A finite element model of perforated panel absorbers including viscothermal effects

Most of the analytical models devoted to determine the acoustic properties of a rigid perforated panel consider the acoustic impedance of a single hole and then use the porosity to determine the impedance for the whole panel. However, in the case of not homogeneous hole distribution or more complex configurations this approach is no longer valid. This work explores some of these limitations and proposes a finite element methodology that implements the linearized Navier Stokes equations in the frequency domain to analyse the acoustic performance under normal incidence of perforated panel absorbers. Some preliminary results for a homogenous perforated panel show that the sound absorption coefficient derived from the Maa analytical model does not match those from the simulations. These differences are mainly attributed to the finite geometry effect and to the spatial distribution of the perforations for the numerical case. In order to confirm these statements, the acoustic field in the vicinities of the perforations is analysed for a more complex configuration of perforated panel. Additionally, experimental studies are carried out in an impedance tube for the same configuration and then compared to previous methods. The proposed methodology is shown to be in better agreement with the laboratorial measurements than the analytical approach.

Three-dimensional finite element analysis of the effects of anisotropy on bone mechanical properties measured by nanoindentation

A three-dimensional finite element analysis (FEA) model with elastic-plastic anisotropy was built to investigate the effects of anisotropy on nanoindentation measurements for cortical bone. The FEA model has demonstrated a capability to capture the cortical bone material response under the indentation process. By comparison with the contact area obtained from monitoring the contact profile in FEA simulations, the Oliver-Pharr method was found to underpredict or overpredict the contact area due to the effects of anisotropy. The amount of error (less than 10% for cortical bone) depended on the indentation orientation. The indentation modulus results obtained from FEA simulations at different surface orientations showed a trend similar to experimental results and were also similar to moduli calculated from a mathematical model. The Oliver-Pharr method has been shown to be useful for providing first-order approximations in the analysis of anisotropic mechanical properties of cortical bone, although the indentation modulus is influenced by anisotropy.

Weak form equation–based finite-element modeling of viscoelastic asphalt mixtures

The objective of this study is to demonstrate using weak form partial differential equation (PDE) method for a finite-element (FE) modeling of a new constitutive relation without the need of user subroutine programming. The viscoelastic asphalt mixtures were modeled by the weak form PDE-based FE method as the examples in the paper. A solid-like generalized Maxwell model was used to represent the deforming mechanism of a viscoelastic material, the constitutive relations of which were derived and implemented in the weak form PDE module of Comsol Multiphysics, a commercial FE program. The weak form PDE modeling of viscoelasticity was verified by comparing Comsol and Abaqus simulations, which employed the same loading configurations and material property inputs in virtual laboratory test simulations. Both produced identical results in terms of axial and radial strain responses. The weak form PDE modeling of viscoelasticity was further validated by comparing the weak form PDE predictions with real laboratory test results of six types of asphalt mixtures with two air void contents and three aging periods. The viscoelastic material properties such as the coefficients of a Prony series model for the relaxation modulus were obtained by converting from the master curves of dynamic modulus and phase angle. Strain responses of compressive creep tests at three temperatures and cyclic load tests were predicted using the weak form PDE modeling and found to be comparable with the measurements of the real laboratory tests. It was demonstrated that the weak form PDE-based FE modeling can serve as an efficient method to implement new constitutive models and can free engineers from user subroutine programming.

Dynamic multi-partitioning for parallel finite element applications

The central product of the DRAMA (Dynamic Re-Allocation of Meshes for parallel Finite Element Applications) project is a library comprising a variety of tools for dynamic re-partitioning of unstructured Finite Element (FE) applications. The input to the DRAMA library is the computational mesh, and corresponding costs, partitioned into sub-domains. The core library functions then perform a parallel computation of a mesh re-allocation that will re-balance the costs based on the DRAMA cost model. We discuss the basic features of this cost model, which allows a general approach to load identification, modelling and imbalance minimisation. Results from crash simulations are presented which show the necessity for multi-phase/multi-constraint partitioning components.

Characterisation and investigation of local variations in mechanical behaviour in cast aluminium using gradient solidification, Digital Image Correlation and finite element simulation

Due to design and process-related factors, there are local variations in the microstructure and mechanical behaviour of cast components. This work establishes a Digital Image Correlation (DIC) based method for characterisation and investigation of the effects of such local variations on the behaviour of a high pressure, die cast (HPDC) aluminium alloy. Plastic behaviour is studied using gradient solidified samples and characterisation models for the parameters of the Hollomon equation are developed, based on microstructural refinement. Samples with controlled microstructural variations are produced and the observed DIC strain field is compared with Finite Element Method (FEM) simulation results. The results show that the DIC based method can be applied to characterise local mechanical behaviour with high accuracy. The microstructural variations are observed to cause a redistribution of strain during tensile loading. This redistribution of strain can be predicted in the FEM simulation by incorporating local mechanical behaviour using the developed characterization model. A homogeneous FEM simulation is unable to predict the observed behaviour. The results motivate the application of a previously proposed simulation strategy, which is able to predict and incorporate local variations in mechanical behaviour into FEM simulations already in the design process for cast components.

