On exotic linear materials: 2D elasticity and beyond. (1st March 2023) - Mou, Guangjin; Desmorat, Boris; Turlin, Robin; Auffray, Nicolas
Abstract: The symmetry classes of a linear constitutive law define the different types of anisotropy that can be modelled by it. However, the spaces of linear materials are very rich and a whole range of intermediate possibilities exists beyond symmetry classes. Geometric methods developed to characterise spaces of linear materials in a very fine way allow these intermediate possibilities to be detected. Materials with non-standard anisotropic properties associated with these intermediate possibilities are called exotic materials. In this paper, we provide a mathematical and mechanical definition of what an exotic material is. Using these definitions, we conclude that, for 2D linear elasticity, there is only one possible exotic material that meets our criteria. An example of a unit cell producing such exotic material is determined. Finally, the enumeration result obtained for elasticity is generalised to other bi-dimensional linear constitutive laws. Highlights: Geometrical tools designed to describe the space of 2D elastic linear materials. Definition of exotic and semi-exotic materials and their application to 2D linear elasticity. Determination of a unit cell producing a periodic exotic linear material. Determination of a formula to determine the number of exotic sets for any 2D linear constitutive laws.