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.
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e-mail: spa21@bath.ac.uk
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March 2008
Research Papers
Elastic Boundary Layers in Two-Dimensional Isotropic Lattices
A. Srikantha Phani,
A. Srikantha Phani
Department of Mechanical Engineering,
e-mail: spa21@bath.ac.uk
University of Bath
, Claverton Down, Bath BA2 7AY, UK
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Norman A. Fleck
Norman A. Fleck
Department of Engineering,
e-mail: naf1@eng.cam.ac.uk
University of Cambridge
, Trumpington Street, Cambridge CB2 1PZ, UK
Search for other works by this author on:
A. Srikantha Phani
Department of Mechanical Engineering,
University of Bath
, Claverton Down, Bath BA2 7AY, UKe-mail: spa21@bath.ac.uk
Norman A. Fleck
Department of Engineering,
University of Cambridge
, Trumpington Street, Cambridge CB2 1PZ, UKe-mail: naf1@eng.cam.ac.uk
J. Appl. Mech. Mar 2008, 75(2): 021020 (8 pages)
Published Online: February 27, 2008
Article history
Received:
February 21, 2007
Revised:
June 15, 2007
Published:
February 27, 2008
Citation
Phani, A. S., and Fleck, N. A. (February 27, 2008). "Elastic Boundary Layers in Two-Dimensional Isotropic Lattices." ASME. J. Appl. Mech. March 2008; 75(2): 021020. https://doi.org/10.1115/1.2775503
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