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Quasistatic small-strain plasticity in the limit of small hardening and its numerical approximation

Please always quote using this URN:urn:nbn:de:0296-matheon-7537
  • The quasistatic rate-independent evolution of the Prager-Ziegler-type model of linearized plasticity with hardening is shown to converge to the rate-independent evolution of the Prandtl-Reuss elastic/perfectly plastic model. Based on the concept of energetic solutions we study the convergence of the solutions in the limit for hardening coefficients converging to 0 by using the abstract method of Gamma-convergence for rate-independent systems. An unconditionally convergent numerical scheme is devised and 2D and 3D numerical experiments are presented. A two-sided energy inequality is a posteriori verified to document experimental convergence rates.

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Metadaten
Author:Sören Bartels, Alexander Mielke, Tomáš Roubíček
URN:urn:nbn:de:0296-matheon-7537
Referee:Carsten Carstensen
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/01/27
Release Date:2011/01/27
Tag:
Institute:Research Center Matheon
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K65 Degenerate parabolic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities [See also 35R35, 49J40]
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Sxx Variational principles of physics (should also be assigned at least one other classification number in this section) / 49S05 Variational principles of physics (should also be assigned at least one other classification number in section 49)
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Cxx Plastic materials, materials of stress-rate and internal-variable type / 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
Preprint Number:760
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