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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.
Berger et al. (Fri,) studied this question.