Regularity of stresses in Prandtl-Reuss perfect plasticity

Regularity of stresses in Prandtl-Reuss perfect plasticity

We study the differential properties of solutions of the Prandtl-Reuss model. We prove that in dimensions n  = 2, 3 the stress tensor has locally square-integrable first derivatives: . The result is based on discretization of time and uniform estimates of solutions of the incremental problems, which...

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Veröffentlicht in:Calculus of variations and partial differential equations 2009, Vol.34 (1), p.23-72
1. Verfasser: Demyanov, A.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Derivatives
Discretization
Estimates
Mathematical analysis
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Plastic strain
Plasticity
Regularity
Systems Theory
Theoretical
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Beschreibung
Zusammenfassung:We study the differential properties of solutions of the Prandtl-Reuss model. We prove that in dimensions n  = 2, 3 the stress tensor has locally square-integrable first derivatives: . The result is based on discretization of time and uniform estimates of solutions of the incremental problems, which generalize the estimates in the case of Hencky perfect plasticity. Counterexamples to the regularity of displacements and plastic strains in the quasistatic case are presented.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-008-0174-5