Repin, S.; Seregin, G. Existence of a weak solution of the minimax problem arising in Coulomb-Mohr plasticity. (English) Zbl 0890.73079 Uraltseva, N. N. (ed.), Nonlinear evolution equations. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 164 (22), 189-220 (1995). The authors obtain existence theorems for weak solutions of variation problems in the theory of plasticity with Coulomb-Mohr yield condition. First they investigate the coercitivity of the Coulomb-Mohr variational functional and establish that this functional is not coercive. This makes impossible to prove the existence theorems in a standard way, and the authors replace the classical setting of the problem describing the equilibrium of an elastic-plastic medium by a minimax problem for a pair of the stress tensors and the displacement. This problem is relaxed, i.e., “natural” Lagrangian is replaced by an extended Lagrangian, and an extended space of admissible displacements is introduced. The authors prove the existence theorem for this relaxed minimax problem and justify the proposed extension. Another variational extension is proposed, which preserves the lower bounds and may be used to generate new variational-difference schemes.For the entire collection see [Zbl 0824.00037]. Reviewer: G.Olenev (Tartu) Cited in 10 Documents MSC: 74S30 Other numerical methods in solid mechanics (MSC2010) 74P10 Optimization of other properties in solid mechanics 74C99 Plastic materials, materials of stress-rate and internal-variable type 49J35 Existence of solutions for minimax problems 49J52 Nonsmooth analysis Keywords:duality; coercitivity of Coulomb-Mohr variational functional; extended Lagrangian; extended space of admissible displacements; variational-difference schemes × Cite Format Result Cite Review PDF