Continuum models of discrete heterogeneous structures and saturated porous media: constitutive relations and invariance of internal interactions

Approaches to mechanical (constructive) modeling of nonhomogeneous media with complicated structure are presented. The constitutive and motion equations of special type discrete systems are obtained as average equations demonstrating the Cosserat type properties of the systems. The equations for saturated porous media are proposed with special attention to the different types of inner interactions. The invariance properties of these interactions and their quantitative contributions are analyzed using the principle of material objectivity and the methods of measurement theory. The invariances of compound (force, moment) internal interactions are studied