Nyashin, Yu. I.; Chernopazov, S. A. On the formulation of the contact problem of elastic plasticity. (English. Russian original) Zbl 0733.73068 J. Appl. Math. Mech. 53, No. 6, 811-815 (1989); translation from Prikl. Mat. Mekh. 53, No. 6, 1023-1027 (1989). Summary: A differential and a variational formulation of the problem of contact interaction between an elastic-plastic body and a rigid support are examined. Equations of the theory of plastic flow with isotropic hardening, which is a particular modification of the Il’yushin theory of elastic-plastic processes, are taken as governing relationships. A proof is presented of the existence and uniqueness of the generalized solution. To simplify the description the problem is considered in a Cartesian rectangular system of coordinates. MSC: 74S30 Other numerical methods in solid mechanics (MSC2010) 74P10 Optimization of other properties in solid mechanics 49J40 Variational inequalities 74A55 Theories of friction (tribology) 74M15 Contact in solid mechanics 74C99 Plastic materials, materials of stress-rate and internal-variable type Keywords:contact interaction; elastic-plastic body; rigid support; theory of plastic flow; isotropic hardening; Il’yushin theory; existence; uniqueness; generalized solution PDFBibTeX XMLCite \textit{Yu. I. Nyashin} and \textit{S. A. Chernopazov}, J. Appl. Math. Mech. 53, No. 6, 811--815 (1989; Zbl 0733.73068); translation from Prikl. Mat. Mekh. 53, No. 6, 1023--1027 (1989) Full Text: DOI References: [1] Il’yushin, A. A., Plasticity: Principles of the Mathematical Theory (1963), Izd. Akad. Nauk SSSR: Izd. Akad. Nauk SSSR Moscow · Zbl 0098.15904 [2] Il’yushin, A. A.; Lenskii, V. S., On relationships and methods of modern plasticity theory, (Progress of the Mechanics of Deformable Media (1975), Nauka: Nauka Moscow) [3] Kravchuk, A. S., Variational method of investigating contact interaction and its realization on an electronic computer, (Strength Analyses, 25 (1984), Mashinostroyeniye: Mashinostroyeniye Moscow) [4] Kus’menko, V. I., On contact problems of plasticity theory under complex loading, PMM, 48, 3 (1984) [5] Kuz’menko, V. I., Contact problems of plasticity theory taking friction into account on the contact surface, Treniye i Iznos, 8, 1 (1987) [6] (Birger, I. A.; Shorr, B. F., Thermal Strength of Machine Components (1985), Mashinostroyeniye: Mashinostroyeniye Moscow) [7] Reddy, B. D.; Griffin, T. B.; Marais, M. J., A penalty approach to the rate problem in small-strain plasticity, IMA, J. Appl. Math., 34, 3 (1985) · Zbl 0588.73057 [8] Kravchuk, A. S., On the Hertz problem for linearly and non-linearly elastic bodies of finite dimensions, PMM, 41, 2 (1977) · Zbl 0395.73019 [9] Kinderlehrer, D.; Stampacchia, G., Introduction to Variational Inequalities and Their Application (1983), Mir: Mir Moscow [10] Duvaut, G.; Lions, J.-L., Inequalities in Mechanics and Physics (1980), Nauka: Nauka Moscow · Zbl 0331.35002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.