Identification of Elastic, Dielectric, and Piezoelectric Constants in Piezoceramic Disks

Three-dimensional modeling of piezoelectric devices requires a precise knowledge of piezoelectric material parameters. The commonly used piezoelectric materials belong to the 6mm symmetry class, which have ten independent constants. In this work, a methodology to obtain precise material constants over a wide frequency band through finite element analysis of a piezoceramic disk is presented. Given an experimental electrical impedance curve and a first estimate for the piezoelectric material properties, the objective is to find the material properties that minimize the difference between the electrical impedance calculated by the finite element method and that obtained experimentally by an electrical impedance analyzer. The methodology consists of four basic steps: experimental measurement, identification of vibration modes and their sensitivity to material constants, a preliminary identification algorithm, and final refinement of the material constants using an optimization algorithm. The application of the methodology is exemplified using a hard lead zirconate titanate piezoceramic. The same methodology is applied to a soft piezoceramic. The errors in the identification of each parameter are statistically estimated in both cases, and are less than 0.6% for elastic constants, and less than 6.3% for dielectric and piezoelectric constants.

Thermal/mechanical simulation and laboratory fatigue testing of an alternative yttria tetragonal zirconia polycrystal core-veneer all-ceramic layered crown design

This study evaluated the stress levels at the core layer and the veneer layer of zirconia crowns (comprising an alternative core design vs. a standard core design) under mechanical/thermal simulation, and subjected simulated models to laboratory mouth-motion fatigue. The dimensions of a mandibular first molar were imported into computer-aided design (CAD) software and a tooth preparation was modeled. A crown was designed using the space between the original tooth and the prepared tooth. The alternative core presented an additional lingual shoulder that lowered the veneer bulk of the cusps. Finite element analyses evaluated the residual maximum principal stresses fields at the core and veneer of both designs under loading and when cooled from 900 degrees C to 25 degrees C. Crowns were fabricated and mouth-motion fatigued, generating master Weibull curves and reliability data. Thermal modeling showed low residual stress fields throughout the bulk of the cusps for both groups. Mechanical simulation depicted a shift in stress levels to the core of the alternative design compared with the standard design. Significantly higher reliability was found for the alternative core. Regardless of the alternative configuration, thermal and mechanical computer simulations showed stress in the alternative core design comparable and higher to that of the standard configuration, respectively. Such a mechanical scenario probably led to the higher reliability of the alternative design under fatigue.

Influence of specimens' design and manufacturing process on microtensile bond strength to enamel: laboratory and FEA comparison

This study evaluated the effect of specimens' design and manufacturing process on microtensile bond strength, internal stress distributions (Finite Element Analysis - FEA) and specimens' integrity by means of Scanning Electron Microscopy (SEM) and Laser Scanning Confocal Microscopy (LCM). Excite was applied to flat enamel surface and a resin composite build-ups were made incrementally with 1-mm increments of Tetric Ceram. Teeth were cut using a diamond disc or a diamond wire, obtaining 0.8 mm² stick-shaped specimens, or were shaped with a Micro Specimen Former, obtaining dumbbell-shaped specimens (n = 10). Samples were randomly selected for SEM and LCM analysis. Remaining samples underwent microtensile test, and results were analyzed with ANOVA and Tukey test. FEA dumbbell-shaped model resulted in a more homogeneous stress distribution. Nonetheless, they failed under lower bond strengths (21.83 ± 5.44 MPa)c than stick-shaped specimens (sectioned with wire: 42.93 ± 4.77 MPaª; sectioned with disc: 36.62 ± 3.63 MPa b), due to geometric irregularities related to manufacturing process, as noted in microscopic analyzes. It could be concluded that stick-shaped, nontrimmed specimens, sectioned with diamond wire, are preferred for enamel specimens as they can be prepared in a less destructive, easier, and more precise way.

A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.

Parametric model for the analysis of concrete expansion due to alkali-aggregate reaction

The alkali-aggregate reaction (AAR) is a chemical reaction that provokes a heterogeneous expansion of concrete and reduces important properties such as Young's modulus, leading to a reduction in the structure's useful life. In this study, a parametric model is employed to determine the spatial distribution of the concrete expansion, combining normalized factors that influence the reaction through an AAR expansion law. Optimization techniques were employed to adjust the numerical results and observations in a real structure. A three-dimensional version of the model has been implemented in a finite element commercial package (ANSYS(C)) and verified in the analysis of an accelerated mortar test. Comparisons were made between two AAR mathematical descriptions for the mechanical phenomenon, using the same methodology, and an expansion curve obtained from experiment. Some parametric studies are also presented. The numerical results compared very well with the experimental data validating the proposed method.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

Importance of considering a material micro-failure criterion in the numerical modelling of the shot peening process applied to parabolic leaf springs

Shot peening is a cold-working mechanical process in which a shot stream is propelled against a component surface. Its purpose is to introduce compressive residual stresses on component surfaces for increasing the fatigue resistance. This process is widely applied in springs due to the cyclical loads requirements. This paper presents a numerical modelling of shot peening process using the finite element method. The results are compared with experimental measurements of the residual stresses, obtained by the X-rays diffraction technique, in leaf springs submitted to this process. Furthermore, the results are compared with empirical and numerical correlations developed by other authors.

The role of crystalline anisotropy in mechanical property extractions through Berkovich indentation

This work uses crystal plasticity finite element simulations to elucidate the role of elastoplastic anisotropy in instrumented indentation P-h(s) curve measurements in face-centered Cubic (fcc) crystals. It is shown that although the experimental fluctuations in the loading stage of the P-h(s) curves can be attributed to anisotropy, the variability in the unloading stage of the experiments Is much greater than that resulting from anisotropy alone. Moreover, it is found that the conventional procedure used to evaluate the contact variables ruling the unloading P-h(s) curve introduces all uncertainty that approximates to the more fundamental influence of anisotropy. In view of these results, a robust procedure is proposed that uses contact area measurements in addition to the P-h(s) curves to extract homogenized J(2)-Plasticity-equivalent mechanical properties from single crystals.

