Abstract: A progressive micromechanical method is presented in order to predict the elastic constants of polydispersed composites including multi-directional or randomly oriented reinforcement particles. Heterogeneities of various types are introduced into the matrices in a gradual manner. At each step, the Mori-Tanaka method is used to obtain the stiffness tensor of the intermediate medium used as a matrix of the following step. The proposed method is capable of introducing any kind of heterogeneities based on their dimensions, orientations, mechanical properties, and volume fractions to the matrix. Furthermore, suitable probability density functions can be defined for physical and structural parameters of the composite, including the level of the filler-matrix interfacial bonding, the aspect ratio, and the orientation of reinforcement particles. The efficiency of the iterative approach and the convergence of the solution are studied by computing the stiffness tensors of unidirectional and bidirectional particulate composites. The results of the present study are also compared with the literature data for a randomly oriented particulate composite.

Key words: polydispersed composite, progressive homogenization, micromechanical modeling, nonlocal elastic stress, nanomechanics, bending, nanobeam, nanoscale, effective nonlocal bending moment, strain gradient