Effective thermoelastic properties of random structure composites reinforced by the clusters of deterministic structure (application to clay nanocomposites) V. A. Buryachenko, Dayton, Ohio, V. I. Kushch, Kiev, Ukraine, and A. Roy, WPAFB, Ohio Received July 20, 2006 Published online: January 9, 2007 Ó Springer-Verlag 2007 Summary. Polymer/clay nanocomposites consisting of an epoxy matrix reinforced by silicate clay plates have been observed to exhibit enhanced mechanical properties at low volume fraction of clay. The matrix and embedded nanoelements are modeled in the framework of continuum mechanics with known mechanical properties previously evaluated by, e.g., molecular dynamic simulation. Nanoclay composite is modeled by the aligned, uniformly distributed in the matrix stacks of parallel clay sheets separated from one another by interlayer matrix galleries of nanometer scale. Interaction of a finite number of oblate spheroidal inclusions modeling an individual stack inside the infinite matrix is carried by the multipole expansion technique. The obtained accurate numerical solution was incorporated into the multiparticle effective field method [5] for the estimation of effective thermoelastic properties. Detailed parametric analyses demonstrate the influence on the effective elastic moduli and stress concentrator factors of such key factors as the shape of nanoelements, interlayer distance, and the number of nanoelements in the stacks of deterministic structure. 1 Introduction A considerable number of methods are known in the linear theory of statistically homogeneous composites; appropriate, but by no means exhaustive, references are provided by the reviews [1]–[7]. It appears today that variants of a self-consistent (or effective medium) method [8] and the mean field method [9], [10] are the most popular and widely used methods. The notion of an effective field in which each particle is located is a basic concept of such powerful methods in micromechanics as the methods of self-consistent fields and effective fields (see for references [5]). The ‘‘quasicrystalline’’ approximation by Lax [11] is often used for truncation of the hierarchy of the involved integral equations leading to neglect of direct multiparticle interac- tions of inclusions. The last deficiency was overcome recently by the multiparticle effective field method (MEFM), put forward and developed by one of the authors (references may be found in the survey [5]). We will analyze in this paper a special sort of clustered materials which are polymeric composites reinforced with clay crystals of nanometer scale which recently attracted tremen- dous attention in the material society (see, e.g., [12] where additional references can be found). Completely exfoliated nanocomposites were intensively analyzed in the framework of Acta Mechanica 192, 135–167 (2007) DOI 10.1007/s00707-006-0421-9 Printed in The Netherlands Acta Mechanica