Auxetic structures are characterised by a negative Poisson's ratio. There are a variety of auxetic structures out of which the relevant ones are highlighted. After a simulative comparison of the thermal and mechanical properties, the most suitable structure and topology is selected for the application in turbomachinery. A parameter variation of this topology leads to an analytical model that describes the mechanical behaviour of the recursive lattice structure as a function of these geometric parameters: the recursive angle 𝛩, the aspect ratio 𝛼, the normalised wall thickness 𝛽, the normalised radius 𝜅 and the cell density 𝑛. Regarding the thermal properties, the so-called resistance length 𝑅L is introduced, which allows a good prediction of the thermal behaviour depending on the cell dimensions. Finally, potential fields of application in the literature are outlined.

Auxetic structures are characterised by a negative Poisson's ratio. There are a variety of auxetic structures out of which the relevant ones are highlighted. After a simulative comparison of the thermal and mechanical properties, the most suitable structure and topology is selected for the application in turbomachinery. A parameter variation of this topology leads to an analytical model that describes the mechanical behaviour of the recursive lattice structure as a function of these geometric sizes: the recursive angle 𝛩, the aspect ratio 𝛼, the normalised wall thickness 𝛽, the normalised radius 𝜅 and the cell density 𝑛. Regarding the thermal properties, the socalled resistance length 𝑅L is introduced, which allows a good prediction of the thermal behaviour depending on the cell dimensions. Finally, potential fields of application in the literature are outlined.