Random residual stresses in elasticity homogeneous medium with inclusions of noncanonical shape

We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of noncanonical inclusions. The elastic properties of the matrix and the inclusions are the same, but the stress-free strains are different. The new general volume integral equation (VIE) is proposed. These equations are obtained by a centering procedure without any auxiliary assumptions such as the effective field hypothesis implicitly exploited in the known centering methods. The results of this abandonment are quantitatively estimated for some modeled composite with homogeneous fibers of nonellipsoidal shape. New effects are detected that are impossible within the framework of a classical background of micromechanics.