Existence of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage. (English) Zbl 1253.35179

Summary: 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-Larché 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-Larché 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-Larché systems coupled with rate-dependent damage processes, we establish a suitable notion of weak solutions and prove existence of weak solutions.


35Q74 PDEs in connection with mechanics of deformable solids
35D30 Weak solutions to PDEs
74A45 Theories of fracture and damage
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
80A22 Stefan problems, phase changes, etc.
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