An analytical and numerical approach for calculating effective material coefficients of piezoelectric fiber composites

Abstract

The present work deals with the modeling of 1-3 periodic composites made of piezoceramic (PZT) fibers embedded in a soft non-piezoelectric matrix (polymer). We especially focus on predicting the effective coefficients of periodic transversely isotropic piezoelectric fiber composites using representative volume element method (unit cell method). In this paper the focus is on square arrangements of cylindrical fibers in the composite. Two ways for calculating the effective coefficients are presented, an analytical and a numerical approach. The analytical solution is based on the asymptotic homogenization method (AHM) and for the numerical approach the finite element method (FEM) is used. Special attention is given on definition of appropriate boundary conditions for the unit cell to ensure periodicity. With the two introduced methods the effective coefficients were calculated for different fiber volume fractions. Finally the results are compared and discussed.

Effective properties evaluation for smart composite materials

“…(2)) have been calculated for one specific fiber volume fraction, that is, 55.5%. The method is applied and the results are compared with analytical and numerical results available in the technical literature by Berger et al (2005) and Moreno et al (2009), respectively. The results are summarized in Table 2.…”

“…The material properties related to the epoxy resin (composite matrix) and piezoelectric fiber (PZT-5A) were taken from Berger et al (2005) and are shown in Table 1, according to orthotropic directions (coordinate system 1-2-3). For theses analyses presented, a fiber volume fraction of 55.5% for circular section, and also, for square section fiber was adopted and the fiber is oriented in direction 3.…”

“…These materials have been largely investigated during the last years. Piezoelectric materials (also denoted as PZT) have the property of converting electrical energy into mechanical energy, and vice versa (Berger et al, 2005). This capability allows applications as sensors or actuators in several industrial fields, for example: noise and vibration control, acoustic speakers, precision position control and structural health monitoring (SHM).…”

“…After that, the research of KarGupta and Venkatesh (2005, 2007aand 2007b have investigated the influence of fiber distribution in piezoelectric composites considering both fiber and matrix with piezoelectric properties. Berger et al (2005 and2006) have evaluated piezoelectric composites effective properties by comparing analytical and numerical techniques. Tan and Vu-Quoc (2005) have presented a solid-shell element formulation, only for displacement and electrical degrees of freedom, to model active composite structures considering large deformation and displacements.…”

Parametric analysis of effective material properties of thickness-shear piezoelectric macro-fibre composites

“…Some analytical methods from the composite materials literature, such as the Asymptotic Homogenization Method (AHM) (Benjeddou and Al-Ajmi, 2009;Otero et al, 2005) and the Uniform Field Method (UFM) (Bent and Hagood, 1997) can be applied to obtain the effective properties of the composite transducer active core from the properties of its components. Alternatively, one may use techniques based on finite element modelling of the composite transducer active core to identify its effective properties (Berger et al, 2005).…”