Numerical calculations of RVE dimensions for two-phase material

A representative volume element (RVE) is a statistical representation of typical material properties. It should contain enough information on the microstructure thereby be sufficiently smaller than the macroscopic structural dimensions. The paper deals with the numerical calculations of the dimensions of the RVE for a two-phase material microstructure. Two and three dimensional models are taken into consideration. The structure of the samples are developed on the base of randomization of elements belonging to one of the phases. The phases volume share is 50/50%. The following series of the models are analyzed: from 10 x 10 to 100 x 100 elements for 2D samples and from 10 x 10 x 10 to 100 x 100 x 100 elements for 3D samples. The element characteristic dimension is 10 jm. The elastic behavior of the base materials (magnesium and alumina) is taken into account. The quasi-static compression tests of the developed structures are carried out with the use of LS-DYNA computer code. The results are presented as the equivalent Young modulus values and compared to the calculations based on the rule of mixtures. The stabilization of the achieved results allows to assess the dimensions of the RVE for two-phase material with random distribution.