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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
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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
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