground force as well as other variables are compared, and the advantages/disadvantages of each standard are discussed and criticised. It was verified that one of the most used design procedures is not representative of realistic rollover phenomena, further supporting a recent change in it.

A new pseudo-energy function to simulate the Mullins effect

Several authors have proposed different parameters to include the softening effect in hyperelastic models; however, for a number of materials, softening parameters could be further improved. This article proposes a new softening parameter to include Mullins effect in hyperelastic material models. The methodology employed can be also used in cases with hysteresis or damage in a hyperelastic material, however this methodology modifies the behavior of the material differently from damage theories. Common hyperelastic constitutive models do not include dissipation effects and so the present work intends to fill this gap. Experimental data for silicone in uniaxial tensile test, equibiaxial, and pure shear tests were modeled in order to calibrate the models. The softening parameters essentially changes the constitutive law from the loading to the unloading path. Therefore, it is still necessary to use a hyperelastic model, and here Ogden and Hoss-Marczak material models were used. The obtained results show good agreement with experimental data even when simulating with a compressible finite element code and it can model isotropic Mullins effect.

Bending analysis of a wire strand analytic model

An analytical approach, using the spatial beam theory, to determine the mechanical response of cables is proposed in this work. Experimental results are limited and expensive to be obtained and there is a lack of good benchmarks solutions to check the FEM models before starting complex analysis. Therefore, in order to obtain the results the parametric spatial description were derived for one strand, considering one wire surrounding a core, since the response of all wires are similar. Solving the differential equilibrium equations of the spatial beam theory and applying bending loads it was possible to obtain the mechanical response of the wire. Six loading cases were analyzed for the wire helix analytically and numerically. Good results were obtained when the both methodologies were compared for the cable bending.

Revisiting Some Developments of Boundary Elements for Thick Plates in Brazil

This work reviews the developments of Boundary Element Method formulations to solve several types of plate bending problems, including non-linear bending. The formulation is developed and solved using the standard BEM procedure, and different integration approaches were discussed and tested. Object oriented implementation issues are commented. Results were obtained for linear and non-linear elastic bending as well as buckling of selected cases of thick plates, including cases of step variation in thickness under large displacements regime.