Multiscale Mechanics of Nonlocal Effects in Microheterogeneous Materials

We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing either deterministic (periodic and non-periodic) or random (statistically homogeneous and inhomogeneous, so-called graded) field of inclusions. For functionally graded materials when the concentration of the inclusions is a function of the coordinates, the rnicromechanical approach is based on the generalization of the "multiparticle effective field" method, previously proposed for statistically homogeneous random structure composites by the author (see for references and details Buryachenko, Appl. Mech. Reviews 2001, 54, 1-47). Both the Fourier transform method and iteration method are analyzed. The nonlocal integral and differential effective operators of elastic effective properties are estimated. The nonlocal dependencies of the effective elastic moduli as well as of conditional averages of the strains in the components on the concentration of the inclusions in a certain neighborhood of point considered are detected; the scale effect is discovered. The proposed theory provides the bridging of length scales which is a paramount factor in understanding and controlling material microinhomogeneity at the microscale and interpreting them at the macroscale. The combined coupled concept of introducing both the integral and differential operator linking microscale and macroscale enables one to address two issues simultaneously.