Analytical modelling of thermal stresses in anisotropic composites

•New analytical model of thermal stresses in two-component composites is determined.•Results are applicable to composites with anisotropic components.•This new model is continuation of the author's work (Acta Mech Sin 26, 2010, 695).•Acta Mech Sin contains extremely extensive final formulae for the thermal stresses.•In contrast to the previous model, numerical determination is not time-consuming.

This paper represents a continuation of the author's previous work which deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid elastic continuum. This continuum consists of anisotropic spherical particles which are periodically distributed in an anisotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with central particles. This multi-particle–matrix system represents a model system which is applicable to two-component materials of the precipitate–matrix type. The thermal stresses, which originate due to different thermal expansion coefficients of components of the model system, are determined within the cubic cell. The analytical modelling results from fundamental equations of continuum mechanics for solid elastic continuum (Cauchy's, compatibility and equilibrium equations, Hooke's law). This paper presents suitable mathematical procedures which are applied to the fundamental equations. These mathematical procedures lead to such final formulae for the thermal stresses which are relatively simple in comparison with the final formulae presented in the author's previous work which are extremely extensive. Using these new final formulae, the numerical determination of the thermal stresses in real two-component materials with anisotropic components is not time-consuming.