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Numerical approaches to rate-independent processes and applications in inelasticity

Please always quote using this URN:urn:nbn:de:0296-matheon-3912
  • A general abstract approximation scheme for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The abstract theory is illustrated on several examples: plasticity with isotropic hardening, damage, debonding, magnetostriction, and two models of martensitic transformation in shape-memory alloys.

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Metadaten
Author:Alexander Mielke, Tomas Roubicek
URN:urn:nbn:de:0296-matheon-3912
Referee:Carsten Carstensen
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/03/13
Release Date:2008/03/13
Tag:
Institute: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] / 35K55 Nonlinear 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] / 49Jxx Existence theories / 49J40 Variational methods including variational inequalities [See also 47J20]
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 / 65Jxx Numerical analysis in abstract spaces / 65J15 Equations with nonlinear operators (do not use 65Hxx)
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)
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Fxx Coupling of solid mechanics with other effects / 74F15 Electromagnetic effects
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Hxx Dynamical problems / 74H15 Numerical approximation of solutions
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Hxx Dynamical problems / 74H20 Existence of solutions
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Nxx Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26] / 74N10 Displacive transformations
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Rxx Fracture and damage / 74R05 Brittle damage
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Sxx Numerical methods [See also 65-XX, 74G15, 74H15] / 74S05 Finite element methods
Preprint Number:487
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