Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

The problems of the description of behaviour of materials with strong heterogeneity of structure are considered which is displayed in dependences of deformation characteristics, criteria of plasticity, phase stratification and durability from the relations of main stress at small deformations. The determining relationships are received, for which main approximation the theorem of uniqueness, and also stability of a material in large is proved. The class of materials is described, for which area of the allowable relations of main stress, in which they are continuous bodies, is limited. The principle of conjugation on a case of confluent potentials is generalized; the determining relationships with internal restrictions are reasonable. The results of application of the given models are resulted.