Effective Electromechanical Coupling Coefficients of Piezoelectric Adaptive Structures: Critical Evaluation and Optimization

This work presents a critical analysis of methodologies to evaluate the effective (or generalized) electromechanical coupling coefficient (EMCC) for structures with piezoelectric elements. First, a review of several existing methodologies to evaluate material and effective EMCC is presented. To illustrate the methodologies, a comparison is made between numerical, analytical and experimental results for two simple structures: a cantilever beam with bonded extension piezoelectric patches and a simply-supported sandwich beam with an embedded shear piezoceramic. An analysis of the electric charge cancelation effect on the effective EMCC observed in long piezoelectric patches is performed. It confirms the importance of reinforcing the electrodes equipotentiality condition in the finite element model. Its results indicate also that smaller (segmented) and independent piezoelectric patches could be more interesting for energy conversion efficiency. Then, parametric analyses and optimization are performed for a cantilever sandwich beam with several embedded shear piezoceramic patches. Results indicate that to fully benefit from the higher material coupling of shear piezoceramic patches, attention must be paid to the configuration design so that the shear strains in the patches are maximized. In particular, effective square EMCC values higher than 1% were obtained embedding nine well-spaced short piezoceramic patches in an aluminum/foam/aluminum sandwich beam.

Failure analysis of low velocity impact on thin composite laminates: Experimental and numerical approaches

The dynamic behavior of composite laminates is very complex because there are many concurrent phenomena during composite laminate failure under impact load. Fiber breakage, delaminations, matrix cracking, plastic deformations due to contact and large displacements are some effects which should be considered when a structure made from composite material is impacted by a foreign object. Thus, an investigation of the low velocity impact on laminated composite thin disks of epoxy resin reinforced by carbon fiber is presented. The influence of stacking sequence and energy impact was investigated using load-time histories, displacement-time histories and energy-time histories as well as images from NDE. Indentation tests results were compared to dynamic results, verifying the inertia effects when thin composite laminate was impacted by foreign object with low velocity. Finite element analysis (FEA) was developed, using Hill`s model and material models implemented by UMAT (User Material Subroutine) into software ABAQUS (TM), in order to simulate the failure mechanisms under indentation tests. (C) 2007 Elsevier Ltd. All rights reserved.

Refined sandwich model for the vibration of beams with embedded shear piezoelectric actuators and sensors

This work extends a previously presented refined sandwich beam finite element (FE) model to vibration analysis, including dynamic piezoelectric actuation and sensing. The mechanical model is a refinement of the classical sandwich theory (CST), for which the core is modelled with a third-order shear deformation theory (TSDT). The FE model is developed considering, through the beam length, electrically: constant voltage for piezoelectric layers and quadratic third-order variable of the electric potential in the core, while meclianically: linear axial displacement, quadratic bending rotation of the core and cubic transverse displacement of the sandwich beam. Despite the refinement of mechanical and electric behaviours of the piezoelectric core, the model leads to the same number of degrees of freedom as the previous CST one due to a two-step static condensation of the internal dof (bending rotation and core electric potential third-order variable). The results obtained with the proposed FE model are compared to available numerical, analytical and experimental ones. Results confirm that the TSDT and the induced cubic electric potential yield an extra stiffness to the sandwich beam. (C) 2007 Elsevier Ltd. All rights reserved.

Experimental analysis of active-passive vibration control using viscoelastic materials and extension and shear piezoelectric actuators

Hybrid active-passive damping treatments combine the reliability, low cost and robustness of viscoelastic damping treatments and the high-performance, modal selective and adaptive piezoelectric active control. Numerous hybrid damping treatments have been reported in the literature. They differ mainly by the relative positions of viscoelastic treatments, sensors and piezoelectric actuators. In this work we present an experimental analysis of three active-passive damping design configurations applied to a cantilever beam. In particular, two design configurations based on the extension mode of piezoelectric actuators combined with viscoelastic constrained layer damping treatments and one design configuration with shear piezoelectric actuators embedded in a sandwich beam with viscoelastic core are analyzed. For comparison purposes, a purely active design configuration with an extension piezoelectric actuator bonded to an elastic beam is also analyzed. The active-passive damping performance of the four design configurations is compared. Results show that active-passive design configurations provide more reliable and wider-range damping performance than the purely active configuration.

A Study on the Relationship of Embedded Sensitivity With Measuring Grid and Mode Shapes

Embedded sensitivity analysis has proven to be a useful tool in finding optimum positions of structure reinforcements. However, it was not clear how sensitivities obtained from the embedded sensitivity method were related to the normal mode, or operational mode, associated to the frequency of interest. In this work, this relationship is studied based on a finite element of a slender sheet metal piece, with preponderant bending modes. It is shown that higher sensitivities always occur at nodes or antinodes of the vibrating system. [DOI: 10.1115/1.4002127]

Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

Chaos-Galerkin solution of stochastic Timoshenko bending problems

This paper presents an accurate and efficient solution for the random transverse and angular displacement fields of uncertain Timoshenko beams. Approximate, numerical solutions are obtained using the Galerkin method and chaos polynomials. The Chaos-Galerkin scheme is constructed by respecting the theoretical conditions for existence and uniqueness of the solution. Numerical results show fast convergence to the exact solution, at excellent accuracies. The developed Chaos-Galerkin scheme accurately approximates the complete cumulative distribution function of the displacement responses. The Chaos-Galerkin scheme developed herein is a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2011 Elsevier Ltd. All rights reserved.