Effective high-pressure compressibility of multiscale cracked media

The effective elastic modulus of a two-scale medium with random elastic mod uli of its phases is calculated. Using the diagram technique of Feynman. no nlocal averaged integrodifferential equations describing the volume deforma tions in this medium are derived. The kernel of the integral equation is ob tained as a sum of a diagram series (more specifically, as a decomposition of the exact average Green function of the non-local elasticity equation. l ocal elasticity equation). A similar method is applied to the estimation of neutron free paths in elastic scattering by density fluctuations in unorde red media. The pressure dependence of the effective nonlocal elastic moduli is determined.