Skip to main content

News about Scitation

In December 2016 Scitation will launch with a new design, enhanced navigation and a much improved user experience.

To ensure a smooth transition, from today, we are temporarily stopping new account registration and single article purchases. If you already have an account you can continue to use the site as normal.

For help or more information please visit our FAQs.

banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
1. M. F. Ashby and L. J. Gibson, Cellular solids: structure and properties, Cambridge University Press, UK, (1997).
2. N. A. Fleck, V. S. Deshpande, and M. F. Ashby, Micro-architectured materials: past, present and future, Proceedings of the Royal Society of London, Series A, 466, 24952516, (2010).
3. W. E. Warren and A. M. Kraynik, Foam mechanics: the linear elastic response of two-dimensional spatially periodic cellular materials, Mechanics of Materials, 6, 2737, (1987).
4. R. M. Christensen, Mechanics of cellular and other low density materials, International Journal of Solids and Structures, 37(1), 93104, (2000).
5. R. S. Lakes, Foam structures with a negative Poisson's ratio, Science, 235, 10381040, (1987).
6. N. Wicks, and J. W. Hutchinson, Optimal truss plates, International Journal of Solids and Structures, 38, 51655183, (2001).
7. A. S. Phani, J. Woodhouse, N. A. Fleck, Wave propagation in two-dimensional periodic lattices, Journal of the Acoustical Society of America, 119(4), 19952005, (2006).
8. O. Sigmund and J. S. Jensen, Systematic design of photonic band-gap materials and structures by topology optimization, Proceedings of the Royal Society of London, Series A, 361, 10011019, (2003).
9. C. Kittel, Elementary solid state physics: a short course, John Wiley & Sons, inc., USA, (1962).
10. D. J. Mead, Wave propagation in continuous periodic structures: research contributions from Southampton 1964-1995, Journal of Sound and Vibration, 190(3), 495524, (1996).
11. R. S. Langley, N. S. Bardell, and H. M. Ruivo, The response of two-dimensional periodic structures to harmonic point loading: a theoretical and experimental study of a beam grillage, Journal of Sound and Vibration, 207(4), 521535, (1997).
12. C. H. Hodges, and J. Woodhouse, Vibration isolation from irregularity in a nearly periodic structure: theory and measurements, Journal of the Acoustical Society of America, 74, 894905, (1983).
13. M. Ruzzene, F. Scarpa, F. Soranna, Wave beaming effects in two-dimensional cellular structures, Smart Materials and Structures, 12, 363372, (2003).
14. M. I. Hussein, Reduced Bloch mode expansion for periodic media band structure calculations, Proceedings of the Royal Society of London, Series A, 465, 28252848, (2009).
15. A. S. Phani, and, N. A. Fleck, Elastic boundary Layers in isotropic periodic lattices, ASME: Journal of Applied Mechanics, 75(2), 021020021027, (2008).
16. R. S. Mackay, and, S. Aubry, Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators, Nonlinearity, 7, 16231643, (1994).
17. S. Aubry, Discrete breathers: Localization and transfer of energy in discrete Hamiltonian nonlinear systems, Physica D, 216, 130, (2006).
18. G. W. Hunt, A. Tordesillas, S. C. Green, and, J. Shi, Force-chain buckling in granular media: a structural mechanics perspective, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368(1910), 249262, (2010).
19. L. Brillouin, Wave propagation in periodic structures, Mineola, NewYork: Dover publicaions, inc., 2nd edn.
20. A. S. Phani, Lattice materials: a unified structural mechanics perspective. Phononics 2011: First International Conference on Phononic Crystals, Metamaterials and Optomechanics Santa Fe, New Mexico, USA.
21. A. S. PhaniSurface waves in lattice materials, Under review.
22. R. S. Langley, A note on the forced boundary conditions for two-dimensional periodic structures with corner freedoms, Journal of Sound and Vibration, 167(2), 377381, (1993).
23. F. Farzbod, M. J. Leamy The treatment of forces in Bloch analysis, Journal of Sound and Vibration, 325(3), 545551, (1993).
24. T. W. Tan, G. R. Douglas, T. Bond, A. S. Phani Compliance and Longitudinal Strain of Cardiovascular Stents: Influence of Cell Geometry, Journal of Medical Devices (ASME), 5(4) (2011).
25. W. Weaver, and P. R. Jonhston, Structural Dynamics by Finite Elements, Prentice-Hall, 1987, Firs edition.,
26. A. Kueh, O. Soykasap, and S. Pellegrino. Thermo-mechanical behaviour of single-ply triaxial weave carbon fibre reinforced plastic. European Conference on Spacecraft Structures, Materials and Testing, Noordwijk, The Netherlands.
27. N. A. Fleck and X. Qiu. The damage tolerance of elastic-brittle, two dimensional isotropic lattices. Journal of Mechanics and Physics of Solids, 55(3):562588, 2007.
28. A. S. Phani. Waves, Buckles, and Homoclinics ASME IMECE 2009 Conference Proceedings, 2009(43888):149–158, 2009.

Data & Media loading...


Article metrics loading...



Lattice materials possessing a spatially periodic microstructure are suitable in weight sensitive multifunctional structural applications such as sandwich panels. They not only possess high specific stiffness but also provide opportunities to tailor acoustic and thermal properties through designing their unit cell topology. This paper seeks to understand their mechanical response under static and dynamic loads from a structural mechanics perspective combining Bloch wave theory with Finite Element Method (FEM). Bringing together results from earlier works, it is shown that three eigenvalue problems, containing the frequency and wave vector as the unknowns, can be used to analyze bulk and surface wave phenomena. The application of eigenvalue problems to band-gaps (spatially extended response), edge effects of Saint Venant type (spatially localised response), and buckling of long cellular structures is shown.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd