Haslinger, Jaroslav; Repin, Sergey; Sysala, Stanislav Guaranteed and computable bounds of the limit load for variational problems with linear growth energy functionals. (English) Zbl 1413.49038 Appl. Math., Praha 61, No. 5, 527-564 (2016). In this paper, the authors consider the problem of finding bounds of the limit load parameter in physically important variational problems represented by energy functionals with linear growth. The main results concerns a new guaranteed upper bound for functionals with purely linear growth and the truncation technique for the ones with linear growth. For illustration, a model problem which is a scalar counterpart of the classical Hencky model of plasticity is investigated. Next, the method is extended to classical plasticity models described by von Mises and Drucker-Prager yield laws. Finally, some numerical experiments based on classical finite element approximation are provided to efficiently compute bounds of the limit load in the generalized Hencky plasticity. Reviewer: Stanisław Migórski (Kraków) Cited in 9 Documents MSC: 49M15 Newton-type methods 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 74S05 Finite element methods applied to problems in solid mechanics 90C25 Convex programming Keywords:functionals with linear growth; limit load; truncation method; perfect plasticity Software:HYPLAS; Matlab × Cite Format Result Cite Review PDF Full Text: DOI Link References: [1] A. Caboussat, R. Glowinski: Numerical solution of a variational problem arising in stress analysis: the vector case. Discrete Contin. Dyn. Syst. 27 (2010), 1447–1472. · Zbl 1387.74105 · doi:10.3934/dcds.2010.27.1447 [2] M. Cermak, J. Haslinger, T. Kozubek, S. 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