A representative volume element and effective thermoelastic material parameters of compositions with periodic structure

In this paper, an iterative algorithm for designing representative volume element (RVE) of a composite with periodic structure and its effective material thermoelastic characteristics is proposed. The features of the RVE are described. A periodic cell of the composite, which is widely and validly used to determine its effective parameters under specific boundary conditions on its surfaces, does not have all the necessary features of the RVE. Therefore, a separated from the composite sequence of cubic samples with increasing characteristic size and consisting of periodic cells is considered. According to the method of contradiction, each sample of the sequence is assumed to be an RVE. A solution to the problem of micromechanics is obtained for them. Based on this solution, the macroscopic properties of the sample are determined. The calculated macroscopic material parameters and the fulfillment of the symmetry conditions of the stiffness matrix for the next cubic sample are compared with the corresponding data for the previous sample, and the essential features of the RVE are verified. Finally, a conclusion is made about the possibility (or impossibility) of recognizing the considered sample as an RVE. The sequences of the values of calculated characteristics and the percentage deviation of the stiffness matrix from symmetry are convergent. The obtained characteristics are taken as the limiting values for the cube representing RVE. They are referred to as effective material characteristics of the composition. It is revealed that the existence of the RVE for a composite is a basis for applying effective modulus theory to the description of its stress-strain state.