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.
Homogenization and Equivalent In-Plane Properties of Hexagonal and Re-Entrant Honeycombs
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Gonella, S, & Ruzzene, M. "Homogenization and Equivalent In-Plane Properties of Hexagonal and Re-Entrant Honeycombs." Proceedings of the 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. pp. 1117-1127. ASME. https://doi.org/10.1115/IMECE2007-42400
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