Elastoplastic constitutive relations for fiber-reinforced solids

In this paper, we make use of a procedure for estimating the effective properties of nonlinear composite materials, proposed recently by Ponte Castañeda (1991, J. Mech. Phys. Solids 39, 45-71), to study the effective constitutive behavior of ductile, fiber-reinforced composites. Both estimates and rigorous bounds are obtained for the effective energy functions of multiple-phase, fiber composites with general ductile behaviors (in the context of deformation theory of plasticity) for the isotropic constituent phases. The resulting expressions for the energy functions may be differentiated in a straightforward manner to obtain corresponding estimates for the anisotropic effective stress-strain relations. Explicit calculations are carried out for the case of an aluminum-matrix composite reinforced with boron fibers. The results reveal some interesting features distinguishing the constitutive behavior of ductile-matrix, fiber-reinforced composites from that of linear-elastic, fiber-reinforced composites. One such feature is the strong coupling between the dilatational and distortional modes for the ductile fiber composites. Finally, comparisons are made with available experimental data.