Julián Bravo-Castillero

Unit cell models of piezoelectric fiber composites for numerical and analytical calculation of effective properties

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.

Overall properties of piezocomposite materials 1-3

Abstract The purpose of this paper is to present analytical expressions of the effective constants of reinforced piezoelectric composite materials with periodically distributed unidirectional cylindrical fibers for transducer applications. Each periodic cell of the medium is a binary piezoelectric composite wherein both constituents are homogeneous piezoelectric materials with hexagonal symmetry. The general formulae obtained allow the prediction of global properties of an important class of piezocomposites. Numerical calculations show an adequate concordance with other theoretical models. In the analysis, the periodicity of the structure is assumed to be much smaller than the elastic wavelength. Finally, we apply these results to a 1–3 material and obtain new piezocomposites with better global properties for biomedical imaging and hydrophone applications.

CLOSED-FORM THERMOELASTIC MODULI OF A PERIODIC THREE-PHASE FIBER-REINFORCED COMPOSITE

ABSTRACT In previous works, using the asymptotic homogenization method (AHM), analytical formulae have been obtained for all global elastic constants of a binary fiber composite with perfect interfaces. In many cases of interest the perfect interphase is not an adequate model and it is necessary to include in the analytical models one or more interphases separating the reinforcement inclusion phase from the host matrix phase. In this article, an extension of AHM to thermoelastic heterogeneous problems is given. A simple closed form of effective properties for a three-phase unidirectional transversely isotropic composite is presented. By using homogenization schemes for periodic media, the local problems are solved and effective thermoelastic properties moduli are determined. The method is based on the assumption that the scale ratio between the periodic cell and the whole composite tends to zero. New universal relations for the three-phase thermoelastic composite are found from the AHM. In order to analyze the interphase effect, the effective thermoelastic moduli are compared with some theoretical approaches and experimental results reported in the literature.

Asymptotic homogenization of periodic thermo-magneto-electro-elastic heterogeneous media

The asymptotic homogenization method is applied to a family of boundary value problems for linear thermo-magneto-electro-elastic (TMEE) heterogeneous media with periodic and rapidly oscillating coefficients. Using a matrix notation, the procedure for constructing the formal asymptotic solution is described. Two ways to validate the asymptotic analysis are explained. The main differences/similarities with respect to the asymptotic homogenization models reported in recent papers are remarked. The analytical expressions for effective coefficients of laminated media with any finite number of anisotropic TMEE layers are explicitly obtained via the matrix notation. Such formulae can be applied to investigate the global behavior of functionally graded TMEE multilayers. The important case of bilaminates composites with anisotropic homogeneous phases is also expressed in a compact form using matrices and vectors depending on the individual geometrical and mechanical properties of the components. The case of a bilaminate with homogeneous transversely isotropic TMEE layers is studied. A chain of equalities relating all thermal (thermoelastic, pyroelectric, pyromagnetic and heat capacity) effective coefficients was found for the example corresponding to a parallel connectivity. An analytical formula to estimate the volume fraction for which the pyroelectric and pyromagnetic effects realize their extreme values is given. Comparisons with recently published results are included.

Modeling of elastic transversely isotropic composite using the asymptotic homogenization method. Some comparisons with other models

The objective of this paper is to apply the asymptotic homogenization method (AHM) to determine the analytical formulae for the elastic effective coefficients of a two-phase fibrous composite provided with a periodic structure. In the analysis, the periodicity of the structure is assumed to be much smaller than the elastic wavelength. The fibres are aligned unidirectional with respect to the x3-axis. The constituents are transversely isotropic materials. The results are used to determine numerically the linear elastic behavior of two types of fibre composites. Some comparisons with different experimental results and theoretical models are shown. D 2002 Elsevier Science B.V. All rights reserved.

