Elastic Boundary Layers in Two-Dimensional Isotropic Lattices

Abstract

The phenomenon of elastic boundary layers under quasistatic loading is investigated using the Floquet–Bloch formalism for two-dimensional, isotropic, periodic lattices. The elastic boundary layer is a region of localized elastic deformation, confined to the free edge of a lattice. Boundary layer phenomena in three isotropic lattice topologies are investigated: the semiregular Kagome lattice, the regular hexagonal lattice, and the regular fully triangulated lattice. The boundary layer depth is on the order of the strut length for the hexagonal and the fully triangulated lattices. For the Kagome lattice, the depth of boundary layer scales inversely with the relative density. Thus, the boundary layer in a Kagome lattice of low relative density spans many cells.