Open AccessThe composites, dispersion-reinforced with inclusions from high-strength and high-modulus materials are widely used in technology. Nanostructure elements can perform the role of such inclusions as well. Possible applications of such composites in heat-stressed structures under heavy mechanical and thermal influences significantly depend on a complex of thermo-mechanical characteristics including the values of the moduli of elasticity and coefficient of linear thermal expansion. There are different approaches to construction of mathematical models that allow calculating dependences to estimate elastic characteristics of composites. Relation between thermoelastic properties of matrix and inclusions of the composite with its temperature coefficient of linear expansion is studied in less detail. Thus, attention has been insufficient in estimating a degree of reliability and a possible error of derived dependencies.
A dual variation formulation of the problem of thermo-elasticity in a non-uniform solids simulating the properties and structure of the composite with dispersed inclusions, makes it possible to define two-sided limits of possible values of the volume elasticity modulus, shear modulus, and coefficient of linear thermal expansion of such composite. These limits allow us to estimate the maximum possible error, if to take a half-sum of the limit values of these parameters as the thermoelastic characteristics of the composite. Implementing this approach to find possible errors, arising when using one or another calculating dependency, improves reliability of predicted thermo-elastic characteristics as applied to existing and promising composites.