CAHN-HILLIARD EQUATION WITH CAPILLARITY IN ACTUAL DEFORMING CONFIGURATIONS

The diffusion driven by the gradient of the chemical potential (by the Fick/Darcy law) in deforming continua at large strains is formulated in the reference configuration with both the Fick/Darcy law and the capillarity (i.e. concentration gradient) term considered at the actual configurations deforming in time. Static situations are analysed by the direct method. Evolution (dynamical) problems are treated by the Faedo-Galerkin method, the actual capillarity giving rise to various new terms as e.g. the Korteweg-like stress and analytical difficulties related to them. Some other models (namely plasticity at small elastic strains or damage) with gradients at an actual configuration allow for similar models and analysis.

Automated summary

The diffusion driven by the gradient of the chemical potential in deforming continua at large strains is analyzed, considering Fick/Darcy law, capillarity, and various methods for static and dynamic situations. The presence of capillarity leads to new terms like Korteweg-like stress and analytical complexities. Other models with gradients at an actual configuration allow for similar analysis.