An analytical and numerical approach for calculating effective material coefficients of piezoelectric fiber composites (original) (raw)
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Composite Structures, 2005
Numerical unit cell models for 1-3 periodic composites made of piezoceramic unidirectional cylindrical fibers embedded in a soft nonpiezoelectric matrix are developed. The unit cell is used for prediction of the effective coefficients of the periodic transversely isotropic piezoelectric cylindrical fiber composite. Special emphasis is placed on the formulation of the boundary conditions that allows the simulation of all modes of overall deformation arising from any arbitrary combination of mechanical and electrical loading. The numerical approach is based on the finite element method (FEM) and it allows the extension to composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective properties. For verification the effective coefficients are evaluated for square and hexagonal arrangements of unidirectional piezoelectric cylindrical fiber composites. The results obtained from the numerical technique are compared with those obtained by means of the analytical asymptotic homogenization method (AHM) for different fiber volume fractions.
Smart Materials and Structures, 2006
Numerical unit cell models of 1-3 periodic composites made of piezoceramic unidirectional cylindrical fibers embedded in a soft non-piezoelectric matrix are developed. The unit cell is used for prediction of the effective coefficients of the periodic transversely isotropic piezoelectric cylindrical fiber composite. Special emphasis is placed on a formulation of the boundary conditions that allows the simulation of all modes of the overall deformation arising from any arbitrary combination of mechanical and electrical loading. The numerical approach is based on the finite element method and it allows extension to composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective properties. For verification, the effective coefficients are evaluated for square and hexagonal arrangements of unidirectional piezoelectric cylindrical fiber composites. The results obtained from the numerical technique are compared with those obtained by means of the analytical asymptotic homogenization method for different volume fractions. Furthermore, the results are compared with other analytical and numerical methods reported in the literature.
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2005
This work deals with the modelling of periodic composites made of piezoceramic (lead zirconate-titanat) fibres embedded in a soft nonpiezoelectric matrix (polymer). The goal is to predict the effective coefficients of such periodic transversely isotropic piezoelectric fibre composites by use of a representative volume element or unit cell. The solution is based on a numerical approach using finite element method (FEM). The necessary basic equations for the piezoelectric material are introduced and the special concept for definition of generalised periodic boundary conditions for the unit cell is explained. For a composite with square arrangements of cylindrical fibres the algorithm is demonstrated and the extension to other fibre arrangements is shown. For different fibre volume fractions the results are compared with analytical solutions.
Numerical representative volume element (RVE) models using ANSYS® finite element package are developed for 1–3 periodic composites made of piezoelectric (PZT) fibers embedded in a soft non-piezoelectric matrix (polymer matrix). The RVE method is used to predict the effective electromechanical coefficients of the periodic transversely isotropic piezoelectric cylindrical fiber composite. Special emphasis is placed on the formulation of the boundary conditions that allows the simulation of all modes of overall deformation arising from any arbitrary combination of mechanical and electrical loading. This numerical approach allows the extension to composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective coefficients. The effective coefficients for hexagonal arrangements of unidirectional piezoelectric cylindrical fiber composites are evaluated for different fiber volume fractions. Then, for verification the homogeniz...
Materials which exhibit piezoelectric behavior generate an electrical field in response to a mechanical deformation or alternatively undergo a mechanical deformation in response to an applied electrical field. This work presents the development of unit cell numerical models of 1-3 periodic composites, with piezoelectric fibers made of PZT embedded in a non-piezoelectric matrix. The common approach for estimating the macro-mechanical properties of 3D piezoelectric fiber composites is carried out by the unit cell approach, also called a representative volume element (RVE), which captures the major features of the underlying micro-structure. The main idea of this method consisting on evaluating a globally homogeneous medium equivalent to the original composite, where the strain energies stored in the two systems are approximately the same, with special emphasis placed on the formulation of suitable boundary conditions. The boundary conditions allow the simulation of all modes of the ov...
