A comprehensive numerical homogenisation technique for calculating effective coefficients of uniaxial piezoelectric fibre composites

This work deals with the modelling of periodic composites made of piezoceramic (lead zirconate-titanat) fibres embedded in a soft non-piezoelectric matrix (polymer). The goal is to predict the effective coefficients of such periodic transversely isotropic piezoelectric fibre composites by use of a representative volume element or unit cell. The solution is based on a numerical approach using finite element method (FEM). The necessary basic equations for the piezoelectric material are introduced and the special concept for definition of generalised periodic boundary conditions for the unit cell is explained. For a composite with square arrangements of cylindrical fibres the algorithm is demonstrated and the extension to other fibre arrangements is shown. For different fibre volume fractions the results are compared with analytical solutions.