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Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials

Montag 28. November 2022

Deadline: 28. November 2022

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:

  • Coupling of dimensions: in many systems a strong interplay of effects on structures with different spatial dimensionality is observed.
  • 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.
  • 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.

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