Effect of influation of initial stresses on the homogenized characteristics of composite

Thermoelastic problem for a composite solid with initial thermal stresses is considered on the basis of the asymptotic homogenization method. The major result of a present paper is that the effective (homogenized) elastic and thermoelastic characteristics of the composite material depend not only on local distributions of all types of material characteristics: local elastic properties, local thermoelastic properties, but also on local initial stresses. Therefore it is shown that for the inhomogeneous (composite) material local initial stresses contribute towards values of the effective characteristics of the material. This kind of interaction is not possible for the homogeneous materials. From the mathematical viewpoint, the above noted phenomenon is based on the fact that in the considering case the G-limit of a sum is not equal to the sum of G-limits. The developed general homogenized model is investigated in the particular case of the small (as compared with the elastic constants) initial stresses, which is common for the practical mechanical problems. The explicit formulas for the effective thermoelastic characteristics and numerical results are obtained for a laminated composite solid with the initial stresses.