We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing 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) proposed by Buryachenko (2010a, 2010b) is implemented. This equation is obtained by a centering procedure without any auxiliary assumptions such as, e.g., 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. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.

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