Application of mathematical modeling to obtaining thermoelastic characteristics of composite materials reinforced with nanostructure inclusions

Two-level mathematical model describing the thermo-mechanical interaction of the elements of the composite structure (nanoclusters formed from randomly assigned anisotropic single-walled carbon nanotubes and the matrix particles) with an isotropic medium with thermoelastic characteristics was built. This model was used for the first time for the self-consistent method of thermo-elastic properties of nanoclusters and then the same method was used to describe the thermo-mechanical interaction of nanoclusters with an isotropic matrix composite. A comparative analysis of the received dependencies for the composite modulus of elasticity and the coefficient of linear thermal expansion with two-sided estimates of these characteristics, based on the dual variational formulation of the thermoelasticity problem, was provided. Also for comparison the results of a numerical experiment was used. Presented relations allow to predict the thermoelastic properties of advanced composite materials reinforced with these nanocluster.