Micromechanical finite element analysis of effective properties of a unidirectional short piezoelectric fiber reinforced composite

A micromechanical finite element analysis of effective properties of a unidirectional short piezoelectric fiber reinforced composite is presented. The identical short piezoelectric fibers in the composite lamina are coaxial, equally spaced and aligned in the plane of lamina. A continuum micromechanics approach is utilized for predicting the effective electro-elastic material coefficients through the evaluation of Hill’s volume average electro-elastic coupled field concentration matrices. An electro-elastic finite element model of unit cell and the corresponding appropriate electro-elastic boundary conditions are presented for numerical evaluation of concentration matrices. The finite element based micromechanics model and the imposed boundary conditions are verified through the evaluation of effective coefficients of an existing unidirectional continuous piezoelectric fiber reinforced composite. The numerical illustrations reveal an improved effective piezoelectric coefficient over that of the fiber counterpart. It is found that the increase in the length ratio between a fiber and the corresponding unit cell not only causes improved piezoelectric coefficients but also makes the cross sectional area ratio (Ar) between the same components as an important parameter for material coefficients. The optimal length and the optimal cross sectional Ar for improved effective piezoelectric coefficients at a specified fiber volume fraction are presented. The effect of fiber aspect ratio on the effective piezoelectric coefficients is also presented that reveals an upper limit of increasing fiber aspect ratio in order to achieve maximum possible improvement in the magnitude of an effective coefficient.