Application of Mathematical Modeling to Determine the Thermoelastic Characteristics of Nano-Reinforced Composites

Abstract

A two-level mathematical model is constructed to describe the thermomechanical interaction between structural elements of a composite (nanoclusters formed by randomly distributed anisotropic single-walled carbon nanotubes and matrix particles) and an isotropic medium possessing the desired thermoelastic characteristics. This model was first employed to obtain the thermoelastic properties of a nanocluster by the self-consistency method and then the same technique was used to describe the thermomechanical interaction of nanoclusters with an isotropic matrix of the composite. A comparative analysis of the calculated dependences for the elastic moduli of the composite and its thermal coefficient of linear expansion was carried out with two-sided estimates of these characteristics based on the dual variational formulation of the thermoelasticity problem. For comparison, the results of a numerical experiment are also used. The presented relationships make it possible to predict the thermoelastic properties of promising composites reinforced by nanoclusters.