Random Structure Matrix Composites in a Half-Space
At first, in the present chapter, the general methods of estimation of both the stress concentrator factors and nonlocal effective operators will be presented for the matrix composites with an arbitrary elastic and thermal mismatch of constituents in a half-space. At the end of the chapter following , a generalization of the method of integral equations  (see Section 14.3) is proposed for the estimation of the first and second moments of random residual microstresses in the constituents of elastically homogeneous composites in a half-space with a free edge. Explicit relations for these statistical moments are obtained taking the binary interactions of the inclusions into account which are expressed through the numerical solution for one inclusion in the half-space. The statistical averages of stress fluctuations varying along the inclusion cross sections are completely defined by the random locations of surrounding inclusions. The numerical results are presented for a half-plane containing a random distribution of circular identical inclusions modeling a random array of aligned quantum wires parallel to a free surface. The solution for one inclusion is obtained in .
KeywordsResidual Stress Integral Operator Free Edge Binary Interaction Thermoelastic Property
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