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Numerical analysis of the equations of small strains quasistatic elastoviscoplasticity. (English) Zbl 0613.73028

(Authors’ summary.) This paper deals with the mathematical and numerical analysis of small strains elastoviscoplasticity. By considering the problem as an evolution equation whose only unknown is the stress field, the quasistatic elastoviscoplastic evolution problem is shown to be well- posed, consistent mixed finite-element methods are introduced, and classical numerical algorithms are interpreted. In particular, augmented Lagrangian methods operating on the velocity appear as standard alternating-direction time-integrations of the stress evolution problem.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74H99 Dynamical problems in solid mechanics
74S99 Numerical and other methods in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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