A Trans-dimensional inversion algorithm to model deformation sources with unconstrained shape in finite element domains

Ground deformation provides valuable insights on subsurface processes with pattens reflecting the characteristics of the source at depth. In active volcanic sites displacements can be observed in unrest phases; therefore, a correct interpretation is essential to assess the hazard potential. Inverse modeling is employed to obtain quantitative estimates of parameters describing the source. However, despite the robustness of the available approaches, a realistic imaging of these reservoirs is still challenging. While analytical models return quick but simplistic results, assuming an isotropic and elastic crust, more sophisticated numerical models, accounting for the effects of topographic loads, crust inelasticity and structural discontinuities, require much higher computational effort and information about the crust rheology may be challenging to infer. All these approaches are based on a-priori source shape constraints, influencing the solution reliability. In this thesis, we present a new approach aimed at overcoming the aforementioned limitations, modeling sources free of a-priori shape constraints with the advantages of FEM simulations, but with a cost-efficient procedure. The source is represented as an assembly of elementary units, consisting in cubic elements of a regular FE mesh loaded with a unitary stress tensors. The surface response due to each of the six stress tensor components is computed and linearly combined to obtain the total displacement field. In this way, the source can assume potentially any shape. Our tests prove the equivalence of the deformation fields due to our assembly and that of corresponding cavities with uniform boundary pressure. Our ability to simulate pressurized cavities in a continuum domain permits to pre-compute surface responses, avoiding remeshing. A Bayesian trans-dimensional inversion algorithm implementing this strategy is developed. 3D Voronoi cells are used to sample the model domain, selecting the elementary units contributing to the source solution and those remaining inactive as part of the crust.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.

Photoelastic And Finite Element Analyses Of Occlusal Loads In Mandibular Body.

This study proposed to evaluate the mandibular biomechanics in the posterior dentition based on experimental and computational analyses. The analyses were performed on a model of human mandible, which was modeled by epoxy resin for photoelastic analysis and by computer-aided design for finite element analysis. To standardize the evaluation, specific areas were determined at the lateral surface of mandibular body. The photoelastic analysis was configured through a vertical load on the first upper molar and fixed support at the ramus of mandible. The same configuration was used in the computer simulation. Force magnitudes of 50, 100, 150, and 200 N were applied to evaluate the bone stress. The stress results presented similar distribution in both analyses, with the more intense stress being at retromolar area and oblique line and alveolar process at molar level. This study presented the similarity of results in the experimental and computational analyses and, thus, showed the high importance of morphology biomechanical characterization at posterior dentition.

Keratoconus prediction using a finite element model of the cornea with local biomechanical properties

PURPOSE: The ability to predict and understand which biomechanical properties of the cornea are responsible for the stability or progression of keratoconus may be an important clinical and surgical tool for the eye-care professional. We have developed a finite element model of the cornea, that tries to predicts keratoconus-like behavior and its evolution based on material properties of the corneal tissue. METHODS: Corneal material properties were modeled using bibliographic data and corneal topography was based on literature values from a schematic eye model. Commercial software was used to simulate mechanical and surface properties when the cornea was subject to different local parameters, such as elasticity. RESULTS: The simulation has shown that, depending on the corneal initial surface shape, changes in local material properties and also different intraocular pressures values induce a localized protuberance and increase in curvature when compared to the remaining portion of the cornea. CONCLUSIONS: This technique provides a quantitative and accurate approach to the problem of understanding the biomechanical nature of keratoconus. The implemented model has shown that changes in local material properties of the cornea and intraocular pressure are intrinsically related to keratoconus pathology and its shape/curvature.

Stress distribution in the cervical region of an upper central incisor in a 3D finite element model

The aim of this study was to evaluate the stress distribution in the cervical region of a sound upper central incisor in two clinical situations, standard and maximum masticatory forces, by means of a 3D model with the highest possible level of fidelity to the anatomic dimensions. Two models with 331,887 linear tetrahedral elements that represent a sound upper central incisor with periodontal ligament, cortical and trabecular bones were loaded at 45º in relation to the tooth's long axis. All structures were considered to be homogeneous and isotropic, with the exception of the enamel (anisotropic). A standard masticatory force (100 N) was simulated on one of the models, while on the other one a maximum masticatory force was simulated (235.9 N). The software used were: PATRAN for pre- and post-processing and Nastran for processing. In the cementoenamel junction area, tensile forces reached 14.7 MPa in the 100 N model, and 40.2 MPa in the 235.9 N model, exceeding the enamel's tensile strength (16.7 MPa). The fact that the stress concentration in the amelodentinal junction exceeded the enamel's tensile strength under simulated conditions of maximum masticatory force suggests the possibility of the occurrence of non-carious cervical lesions such as abfractions.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

