A novel determination of the minimal size of a probabilistic representative volume element for fiber-reinforced composites’ thermal analysis

In order to provide an accurate thermal analysis method of fiber-reinforced composites, a novel model based on a probabilistic representative volume element (RVE) is presented in this paper. Monte Carlo methods, probability analysis and finite element analysis have been applied together. The effective transverse thermal conductivity, heat flux field, and thermal gradient field of typical fiber-reinforced composites are examined. The criteria of RVE have been determined, and the minimal size for thermal analysis is obtained using the main statistics and the cross-entropy theory. At the same time, the fiber-to-matrix ratio of thermal conductivity and volume fraction have been changed to determine the influence on heat transfer inside fiber-reinforced composites. It is shown that different purposes of simulations lead to different minimal RVE sizes. The numerical results indicate that the non-dimensional minimal RVE sizes for calculating the effective thermal conductivity, heat flux, and thermal gradient are 30, 80, and 80, respectively. Compared with the volume fraction, the fiber-to-matrix ratio of the thermal conductivity has a more significant effect on minimal RVE size. When the thermal conductivity ratio increases, the minimal size of the RVE increases at first, then it remains almost unchanged