Abstract
Prediction of elastic moduli and some physical properties of heterogeneous media on the basis of known characteristics of constituents, their volumetric concentrations, shapes and orientation of inclusions and the type of lattice formed by the set of inclusions, is a developed area of the theory. This chapter is devoted to expansion of the theory to viscoelastic systems mostly made from viscoelastic polymeric matrices and elastic fillers. The method is based on elasto-viscoelastic analogy, in which the elastic moduli of constituents participating in the formulae for the effective moduli are replaced by corresponding integral operators of the theory of viscoelasticity. The next step is the decoding of the functions of operators, i.e. in replacing the expressions containing several operators by one equivalent operator with effective parameters. The difference between application of the theory to composites and nanocomposites is discussed. The prediction of elastic and viscoelastic behavior of composites and nanocomposites of geometrically similar structures is proposed. Prediction of the failure for composites and nanocomposites has to be done differently. Prediction of viscoelastic behavior is described for composites made from polymeric matrices and spherical, short cylindrical inclusions, platelets, hollow spherical and cylindrical inclusions, and spherical voids. Influence of stiffness ratio of matrix and inclusion on the effective properties is analyzed.