Finite element unit cell predictions of the entire overall elastic, piezoelectric, and dielectric behavior of 1-3 composites

Abstract
A comprehensive unit cell model was employed for studying composites with continuous piezoelastic fibers embedded in a dielectric matrix by means of the finite element method. The aim was to predict the full set of material moduli, i.e. to determine the complete tensors associated with the overall elastic, dielectric, and piezoelectric behavior. So, the linear response to any mechanical and electrical load, or any combination of both, will be determined. In addition to the capability of predicting the complete set of overall composite properties, the local fields as response to arbitrary overall loads can be obtained with high resolution. Due to the coupling of normal and shear behavior a 3/D slice model was employed. The presentedunit cell model is an extension of the widely used standard models, but it relieves their limitations to some specific loading modes. Since the deformations along a boundary between two corners are not known a priori, the boundary conditions must allow for the adjustment to the deformation in an appropriate manner. Special care has to be taken to avoid over- or under-constraining. Comparisons of the predictions by the present approach to theoretical bounds from the literature for the effective piezoelastic behavior were carried out comprehensively. It was shown, that all results obtained by the present model comply with the given bounds. Circular as well as square shaped fibers in various arrangements were investigated and the effect on the overall behavior was discussed. Comparing the overall properties of the composite to the properties of a monolithic piezo-material one can observe that some coupling moduli are at least one order of magnitude lower for the composite. In such cases the compliant matrix accommodates almost all overall strains and the fibers experience low strains so that the piezoelectric effect does not act in a pronounced manner. A high value was found for the overall piezoelectric modulus in fiber direction because the continuous fibers are forced to carry the overall strain. Finally, predictions by the present model were compared to experimental results from the literature, which complied very well.