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Homogenization and Equivalent In-Plane Properties of Hexagonal and Re-Entrant Honeycombs

[+] Author Affiliations
Stefano Gonella, Massimo Ruzzene

Georgia Institute of Technology, Atlanta, GA

Paper No. IMECE2007-42400, pp. 1117-1127; 11 pages
doi:10.1115/IMECE2007-42400
From:
  • ASME 2007 International Mechanical Engineering Congress and Exposition
  • Volume 10: Mechanics of Solids and Structures, Parts A and B
  • Seattle, Washington, USA, November 11–15, 2007
  • Conference Sponsors: ASME
  • ISBN: 0-7918-4304-1 | eISBN: 0-7918-3812-9
  • Copyright © 2007 by ASME

abstract

The investigation of equivalent in-plane properties for hexagonal and re-entrant (auxetic) lattices can be carried out through the analysis of the partial differential equations associated with their homogenized continuum models. A homogenization technique is adopted based on the approximation of the discrete lattice equations according to the finite differences formalism. The technique can be used in conjunction with a finite element (FE) description of the lattice unit cell and therefore allows handling structures with different levels of complexity and various internal geometries within a general and compact framework that can be easily implemented in a numerical code. The in-plane wave propagation characteristics of honeycombs can be investigated with the proposed approach: approximate phase velocities can be calculated from the equations of motion for the low-frequency modes and compared with the exact values obtained through a Fourier analysis of the unit cell.

Copyright © 2007 by ASME

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