Existence of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage

Please always quote using this URN:urn:nbn:de:0296-matheon-9505
  • A typical phase field approach for describing phase separation and coarsening phenomena in alloys is the Cahn-Hilliard model. This model has been generalized to the so-called Cahn-Larche system by combining it with elasticity to capture non-neglecting deformation phenomena, which occur during phase separation and coarsening processes in the material. In order to account for damage effects, we extend the existing framework of Cahn-Hilliard and Cahn-Larche systems by incorporating an internal damage variable of local character. This damage variable allows to model the effect that damage of a material point is influenced by its local surrounding. The damage process is described by a unidirectional rate-dependent evolution inclusion for the internal variable. For the introduced Cahn-Larche systems coupled with rate-dependent damage processes, we establish a suitable notion of weak solutions and prove existence of weak solutions.

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Metadaten
Author:Christiane Kraus, Christian Heinemann
URN:urn:nbn:de:0296-matheon-9505
Referee:Carsten Carstensen
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/12/28
Release Date:2011/12/28
Tag:Cahn-Hilliard systems; damage; doubly nonlinear differential inclusions; elliptic-parabolic systems; existence results; phase separation; rate-dependent systems; weak solution
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J50 Variational methods for elliptic systems
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K35 Initial-boundary value problems for higher-order parabolic equations
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]
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Cxx Plastic materials, materials of stress-rate and internal-variable type / 74C10 Small-strain, rate-dependent theories (including theories of viscoplasticity)
Preprint Number:838
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