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search.filters.applied.f.access: openAccess × Start date: 2010 × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: Cahn-Hilliard systems × Subject: phase separation × Subject: rate-dependent systems ×

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    Existence of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Heinemann, Christian; Kraus, Christiane
    The Cahn-Hilliard model is a typical phase field approach for describing phase separation and coarsening phenomena in alloys. This model has been generalized to the so-called Cahn-Larché system by combining it with elasticity to capture non-neglecting deformation phenomena, which occurs during phase separation in the material. Evolving microstructures such as phase separation and coarsening processes have a strong influence on damage initiation and propagation in alloys. We develop the existing framework of Cahn-Hilliard and Cahn-Larché systems by coupling these systems with a unidirectional evolution inclusion for an internal variable, describing damage processes. After establishing a weak notion of the corresponding evolutionary system, we prove existence of weak solutions for rate-dependent damage processes under certain growth conditions of the energy functional
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    Existence results for diffuse interface models describing phase separation and damage
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Heinemann, Christian; Kraus, Christiane
    In this paper we analytically investigate Cahn-Hilliard and Allen-Cahn systems which are coupled with elasticity and uni-directional damage processes. We are interested in the case where the free energy contains logarithmic terms of the chemical concentration variable and quadratic terms of the gradient of the damage variable. For elastic Cahn-Hilliard and Allen-Cahn systems coupled with uni-directional damage processes, an appropriate notion of weak solutions is presented as well as an existence result based on certain regularization methods and an higher integrability result for the strain Literaturverz.