Applicability of Conventional Multi-Scale Method for Random Heterogeneous Structures in Quasi-Brittle Materials

In this paper, the possibility of existence of the multi-scale approach which is capable of modeling structures with softening representative volume element (RVE) is explored. In order to investigate the existence of RVE for softening quasi-brittle materials, a random heterogeneous material is introduced as a two phase material, specifically a material with matrix and inclusions in a circular shape. In the next stage, the aim is to verify whether the response of the direct numerical simulation (DNS) is objective with respect to the micro-structures volume fraction, minimum and maximum size of inclusions. To this aim, the uniaxial tension test is performed over different DNS models which are constructed of random heterogeneous micro-structures of different sizes and realizations.