Assessment of existing and introduction of a new and robust efficient definition of the representative volume element

Accurate numerical homogenization necessitates the thorough determination of the Representative Volume Element (RVE). This paper demonstrates that common techniques, based on studying the convergence rate of the effective properties with respect to the volume element size, are invalid for a certain range of microstructures and yield erroneous estimates of their effective properties. Different RVE determination methods were tested for the case of composites reinforced by randomly oriented and high aspect ratio fibers. Following the failure of traditional RVE determination methods, we proposed a new RVE determination criterion that is not based on the average property stability, but its statistical variations. Our new proposed criterion has been shown to be more accurate than other criteria in computing the effective properties of composites for aspect ratios up to 60. Moreover, the proposed criterion does not necessitate a convergence study over the volume element size, hence reducing considerably the RVE determination cost. Finally, our work questions the validity of many published works dealing with composites including heterogeneities of high aspect ratios.

Mots clés

numerical homogenization; representative volume element; finite element; random orientation; fiber composites.