Elasticity and symmetry of triangular lattice materials

[摘要] The elastic tensor of any triangular (2D) lattice material is given with respect 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 microstructure'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 fracturation (weak direction) are shown. The proposed set of equations can be used in an engineering process to create a 2D triangular lattice material of the desired elasticity. (C) 2017 Elsevier Ltd. All rights reserved.

[发布日期] 2017-12-15

[关键词] Anisotropy;Lattice material;Trusses;Symmetry;Elasticity;Invariant;Microstructural