Equivalent inclusion method for the work-hardening behavior of piezoelectric composites

The work-hardening behavior of piezoelectric composites is investigated by utilizing the variational principle and the equivalent inclusion method. When the matrix of a piezoelectric composite subjected to a uniaxial tension is perfectly plastic and the piezoelectric inhomogeneities are elastic, the linear work-hardening rate is predicted. In particular, when both the matrix and the inhomogeneities of the piezoelectric material are transversely isotropic with different electroelastic moduli, and shapes of the inhomogeneities are elliptical, ribbon-like, rod-shaped and penny-shaped, the yielding stress and the work-hardening rate are obtained in closed forms. The results show that the work-hardening rate is proportional to the volume fraction of the inhomogeneities. Moreover, it is found that the work-hardening rate and the yielding stress are dependent on the shape and the volume fraction of the inhomogeneities but are independent on the size of the inhomogeneities.