On Exotic Linear Materials: 2D Elasticity And Beyond

Guangjin Mou (1) , Boris Desmorat (1) , Robin Turlin (2) , Nicolas Auffray (1)

1 DALEMBERT - Institut Jean Le Rond d'Alembert
2 MSME - Laboratoire Modélisation et Simulation Multi-Echelle

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 nonstandard 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.

Domaines: Mécanique des solides [physics.class-ph]

Guangjin Mou, Boris Desmorat, Robin Turlin, Nicolas Auffray. On Exotic Linear Materials: 2D Elasticity And Beyond. International Journal of Solids and Structures, 2023, 264, pp.112103. ⟨10.1016/j.ijsolstr.2022.112103⟩. ⟨hal-03834502⟩