Multiparticle interactions in composites
The version of the effective field method considered in Chapter 7 allows us to solve the homogenization problem and to calculate effective elastic and thermoelastic properties of matrix composites with various types of inclusions. But for composites with spherical inclusions that are much harder than the matrix, the predictions of the method deviate essentially from experimental data and results of numerical simulations when the volume concentration of the inclusions exceeds 0.4. The reason for this discrepancy is that the hypotheses of the EFM do not conform to the actual distribution of elastic fields in composites with high volume concentrations of inclusions. In order to correct the predictions of the EFM, its hypotheses should be changed. In this chapter we develop a modification of the EFM accounting for multiparticle interactions between inclusions. This modification allows us to improve the predictions of the method, to calculate higher statistical moments of physical fields in composites, and to describe nonlocal connections between the mean stress and strain fields in regions where these fields change rapidly.
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