Elastic gradient theories and dislocation theories and their application to defects and microstructures

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Materials with dislocation structures and microstructures are of fundamental interest and play an important role in nature and technology. From the technical point of view, physical properties caused by the microstructure are of importance. From the mathematical point of view, the underlying models which describe the dislocation structures are of interest (e.g. theory of partial differential equations). Consequently, the project is situated between areas of materials science, mechanics, solid state physics, and applied mathematics. At the atomic level, the description of the dislocation microstructure is very complex. Many important properties can be understood, if the microstructure is modeled as a continuum with additional degrees of freedom. Thus, the microstructure can be described by generalized mechanical continuum theories such as gradient theories, nonlocal theories, and dislocation field theories.The project is devoted to aspects of dislocations on the micro-scale, and the generalization of dislocation continuum theories. In particular, dynamic effects such as retardationand anisotropic effects are considered. Materials like quasicrystals and graphene are currently of great interest. It opens new perspectives for a better modeling, and considers new aspects (e.g. new mathematical solutions for dislocations). As much as possible analytical theoretical methods will be used.In addition, the foundations for numerical implementations shall be expanded and strengthened.