Elasticity and symmetry of triangular lattice materials

M.L.M. François (1) , Lin Chen (1) , Michel Coret (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

The elastic tensor of any triangular (2D) lattice material is given with re- spect to the geometry and the mechanical properties of the links between the nodes. The links can bear central forces (tensional material, for example with hinged joints), momentums (flexural materials) or a combination of the two. The symmetry class of the stiffness tensor is detailed in any case by using the invariants of Forte and Vianello. A distinction is made between the trivial cases where the elasticity symmetry group corresponds to the mi- crostructure’s symmetry group and the non-trivial cases in the opposite case. Interesting examples of isotropic auxetic materials (with negative Poisson’s ratio) and non-trivial materials with isotropic elasticity but anisotropic frac- turation (weak direction) are shown. The proposed set of equations can be used in a engineering process to create a 2D triangular lattice material of the desired elasticity.

Mots clés: elasticity; symmetric; anisotropic; lattice material; trusses; invariant; microstructural

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

M.L.M. François, Lin Chen, Michel Coret. Elasticity and symmetry of triangular lattice materials. International Journal of Solids and Structures, 2017, ⟨10.1016/j.ijsolstr.2017.09.019⟩. ⟨hal-01614317⟩