Elastic boundary layers in isotropic periodic lattices

Reference:

Phani, A.-S. and Fleck, N. A., 2007. Elastic boundary layers in isotropic periodic lattices. Journal Of Applied Mechanics

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Abstract

The phenomenon of elastic boundary layers under quasi-static loading is investigated using the Floquet-Bloch formalism for two-dimensional, isotropic, periodic lattices. The elastic boundary layer is a region of localised elastic deformation, confined to the free-edge of a lattice. Boundary layer phenomena in three isotropic lattice topologies are investigated: the semi-regular 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.

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