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Priority Programme "Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials" (SPP 2256)
Deutsche Forschungsgemeinschaft (DFG)
The design of new solid materials with specific properties in order to provide optimal solutions to engineering problems is a challenging task. Progress in this area is not possible without fundamental contributions from the mathematical sciences, which offer both analytical and numerical tools for the solution of complex problems. In order to further advance this design process, a concerted effort of experts in both mathematics and mechanics is needed. It is the aim of this Priority Programme to support the development of new mathematical methods in the variational setting with broad applicability and to demonstrate their power at well-chosen problems from mechanics or materials science.
Variational methods that have proven to be successful include the theories of homogenisation, relaxation, Gamma convergence and variational time evolution. Applications may involve passage from atomistic models to continuum models, models of nonlinear elasticity, finite plasticity and phase transformations in general and the analysis of fracture, damage, motion of dislocations and the formation of microstructure in particular.
The Priority Programme has the following three major research directions:
o Coupling of dimensions: In many systems a strong interplay of effects on structures with different spatial dimensionality is observed.
o Coupling of processes: The overall response of many materials depends critically on interacting processes taking place at different scales ranging from atomistic or nanoscales to macroscopic ones.
o Coupling of structure and evolution: A major challenge is the combination of prediction of structures based on energetic considerations and the evolution of these structures in response to dynamic loadings.
Proposals within this Priority Programme must address a mathematical and/or mechanical problem. Successful proposals with an emphasis on mathematics address models that are relevant for applications in mechanics. Successful proposals with an emphasis on mechanics focus on an application of variational methods with a perspective towards the derivation of new mathematical methods and results; they are not exclusively limited to high performance computational aspects, atomistic or DFT simulations without any coupling to the continuum scale, or modelling in the framework of continuum mechanics or thermodynamics.
Tandem projects that typically combine two groups, one from the mathematical sciences and one from the engineering sciences, are encouraged. The work programme within the proposal should include detailed information on the role and tasks of the different groups and their synergies for the success of the envisaged project proposal and the specific role of the doctoral and/or postdoctoral researchers, respectively. From the work programme within the proposal it should become clear which parts are assigned to which scientific coworker, especially which tasks should be fulfilled by PhD students or postdocs. In case of joint proposals the assignment of requested funds to the individual principal investigators should also become clear. The proposals should also indicate how they fit into the programme as a whole.
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