BOUNDS AND ESTIMATES FOR LINEAR COMPOSITES WITH STRAIN GRADIENT EFFECTS

Overall mechanical properties are studied for linear composites demons trating a size effect. Variational principles of Hashin-Shtrikman type are formulated for incompressible composites involving the gradient o f strain in their constitutive description. These variational principl es are applied to linear, statistically homogeneous and isotropic two- phase composites. Upper and lower bounds of Hashin-Shtrikman type for the effective shear modulus and related self-consistent estimates are derived in terms of volume fraction and a two-point correlation functi on accounting for the scale of microstructure. An alternative self-con sistent scheme for matrix-inclusion strain-gradient composites is also proposed by a development of the approach laid down by Budiansky and Hill. Some numerical results are given to demonstrate the size effect.