Inclusion method in the work-hardening behavior of transversely isotropic composites

This study presents the work-hardening behavior of fibrous composite materials in uniaxial tension for embracing the variational principle and the equivalent inclusion method. The linear work-hardening rate is forecast with the composite matrix perfectly plastic and the fibers (inhomogeneities) plastically nondeforming. Notably, when both the matrix and inhomogeneities are transversely isotropic with different elastic moduli, the yielding stress and the work-hardening rate are obtained in closed forms with the shapes of the inhomogeneities being elliptical, ribbon-like, rod-shaped, and penny-shaped. The results of the study show that the work-hardening rate is proportional to the volume fraction of the inhomogeneities. Meanwhile, the work-hardening rate and the yielding stress are dependent on the shape and the volume fraction of the inhomogeneities but not on the size of the inhomogeneities.