Numerical analysis of different methods to calculate residual stresses in thin films based on instrumented indentation data

In this work, different methods to estimate the value of thin film residual stresses using instrumented indentation data were analyzed. This study considered procedures proposed in the literature, as well as a modification on one of these methods and a new approach based on the effect of residual stress on the value of hardness calculated via the Oliver and Pharr method. The analysis of these methods was centered on an axisymmetric two-dimensional finite element model, which was developed to simulate instrumented indentation testing of thin ceramic films deposited onto hard steel substrates. Simulations were conducted varying the level of film residual stress, film strain hardening exponent, film yield strength, and film Poisson's ratio. Different ratios of maximum penetration depth h(max) over film thickness t were also considered, including h/t = 0.04, for which the contribution of the substrate in the mechanical response of the system is not significant. Residual stresses were then calculated following the procedures mentioned above and compared with the values used as input in the numerical simulations. In general, results indicate the difference that each method provides with respect to the input values depends on the conditions studied. The method by Suresh and Giannakopoulos consistently overestimated the values when stresses were compressive. The method provided by Wang et al. has shown less dependence on h/t than the others.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Finite element analysis of stress distribution in anchor teeth in surgically assisted rapid palatal expansion

The treatment of a transverse maxillary deficiency in skeletally mature individuals should include surgically assisted rapid palatal expansion. This study evaluated the distribution of stresses that affect the expander's anchor teeth using finite element analysis when the osteotomy is varied. Five virtual models were built and the surgically assisted rapid palatal expansion was simulated. Results showed tension on the lingual face of the teeth and alveolar bone, and compression on the buccal side of the alveolar bone. The subtotal Le Fort I osteotomy combined with intermaxillary suture osteotomy seemed to reduce the dissipation of tensions. Therefore, subtotal Le Fort I osteotomy without a step in the zygomaticomaxillary buttress, combined with intermaxillary suture osteotomy and pterygomaxillary disjunction may be the osteotomy of choice to reduce tensions on anchor teeth, which tend to move mesiobuccally (premolar) and distobuccally (molar)

Morse taper implants at different bone levels: a finite element analysis of stress distribution

AIM: To explore the biomechanical effects of the different implantation bone levels of Morse taper implants, employing a finite element analysis (FEA). METHODS: Dental implants (TitamaxCM) with 4x13 mm and 4x11 mm, and their respective abutments with 3.5 mm height, simulating a screwed premolar metal-ceramic crown, had their design performed using the software AnsysWorkbench 10.0. They were positioned in bone blocks, covered by 2.5 mm thickness of mucosa. The cortical bone was designed with 1.5 mm thickness and the trabecular bone completed the bone block. Four groups were formed: group 11CBL (11 mm implant length on cortical bone level), group 11TBL (11 mm implant length on trabecular bone level), group 13CBL (13mm implant length on cortical bone level) and group 13TBL (13 mm implant length on trabecular bone level). Oblique 200 N loads were applied. Von Mises equivalent stresses in cortical and trabecular bones were evaluated with the same design program. RESULTS: The results were shown qualitatively and quantitatively by standard scales for each type of bone. By the results obtained, it can be suggested that positioning the implant completely in trabecular bone brings harm with respect to the generated stresses. Its implantation in the cortical bone has advantages with respect to better anchoring and locking, reflecting a better dissipation of the stresses along the implant/bone interfaces. In addition, the search for anchoring the implant in its apical region in cortical bone is of great value to improve stabilization and consequently better stress distribution. CONCLUSIONS: The implant position slightly below the bone in relation to the bone crest brings advantages as the best long-term predictability with respect to the expected neck bone loss.

Effect of parametric uncertainties on the performance of a piezoelectric energy harvesting device

The use of piezoelectric materials for the development of electromechanical devices for the harvesting or scavenging of ambient vibrations has been extensively studied over the last decade. The energy conversion from mechanical (vibratory) to electrical energy is provided by the electromechanical coupling between mechanical strains/stresses and electric charges/voltages in the piezoelectric material. The majority of the studies found in the open literature present a tip-mass cantilever piezoelectric device tuned on the operating frequency. Although recent results show that these devices can be quite effective for harvesting small amounts of electrical energy, little has been published on the robustness of these devices or on the effect of parametric uncertainties on the energy harvested. This work focuses on a cantilever plate with bonded piezoelectric patches and a tip-mass serving as an energy harvesting device. The rectifier and storage electric circuit was replaced by a resistive circuit (R). In addition, an alternative to improve the harvesting performance by adding an inductance in series to the harvesting circuit, thus leading to a resonant circuit (RL), is considered. A coupled finite element model leading to mechanical (displacements) and electrical (charges at electrodes) degrees of freedom is considered. An analysis of the effect of parametric uncertainties of the device on the electric output is performed. Piezoelectric and dielectric constants of the piezoelectric active layers and electric circuit equivalent inductance are considered as stochastic parameters. Mean and confidence intervals of the electric output are evaluated.

Numerical Model for the Dynamic Analysis of Pile Foundations

Programa de doctorado: Sistemas Inteligentes y Aplicaciones Numéricas en Ingeniería Instituto Universitario (SIANI)

Three-dimensional finite element modelling of stack pollutant emissions

[EN]In this paper we propose a finite element method approach for modelling the air quality in a local scale over complex terrain. The area of interest is up to tens of kilometres and it includes pollutant sources. The proposed methodology involves the generation of an adaptive tetrahedral mesh, the computation of an ambient wind field, the inclusion of the plume rise effect in the wind field, and the simulation of transport and reaction of pollutants. The methodology is used to simulate a fictitious pollution episode in La Palma island (Canary Island, Spain)…

The meccano method for finite element and isogeometric analysis

Congresos y conferencias

Local scale finite element modelling of stack pollutant emissions

Congresos y conferencias

Application of genetic algorithms for the calibration of an air quality model and its validation using pollutant measures from the surroundings of an electric power plant

[EN]This work presents the calibration and validation of an air quality finite element model applied to emissions from a thermal power plant located in Gran Canaria. The calibration is performed using genetic algorithms. To calibrate and validate the model, the authors use empirical measures of pollutants concentrations from 4 stations located nearby the power plant; an hourly record per station during 3 days is available. Measures from 3 stations will be used to calibrate, while validation will use measures from the remaining station…