Composite plasticity based on matrix average second order stress moment

An effective stress of a ductile matrix is defined directly from the average second order stress moment. It is evaluated exactly provided that an estimation of the composite effective moduli is given. On the basis of this effective stress and the secant moduli concept originally proposed by Berveiller and Zaoui (Berveiller, M. and Zaoui, A. (1979). An extension of the self-consistent scheme to plastically-flowing polycrystals. J. Mech. Phys. Solids 35, 325-344) and modified for composite materials by Tandon and Weng (Tandon, G. P. and Weng, G. J. (1988). A theory of particle reinforced plasticity. ASME J. Appl. Mech. 55, 126-135), a method for composite plasticity is then proposed. The method is capable of predicting the influence of hydrostatic stress on particle-reinforced composite yielding, especially for porous materials at high triaxiality. Compared to Tandon and Weng's model, the proposed method gives always softer predictions. For particle reinforced composites, the new matrix average effective stress coincides with that obtained by Ponte Castaneda's variational procedure (Ponte Castaneda, P. (1991). The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids 39, 45-71).