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The results of experimental studies of irreversible deformation of heterogeneous materials that contain micro-cracks, pores, inclusions, and other structural heterogeneities are analysed. The dependencies of deformation properties of the materials on loading conditions are examined and common mechanisms and some features of their behaviour are specified. The constitutive relations for elastoplastic materials, which properties are susceptible to the stress state types are proposed. The features of irreversible bulk deformation are studied and the conditions for unique solution of boundary value problem are formulated. The applicability of proposed constitutive relations is demonstrated on the solution of plane stress crack problem for materials under consideration.