Closed-form expressions for the effective coefficients of a fibre-reinforced composite with transversely isotropic constituents. II: Piezoelectric and hexagonal symmetry. (English) Zbl 1017.74056

Summary: The purpose is to determine effective elastic, piezoelectric and dielectric properties of reinforced piezoelectric composite materials with unidirectional cylindrical fibres periodically distributed in two directions at an angle \(\pi/3\) by means of asymptotic homogenization method. Each periodic cell of the medium is a binary piezoelectric composite, wherein both constituents are homogeneous piezoelectric materials with transversely isotropic properties. This paper makes use of some results obtained in part I [see the foregoing entry]. Simple closed-form expressions for overall properties are obtained by means of potential method of complex variable and Weierstrass elliptic and related functions. Schulgasser-type universal relations are derived in a new way by means of homogenized asymptotic method.


74Q15 Effective constitutive equations in solid mechanics
74E30 Composite and mixture properties
74F15 Electromagnetic effects in solid mechanics
74E10 Anisotropy in solid mechanics
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