2009 Brazilian Symposium on …, 2009
Piezoelectric fiber composites have several potential applications in aerospace industry due the high level design requirements that can be provided for this kind of material in applications such as structure health monitoring, precision positioning and vibration control or suppression. Difficulties in fiber manufacturing techniques and behavior prediction are the main obstacles to the practical implementation of this technology. In this work one procedure for determining effective properties of one ply made of unidirectional fibers from individual properties of the constituent materials and composite characteristics is presented and discussed. The procedure is based in the modeling of a Representative Volume Element (RVE) or a unit cell by finite element method. The RVE is analyzed under several loading and boundary conditions in order to evaluate of the effective material coefficients (elastic, dielectric end piezoelectric). The results are discussed and compared with analytical and numerical results presented by other researchers.
Different numerical unit cells models using ANSYS® finite element package are developed for unidirectional periodic composites made of piezoelectric (PZT) fibers embedded in a soft non-piezoelectric matrix. These finite element models are used for prediction of the effective electromechanical coefficients of the periodic transversely isotropic piezoelectric cylindrical fiber composite. Special emphasis is placed on the formulation of the boundary conditions that allows the simulation of all modes of overall deformation arising from any arbitrary combination of mechanical and electrical loading. These numerical models providing a powerful tools for fast calculation of the effective electromechanical properties of 1-3 piezocomposites with arbitrary geometrical inclusion configurations. The developed models has been applied to unidirectional piezoelectric fiber composites with periodic hexagonal arrangement of piezoelectric fibers. The effective coefficients of elastic stiffness, piezo...
Numerical and analytical analyses for active fiber composite piezoelectric composite materials
Journal of Intelligent Material Systems and Structures, 2014
This work consists of the calculation of the effective properties for Active Fiber Composites (AFCs) made of either circular or square cross-section fibers not only by using Finite Element Analysis (FEA) and Representative Volume Elements (RVE), but also based on Asymptotic Homogenization Method (AHM). Thus, there is an investigation about different approaches, which have specific mathematical formulations and unique characteristics. The comparison between numerical and analytical approaches shows that the numerical results are in good agreement with investigations performed by both analytical and semi-analytical methods (SAM), mainly the predictions for loading applied in fiber direction. For AFC made of circular cross-section fibers, the maximum difference between AHM and FEA is from 1.29% to 5.49% for mechanical and piezoelectric effective properties, respectively, considering RVE in square arrangement. However, for AFC made of square cross-section fibers, the maximum difference between SAM and FEA is from 2.15% to 17.09% for mechanical and piezoelectric effective properties, respectively, considering RVE in square arrangement.
Electromechanical properties of continuous fibre-reinforced piezoelectric composites
Mechanics of Composite Materials, 1997
A composite material with unidirectional cylindrical ®bers periodically distributed is considered here, where each periodic cell is a binary homogeneous piezoelectric medium with square symmetry in welded contact at the interface. This paper makes use of some results obtained for a similar elastic composite in Rodr õguez-Ramos et al. [Mech. Mater. 33 (2001) 223±235]. Relatively simple closed-form expressions for the overall properties are obtained by the asymptotic homogenization method. The local problems that arise are solved by means of potentials methods of a complex variable and Weierstrass elliptic and related functions. Benveniste and Dvorak universal type of relations for some of the overall properties are derived in a simple new way without solving any local problem. The number of local problems to get all coecients is 3. The numerical computation of the eective properties is simple. Averaged properties of these piezocomposites relevant to hydrostatic and medical imaging transducer applications are computed and compared with existing experimental results. The comparison shows quite a good agreement with experimental data. Ó
Investigation of the effective response of 2-1-2 piezoelectric composites
The question of the effective response of two-phase hybrid "fibrous-laminate" piezoelectric composites, with periodic microstructure, is adressed with two homogenization approaches: a full-field numerical scheme based on Fourier transform and a simplifying approach relying on a decoupled two-step homogenisation process. In the case of a two-phase epoxy/PZT composite, this latter is shown to overestimate out-of-plane effective piezoelectric coefficients. (C) 2012 Published by Elsevier B.V. Selection and/or peer review under responsibility of Dr. Oana Cazacu.