Three-dimensional finite element thermal analysis of dental tissues irradiated with Er,Cr:YSGG laser

In the present study, a finite element model of a half-sectioned molar tooth was developed in order to understand the thermal behavior of dental hard tissues (both enamel and dentin) under laser irradiation. The model was validated by comparing it with an in vitro experiment where a sound molar tooth was irradiated by an Er,Cr:YSGG pulsed laser. The numerical tooth model was conceived to simulate the in vitro experiment, reproducing the dimensions and physical conditions of the typical molar sound tooth, considering laser energy absorption and calculating the heat transfer through the dental tissues in three dimensions. The numerical assay considered the same three laser energy densities at the same wavelength (2.79 mu m) used in the experiment. A thermographic camera was used to perform the in vitro experiment, in which an Er, Cr: YSGG laser (2.79 mu m) was used to irradiate tooth samples and the infrared images obtained were stored and analyzed. The temperature increments in both the finite element model and the in vitro experiment were compared. The distribution of temperature inside the tooth versus time plotted for two critical points showed a relatively good agreement between the results of the experiment and model. The three dimensional model allows one to understand how the heat propagates through the dentin and enamel and to relate the amount of energy applied, width of the laser pulses, and temperature inside the tooth. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2953526]

Aerodynamic study of three-dimensional larynx models using finite element methods

The airflow velocities and pressures are calculated from a three-dimensional model of the human larynx by using the finite element method. The laryngeal airflow is assumed to be incompressible, isothermal, steady, and created by fixed pressure drops. The influence of different laryngeal profiles (convergent, parallel, and divergent), glottal area, and dimensions of false vocal folds in the airflow are investigated. The results indicate that vertical and horizontal phase differences in the laryngeal tissue movements are influenced by the nonlinear pressure distribution across the glottal channel, and the glottal entrance shape influences the air pressure distribution inside the glottis. Additionally, the false vocal folds increase the glottal duct pressure drop by creating a new constricted channel in the larynx, and alter the airflow vortexes formed after the true vocal folds. (C) 2007 Elsevier Ltd. All rights reserved.

Finite element homogenization technique for the characterization of d(15) shear piezoelectric macro-fibre composites

A finite element homogenization method for a shear actuated d(15) macro-fibre composite (MFC) made of seven layers (Kapton, acrylic, electrode, piezoceramic fibre and epoxy composite, electrode, acrylic, Kapton) is proposed and used for the characterization of its effective material properties. The methodology is first validated for the MFC active layer only, made of piezoceramic fibre and epoxy, through comparison with previously published analytical results. Then, the methodology is applied to the seven-layer MFC. It is shown that the packaging reduces significantly the shear stiffness of the piezoceramic material and, thus, leads to significantly smaller effective electromechanical coupling coefficient k(15) and piezoelectric stress constant e(15) when compared to the piezoceramic fibre properties. However, it is found that the piezoelectric charge constant d(15) is less affected by the softer layers required by the MFC packaging.

Improved finite element for 3D laminate frame analysis including warping for any cross-section

The most ordinary finite element formulations for 3D frame analysis do not consider the warping of cross-sections as part of their kinematics. So the stiffness, regarding torsion, should be directly introduced by the user into the computational software and the bar is treated as it is working under no warping hypothesis. This approach does not give good results for general structural elements applied in engineering. Both displacement and stress calculation reveal sensible deficiencies for both linear and non-linear applications. For linear analysis, displacements can be corrected by assuming a stiffness that results in acceptable global displacements of the analyzed structure. However, the stress calculation will be far from reality. For nonlinear analysis the deficiencies are even worse. In the past forty years, some special structural matrix analysis and finite element formulations have been proposed in literature to include warping and the bending-torsion effects for 3D general frame analysis considering both linear and non-linear situations. In this work, using a kinematics improvement technique, the degree of freedom ""warping intensity"" is introduced following a new approach for 3D frame elements. This degree of freedom is associated with the warping basic mode, a geometric characteristic of the cross-section, It does not have a direct relation with the rate of twist rotation along the longitudinal axis, as in existent formulations. Moreover, a linear strain variation mode is provided for the geometric non-linear approach, for which complete 3D constitutive relation (Saint-Venant Kirchhoff) is adopted. The proposed technique allows the consideration of inhomogeneous cross-sections with any geometry. Various examples are shown to demonstrate the accuracy and applicability of the proposed formulation. (C) 2009 Elsevier Inc. All rights reserved.