EFFECTIVE COEFFICIENTS FOR TWO PHASE MAGNETO-ELECTROELASTIC FIBROUS COMPOSITE WITH SQUARE SYMMETRY CELL IN-PLANE MECHANICAL DISPLACEMENT AND OUT-OF-PLANE ELECTRIC AND MAGNETIC FIELD CASE

ABSTRACT The purpose of the present work is to determine the magneto-electroelastic effective properties of reinforced piezoelectric composite materials with unidirectional cylindrical fibers periodically distributed in a square array through the Asymptotic Homogenization Method (AHM). The case when mechanical displacement is in-plane and electric and magnetic fields are out-of-plane is studied. Each periodic cell of the medium is a binary composite wherein both constituents are homogeneous magneto-electroelastic materials with transversely isotropic properties. Closed-form expressions for the overall properties are obtained. Numerical calculations are carried out for the BaTiO3/CoFe2O4 composite. A good match is obtained between AHM and other calculations reported in the literature. These results may be considered as congruent with the experimental experience.

Interfacial waves between two piezoelectric half-spaces with electro- mechanical imperfect interface

We study the propagation of shear horizontal waves between the interface of two piezoelectric materials with an electro-mechanical imperfect contact. Mechanical and electrical imperfections are modeled by means of a spring and a capacitor, respectively. The corresponding mathematical expressions for the imperfect contact are given in this article. The system of differential equations for the waves in the considered half-space is derived and the associate solutions are found. A general expression for the dispersion relation, not reported previously in the literature, is given in an explicit form, with the diverse limit cases analyzed in detail. In some of these limit cases, new expressions are also obtained, which predict the existence of interfacial waves. In the other cases, where already reported results exist, a comparison with them is done. Some physical interpretations are derived from the limit cases. The influence of mechanical and electrical imperfect contacts are shown in some numerical examples.

Plane Magneto-Electro-Elastic Moduli of Fiber Composites with Interphase

In the present article, using the asymptotic homogenization method (AHM), the derivation of the plane effective properties for three-phase magneto-electro elastic fiber unidirectional reinforced composite with hexagonal and square cell symmetry is reported. Closed form of the analytical expressions and universal relations for the effective coefficients are given. Matrix and inclusion materials belong to symmetry class 6mm [1] (the number of independent components are five elastic, three piezoelectric, two dielectric, three piezomagnetic, and two magnetic). Numerical calculations for all plane effective properties are done. Some comparisons with other theoretical models are presented.

Modeling of Three-Phase Fibrous Composite Using the Asymptotic Homogenization Method

A three-phase concentric fiber-reinforced periodic composite is considered wherein the constituents exhibit piezoelectric properties. The cross-section of the periodic cell is a regular hexagon with two concentric circles and the periodicity is the same in two directions at an angle ~ /3. Simple closed-form expressions are obtained for the effective properties of this composite by means of the asymptotic homogenization method. Numerical computations have been done. The analytical solution of the required resulting plane- and antiplane-strain local problems, which turns out to be only two, makes use of potential methods of a complex variable and properties of Weierstrass elliptic and related functions of periods (1,0) and (cos ~ /3, sin ~ /3). Benvenistes universal type of relations for this composite are satisfied. Comparison with other models is shown.

Numerical and analytical analyses for active fiber composite piezoelectric composite materials

This study consists of the calculation of the effective properties for active fiber composites made of either circular or square cross-section fibers not only by using finite element analysis and representative volume elements, but also based on the asymptotic homogenization method. 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, mainly the predictions for loading applied in fiber direction. For active fiber composites made of circular cross-section fibers, the maximum difference between asymptotic homogenization method and finite element analysis is from 1.29% to 5.49% for mechanical and piezoelectric effective properties, respectively, considering representative volume element in square arrangement. However, for active fiber composites made of square cross-section fibers, the maximum difference between semi-analytical method and finite element analysis is from 2.15% to 17.09% for mechanical and piezoelectric effective properties, respectively, considering representative volume element in square arrangement.