Almost every natural as well as industrial material displays a heterogeneous structure on several scales of observation. The individual phases present in these material systems define the material microstructure. Properties of the microstructural constituents together with the character of applied loading determine the macroscopic behaviour of these multi-phase material systems. Multi-scale modelling is a recent multi-disciplinary research discipline that aims to describe and predict the macroscopic behaviour of heterogeneous materials on a well-defined and systematic basis.
The success of this method depends on the accuracy of microstructure description, as well as the technique that is used to define behaviour of the material system on the macroscopic level. This procedure, well known in various research disciplines, is usually referred to as homogenisation. Although this area of research has been very active in the past decades, homogenisation theories are now well established only for modelling of material systems subjected to slowly varying macroscopic fields. For problems when highly localized macroscopic response is of main interest, the situation is much more complex. In particular, it seems to be necessary to introduce non-local continuum theories, which take into account mutual interaction of material points, in order to correctly capture these phenomena.
Understanding the fundamental mechanisms determining the response of heterogeneous materials subjected to highly varying macroscopic fields is of paramount theoretical and practical relevance, as this behaviour determines their overall reliability and capacity. The main objective of the project is to further investigate advanced issues in the multi-scale non-local homogenisation techniques. The research will focus on applications related to the development of computational homogenisation techniques in general and theories related to non-local continua in particular.
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