15.07.2024–14.07.2027
Austrian Science Fund project (ESP1887024)
Principle investigator: Lorenza D'ELIA (E101-01-3)

Since their discovery, quasi-crystalline or quasi-periodic microstructures have drawn wide attention among the practitioners of Materials Science. They differ from the random microstructure since fine structure is ordered, but it is not periodic since it exhibits forbidden symmetries for periodic structures, such as 5-, 7-, 8- and 10-fold symmetries. Thanks to such a peculiar arrangement, quasi-periodic composites enjoy extraordinary features and find applications in many different fields ranging from  engineering to Materials Science. In view of the wide range of applications, it is of primary interest to understand the effective response of quasi-periodic materials. 

In the FWF-funded research project "Effective theories for quasi-crystalline microstructures",  we lay the foundations for the investigation of aperiodic microstructures in different scenarios. We will investigate double porosity problems, bilayered composites and phase transitions. These settings have been chosen for their relevance for applications and the high level of challenges they pose. Indeed, the tools developed in the periodic and stochastic homogenization are inadequate to characterize the effective response of quasi-periodic materials.  This calls for peculiar and novel methods to be tackled, and to describe the possible new phenomena arising in the three scenarios described above.