Numerical and analytical analyses for active fiber composite piezoelectric composite materials

This study consists of the calculation of the effective properties for active fiber composites made of either circular or square cross-section fibers not only by using finite element analysis and representative volume elements, but also based on the asymptotic homogenization method. Thus, there is an investigation about different approaches, which have specific mathematical formulations and unique characteristics. The comparison between numerical and analytical approaches shows that the numerical results are in good agreement with investigations performed by both analytical and semi-analytical methods, mainly the predictions for loading applied in fiber direction. For active fiber composites made of circular cross-section fibers, the maximum difference between asymptotic homogenization method and finite element analysis is from 1.29% to 5.49% for mechanical and piezoelectric effective properties, respectively, considering representative volume element in square arrangement. However, for active fiber composites made of square cross-section fibers, the maximum difference between semi-analytical method and finite element analysis is from 2.15% to 17.09% for mechanical and piezoelectric effective properties, respectively, considering representative volume element in square arrangement.