Does representative volume element exist for quasi-brittle composites?

The validity on the use of representative volume element (RVE) to predict the mechanical behavior of quasi-brittle composites is addressed based on studies of porous epoxy under tensile action. For the elastic behavior, the more efficient single particle (SP) RVE approach predicts accurately when the volume fraction is less than a critical value of 15–20% depending on the relative stiffness of the matrix and the inclusion. At higher volume fraction, the multiple particle (MP) RVE provides accurate predictions with less than 6% error, for MP-RVE sizes that are at least 6 times larger than the size of the inclusion. In the inelastic softening regime, the RVE does not exist for the homogenized stress–strain behavior due to the high localization of damage. Instead, the fracture energy or toughness should be used as a size-independent measure in the RVE approach to describe the fracture response in quasi-brittle composites. The fracture toughness predicted with the MP-RVE models shows size invariance and compares well with the experiments for volume fractions of up to 20% with deviations of less than 6%, while the SP-RVE models are only recommended for use at volume fractions of less than 10%.