Abstract
A simple explicit result is introduced for the effective shear modulus of a random isotropic suspension of rigid n-spheres (n=3,2), each having identical size, firmly embedded in an isotropic incompressible elastic matrix. By construction, the result is in quantitative agreement with all the classical rigorous asymptotic results in the dilute (c↘0) and percolation (c↗pn) limits, as well as with new computational results for intermediate values c∈[0,pn] of the volume fraction of n-spheres. Moreover, as demonstrated by means of iterated homogenization, the proposed result has the added merit of being realizable by a certain class of random isotropic suspension of rigid n-spheres with infinitely many sizes. That the proposed result is descriptive of both isotropic suspensions with monodisperse and with (a specially selected class of) polydisperse rigid n-spheres is nothing more than a manifestation of the richness in behaviors that suspensions of polydisperse rigid n-spheres can exhibit.
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