Internal residual stresses in elastically homogeneous solids: I. Statistically homogeneous stress fluctuations

We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a homogeneous and statistically uniform random set of ellipsoidal inclusions. The elastic properties of the matrix and the inclusions are the same, but the stress-free strains are di€erent. One obtains the estimation of n-degree moments of stresses averaged over the components. A relation for the statistical stress moments in the matrix in the vicinity of an individual inclusion is also derived. Furthermore one estimates an in¯uence of the fractional composition of the inclusions on the inhomogeneous nature of stress moments inside the inclusions. The expression for the correlation function of stresses is also derived.