Zur Formulierung und zum mikromechanischen Ursprung von Diffusionsmodellen

Zur Formulierung und zum mikromechanischen Ursprung von Diffusionsmodellen

(Drittmittelfinanzierte Einzelförderung)

Titel des Gesamtprojektes:
Projektstart: 1. Juli 2012
Projektende: 31. Juli 2019
Mittelgeber: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)


Diffusion, especially when coupled with deformation, is of utmost scientific and technological im-portance in various fields of engineering, materials science, natural sciences and their intersections. Prominent examples are the modelling and simulation of solder joints, micro-structure evolution in advanced materials as used e.g. in modern and future turbine blades produced from single crystals, mineral unmixing in geology, contaminant distribution in environmental systems, and drug transport and delivery in biological tissues. In many of these instances classical diffusion models of Fick-type do not accurately describe the observed phenomena, thus requiring non-classical diffusion models. Specific examples for non-classical models of diffusion are the Cahn-Hillard equation and Gurtin's microforce balance.The long-term goals of this project are therefore (i) the formulation and simulation of a generic class of non-classical three-dimensional models of diffusion, (ii) the exploration of their micromechanical origin and (iii) their coupling to deformation. Thereby it is noted that gradient-type and micromorphic-type models as paradigms of extended continuum models are intimately related and offer different benefits and drawbacks2. Thus, as a mid-term goal, gradient-type and micromorphictype formulations of diffusion shall be considered alternatively in Phase I. In order to explore their micromechanical origin, relevant response quantities that participate in the corresponding field equations at the macro-level shall be determined from the micro-level by a second-order computational homogenization.The expected output of this project in Phase I is thus the clarification of the underlying micromechani-cal origin of a generic class of non-classical models of diffusion. Phase II will then concentrate mainly on the coupling of diffusion and deformation. The overall outcome of the project will be of great im-portance in various fields such as engineering, materials science and natural sciences from both the scientific and the technological view point. In particular the design and understanding in the area of novel and advanced materials will be strongly enhanced by the expected findings of this project.