BOUNDS AND ESTIMATES FOR THE OVERALL PLASTIC BEHAVIOR OF COMPOSITES WITH STRAIN GRADIENT EFFECTS

The macroscopic plastic response is estimated for a composite with eac h phase satisfying a strain gradient constitutive description. In a J( 2) deformation theory of strain gradient plasticity, the: strain energ y function is assumed to depend on both the von Mises strain invariant epsilon(e) and on a curvature invariant chi(e). For a general couplin g between epsilon(e) and chi(e), a nonlinear variational principle is formulated generalizing that of Ponte Castaneda (1992 J. Mech. Phys. S olids 40, 1757). The minimum principle is used to derive bounds and es timates for the overall plastic response of statistically homogeneous and isotropic strain gradient composites. An essential ingredient of t he strategy is the use of previous results of the authors (1994 J. Mec h. Phys. Solids 42, 1851) for a linear comparison composite. For a par ticular coupling between epsilon(e) and chi(e), Suggested earlier by F leck & Hutchinson (1993), the Hashin-Shtrikman upper bounds and lower estimates are calculated for a power-law hardening solid (including th e rigid-perfectly plastic limit). The results demonstrate a size effec t.