Matrix laminate composites: Realizable approximations for the effective moduli of piezoelectric dispersions
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Matrix laminate composites: Realizable approximations for the effective moduli of piezoelectric dispersions L. V. Gibiansky and S. Torquato Department of Civil Engineering and Operations Research and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544 (Received 26 November 1997; accepted 16 March 1998)
This paper is concerned with the effective piezoelectric moduli of a special class of dispersions called matrix laminates composites that are known to possess extremal elastic and dielectric moduli. It is assumed that the matrix material is an isotropic dielectric, and the inclusions and composites are transversely isotropic piezoelectrics that share the same axis of symmetry. The exact expressions for the effective coefficients of such structures are obtained. They can be used to approximate the effective properties of any transversely isotropic dispersion. The advantages of our approximations are that they are (i) realizable, i.e., correspond to specific microstructures; (ii) analytical and easy to compute even in nondegenerate cases; (iii) valid for the entire range of phase volume fractions; and (iv) characterized by two free parameters that allow one to “tune” the approximation and describe a variety of microstructures. The new approximations are compared with known ones.
I. INTRODUCTION
Piezoelectric composite materials are important for many applications such as acoustic hydrophones, transducers, and actuators. They are especially useful because composite structures offer the opportunity for enhancement of piezoelectric performance characteristics compared to the pure piezoelectric ceramic. Often composites are the only materials capable of achieving a desired combination of properties, such as high compliance, low density, acoustic impedance matching impedance of water, and high performance characteristics. Experiments for specific polymer/ceramic systems show1–3 that composites with high sensitivity can be achieved by combining oriented piezoceramic rods and a soft polymer matrix. Using simple models in which the elastic and electric fields were taken to be uniform in the different phases, Haun and Newnham,4 Chan and Unsworth,5 and Smith6,7 qualitatively explained the enhancement due to Poisson’s ratio effect. Rigorous prediction of the effective properties of piezoelectric-polymer composites is a technologically important but difficult problem. The effective properties are quite sensitive to the details of the microstructure due to the high contrast in the properties of the stiff piezoelectric phase with high dielectric constant, and a soft polymer with low dielectric constant. A number of approximations have been developed to describe effective elastic and dielectric properties of composites, including the self-consistent, differential, and Mori–Tanaka schemes. Such approximations are based on the solution of the elastic and dielectric problems for a single inclusion (usually ellipsoidal) embedded in an infinite matrix subject to
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