Large strain behavior of two-phase materials with random inclusions

The large strain behavior of a two-phase material with random inclusions is investigated using the periodic microfield approach. Two- and three-dimensional representative volume elements (RVEs) with different boundary conditions are compared. For low volume fractions of second-phase particles up to about 2% and moderate strains, no marked differences with respect to the stress-strain curves are found between the various models. For higher volume fractions, the differences between the 2D and the 3D representations cannot be neglected anymore. For the simulation of a sheet material, no constraint must be imposed in the thickness direction of a 3D model; otherwise, necking - an essential feature for the large deformation behavior of sheets - cannot be captured. This type of RVE is different from the RVEs normally used for the simulation of the material behavior in bulky specimens.