Abstract
The method proposed by the authors in their earlier paper on thermal conductivity has been utilized to estimate the effective elastic constants and the coefficient of thermal expansion of a statistically isotropic heterogeneous medium. The method considers the inclusion geometry in the lower-order correlation functions, that is, those of order two and less. The upper and lower bounds and the improvements on these bounds have been derived for the elastic constants. Expressions containing the two-point correlation functions are also derived for the coefficient of thermal expansion and the related stress tensor. The theoretical values are compared with the experimental results and the comparison can be considered satisfactory in view of the difficulty in obtaining perfectly isotropic distribution experimentally and the sensitivity of the final properties to mild anisotropy when the difference in the constituent properties is large as in the case of Araldite and copper. The theoretical results for the aluminium-copper system show that convergence of the bounds is extremely good when properties of the constituents are of the same order.
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