Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots

Journal of the Mechanics and Physics of Solids

Volumn 61, Issue 7, 2013, Pages 1543-1560

  Milton, Graeme Walter ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

Foam material; Inhomogeneous material; Microstructures; Rods and cables; Unimode material

Indexed keywords

AFFINE DEFORMATION; DEGREE OF APPROXIMATION; DIMENSIONAL SPACES; EXPLICIT CONSTRUCTIONS; FOAM MATERIAL; INHOMOGENEOUS MATERIALS; MACROSCOPIC DEFORMATIONS; MODE OF DEFORMATION;

BARS (METAL); CHARACTERIZATION; MATERIALS; METAMATERIALS; MICROSTRUCTURE; TRAJECTORIES;

DEFORMATION;

EID: 84877579754     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2012.08.011     Document Type: Article

References (25)

1. R.F. Almgren An isotropic three-dimensional structure with Poisson's ratio=-1 J. Elasticity 15 1985 427 430
2. Artobolevskii, I., 1964. Mechanisms for the Generation of Plane Curves. Pergamon, Oxford. xv + 278 pp.
3. translated from the 1959 Russian Book by R.D. Wills. LCCN 63-11926
4. Bückmann, T., Kadic, M., Milton, G., Thiel, M., Wegener, M. Realizability of three-dimensional dilational materials, in preparation.
5. T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener Tailored 3d mechanical metamaterials made by dip-in direct-laser-writing optical lithography Adv. Mater. 24 20 2012 2710 2714
6. G.N. Greaves, A.L. Greer, R. Lakes, and T. Rouxel Poisson's ratio and modern materials Nat. Mater. 10 2011 823 837
7. J.N. Grima, and K.E. Evans Auxetic behaviour from rotating squares J. Mater. Sci. Lett. 19 2000 1563 1565
8. J.N. Grima, and K.E. Evans Auxetic behaviour from rotating triangles J. Mater. Sci. 41 2006 3193 3196
9. S.D. Guest, and J.W. Hutchinson On the determinacy of repetitive structures J. Mech. Phys. Solids 51 2003 383 391
10. R.G. Hutchinson, and N.A. Fleck The structural performance of the periodic truss J. Mech. Phys. Solids 54 2006 756 782
11. M. Kadic, T. Bückmann, N. Stenger, M. Thiel, and M. Wegener On the practicability of pentamode mechanical metamaterials Appl. Phys. Lett. 100 19 2012 191901
12. V. Kapko, M.M.J. Treacy, M.F. Thorpe, and S.D. Guest On the collapse of locally isostatic networks Proc. Phys. Soc. A 465 2009 3517 3530
13. M. Kapovich, and J.J. Millson Universality theorems for configuration spaces of planar linkages Topology 41 2002 1051 1107
14. J.P. Keener Principles of Applied Mathematics Transformation and Approximation 2000 Westview Press Cambridge, MA pp. 69-72. ISBN 0-7382-0129-4
15. A.B. Kempe On a general method of describing plane curves of the n-th degree by linkwork Proc. Lond. Math. Soc. 7 1875 213 216
16. R. Lakes Foam structures with a negative Poisson's ratio Science 235 1987 1038 1040
17. U.D. Larsen, O. Sigmund, and S. Bouwstra Design and fabrication of compliant micro-mechanisms and structures with negative Poisson's ratio J. Microelectromech. Syst. 6 1997 99 106
18. G.W. Milton Composite materials with Poisson's ratios close to -1 J. Mech. Phys. Solids 40 5 1992 1105 1137
19. G.W. Milton The Theory of Composites 2002 Cambridge University Press Cambridge, United Kingdom xxviii + 719 pp. ISBN: 0-521-78125-6 (LCCN TA418.9.C6M58 2001)
20. G.W. Milton, and A.V. Cherkaev Which elasticity tensors are realizable? ASME J. Eng. Mater. Technol. 117 1995 483 493
21. H. Mitschke, J. Schwerdtfeger, F. Schury, M. Stingl, C. Körner, R.F. Singer, V. Robins, K. Mecke, and G.E. Schröder-Turk Finding auxetic frameworks in periodic tessellations Adv. Mater. 23 2011 2669 2674
22. A.N. Norris Acoustic cloaking theory Proc. R. Soc. A 464 2097 2008 2411 2434
23. D. Prall, and R.S. Lakes Properties of a chiral honeycomb with a Poisson's ratio -1 Int. J. Mech. Sci. 39 1996 305 314
24. A. Sartbaeva, S.A. Wells, M.M.J. Treacy, and M.F. Thorpe The flexibility window in zeolites Nat. Mater. 5 2006 962 965
25. Sun, K., Souslov, A., Mao, X., Lubensky, T.C., 2012. Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices. arxiv:hepth/1112.1109v1 (cond-mat.soft).