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Worst scenario approach for elastoplasticity with hardening and uncertain input data. (English) Zbl 1099.74505
Summary: Coefficients of the stress-strain relations, yield function, and the hardening parameters in a model of isotropic hardening are considered to be uncertain. Using simplest finite elements in \(\mathbb R^3\) and backward differenences in time, an approximate solution is defined and its continuous dependence on the uncertain input data investigated. Three different criteria are chosen to find the worst input data in a given set of admissible data. Some existence and convergence results are proven.

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74E35 Random structure in solid mechanics
49J40 Variational inequalities
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
93C41 Control/observation systems with incomplete information
74S05 Finite element methods applied to problems in solid mechanics
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
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