Many materials or media in nature and technology possess a microstructure, which determines their macro behaviour. Despite of possible difficulties to describe the morphology of this structure, the knowledge of the relevant mechanisms is often more comprehensive on the micro than on the macro scale. On the other hand, not all information on the micro level is relevant for the understanding of the macro behaviour. Therefore, averaging and homogenization methods are needed to select only the specific information from the micro scale, which influences the macro scale. These methods would also open the possibility to design or to influence microstructures with the objective to optimize their macro behaviour. Study and development of new methods in this interdisciplinary field of actual research will be under the supervision of professors from different engineering branches, applied mathematics, theoretical, and computational physics.
The computational investigation of the relation between microscopic and macroscopic behaviour of materials with a micro structure has become an important tool in engineering. Out of a large number of applications of this approach we have chosen two areas: (1) solid metals with micro structures such as textures, phases, voids, inclusions etc., (2) systems of solid particles in fluid flow or in other interaction with fluid phases.
In both areas we plan to study problems that have different characteristic properties on two differing scales. In the metallic solids these are materials with microstructures such as grains, voids, inclusions, phases, cracks etc. In particle agglomerates these are particles with substructures and pore networks that contain and interact with fluids, as is the case in mechanical dehydration of suspensions, particle formation in fluidised beds, thermal drying of particle systems etc.
On the micro scale we usually have more physical insight than on the macroscopic scale. Therefore, we will use numerical simulations on this scale to provide information that we need on the macroscopic scale of engineering applications. On the latter, one works with averaged quantities. These are determined through homogenisations that have to be tailored to the specific problem. For the technical applications we have to develop models on the macroscopic scale that can be used in the simulation and design of practical industrial processes.