Effects of high order deformations on elastic modulus and collapse of planar lattice materials

Lattice materials have been attractive over the last decade for use as loading carrying structures, energy absorbing elements and heat exchanging structures for their superior mechanical properties and multifunctional characters. The deformation modes of perfect planar lattice materials show a rich diversity according to the magnitude of connectivity, including the bending and stretching dominated modes. Noting that the quantitative influence of the high order deformations upon the elastic modulus and collapse of lattice materials which is important for their applications has been scarcely reported, an analytical investigation of the elastic modulus and initial yield surface considering the high order deformations is carried out for three typical planar lattice materials: hexagonal, Kagome and triangular lattices. The analytical results are validated by the finite element (FE) simulations. Based on the analytical results, minimum weight designs of axially compressed hollow square columns made from planar lattice materials are performed, taking into account the failure mechanisms of global column buckling, local plate buckling, local beam buckling and beam yielding. It is found that the effect of high order deformation on the elastic modulus and yield strength increases with the relative density. The bending effect of the Kagome lattice is more obvious than that of the triangular one with the same relative density and stress state. The yield strength of the Kagome lattice calculated by neglecting the bending effect overestimates the result by more than 10% when the relative density is higher than about 11.1%.