A two-phase self-consistent model for the grid indentation testing of composite materials

The indented composite material is assumed to consist of two phases modeled as hemispherical inhomogeneities embedded at the surface of the semi-infinite homogenized medium with unknown properties. The radii of the hemispherical inhomogeneities are chosen in such a way that the indentation is performed at the center of the corresponding phase site. The effective properties of the homogenized medium are evaluated using the Mori-Tanaka homogenization scheme. Both Poisson's ratios of the phases and the phase concentrations are assumed to be known. The two-phase self-consistent model is based on the first-order asymptotic model for the incremental indentation stiffness of an embedded hemispherical inhomogeneity.