Mechanics of elastic networks

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 470, Issue 2172, 2014, Pages

  Norris, Andrew N ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Elasticity; Lattice; Pentamode

Indexed keywords

ELASTICITY; MATERIALS PROPERTIES;

ALGEBRAIC FORMULAS; ANALYTICAL EXPRESSIONS; EFFECTIVE PROPERTY; ELASTIC NETWORKS; LATTICE; PENTAMODE; PERIODIC LATTICES; THEORETICAL APPROACH;

LATTICE CONSTANTS;

EID: 84907833329     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2014.0522     Document Type: Article

References (30)

1. Bell AG. 1903 Tetrahedral principle in kite structures. Nat. Geogr. Mag. 16, 219-251.
2. Zheng X et al. 2014 Ultra-light, ultra-stiff mechanical metamaterials. Science 344, 1373-1377. (doi:10.1126/science.1252291)
3. Gurtner G, Durand M. 2009 Structural properties of stiff elastic networks. Europhys. Lett. 87, 24001. (doi:10.1209/0295-5075/87/24001)
4. Gurtner G, Durand M. 2014 Stiffest elastic networks. Proc. R. Soc. A 470, 20130611. (doi:10.1098/rspa.2013.0611)
5. Milton GW, Cherkaev AV. 1995 Which elasticity tensors are realizable? J. Eng. Mater. Tech. 117, 483-493. (doi:10.1115/1.2804743)
6. Milton GW. 2001 The theory of composites. Cambridge, UK: Cambridge University Press.
7. Fleck NA, Deshpande VS, Ashby MF. 2010 Micro-architectured materials: past, present and future. Proc. R. Soc. A 466, 2495-2516. (doi:10.1098/rspa.2010.0215)
8. Maxwell JC. 1864 On the calculation of the equilibrium and stiffness of frames. Phil. Mag. 27, 294-299.
9. Sun K, Souslov A, Mao X, Lubensky TC. 2012 Surface phonons, elastic response, and conformal invariance in twisted kagome lattices. Proc. Natl Acad. Sci. USA 109, 12369-12374. (doi:10.1073/pnas.1119941109)
10. Deshpande VS, Fleck NA, Ashby MF. 2001 Effective properties of the octet-truss lattice material. J. Mech. Phys. Solids 49, 1747-1769. (doi:10.1016/s0022-5096(01)00010-2)
11. Deshpande VS, Ashby MF, Fleck NA. 2001 Foam topology: bending versus stretching dominated architectures. Acta Mater. 49, 1035-1040. (doi:10.1016/s1359-6454(00)00379-7)
12. Hutchinson RG, Fleck NA. 2006 The structural performance of the periodic truss. J. Mech. Phys. Solids 54, 756-782. (doi:10.1016/j.jmps.2005.10.008)
13. Thomson W. 1856 Elements of a mathematical theory of elasticity. Phil. Trans. R. Soc. Lond. 146, 481-498. (doi:10.1098/rstl.1856.0022)
14. Norris AN. 2008 Acoustic cloaking theory. Proc. R. Soc. A 464, 2411-2434. (doi:10.1098/rspa.2008.0076)
15. Kadic M, Bückmann T, Schittny R, Wegener M. 2013 On anisotropic versions of three-dimensional pentamode metamaterials. New J. Phys. 15, 023029. (doi:10.1088/1367-2630/15/2/023029)
16. Christensen RM. 2000 Mechanics of cellular and other low-density materials. Int. J. Solids Struct. 37, 93-104. (doi:10.1016/s0020-7683(99)00080-3)
17. Nye JF. 1985 Physical properties of crystals. Oxford, UK: Clarendon Press.
18. Tollenaere H, Caillerie D. 1998 Continuous modeling of lattice structures by homogenization. Adv. Eng. Softw. 29, 699-705. (doi:10.1016/S0965-9978(98)00034-9)
19. Martinsson PG, Babuška I. 2007 Homogenization of materials with periodic truss or frame micro-structures. Math. Models Methods Appl. Sci. 17, 805-832. (doi:10.1142/S0218 20250700211X)
20. Martinsson PG, Babuška I. 2007 Mechanics of materials with periodic truss or frame microstructures. Arch. Rat. Mech. Anal. 185, 201-234. (doi:10.1007/s00205-006-0044-2)
21. Wang XL, Stronge WJ. 1999 Micropolar theory for two-dimensional stresses in elastic honeycomb. Proc. R. Soc. Lond. A 455, 2091-2116. (doi:10.1098/rspa.1999.0394)
22. Kumar RS, McDowell DL. 2004 Generalized continuum modeling of 2-D periodic cellular solids. Int. J. Solids Struct. 41, 7399-7422. (doi:10.1016/j.ijsolstr.2004.06.038)
23. Wang Y, Cuitino A. 2000 Three-dimensional nonlinear open-cell foams with large deformations. J. Mech. Phys. Solids 48, 961-988. (doi:10.1016/S0022-5096(99)00060-5)
24. Christensen RM. 1995 The hierarchy of microstructures for low density materials. In Theoretical, experimental, and numerical contributions to the mechanics of fluids and solids (eds J. Casey, M. Crochet), pp. 506-521. Basle, Switzerland: Birkhäuser.
25. Warren WE, Kraynik AM. 1997 Linear elastic behavior of a low-density Kelvin foam with open cells. J. Appl. Mech. 64, 787-794. (doi:10.1115/1.2788983)
26. Zhu HX, Knott JF, Mills NJ. 1997 Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells. J. Mech. Phys. Solids 45, 319-343. (doi:10.1016/s0022-5096(96)00090-7)
27. Walpole LJ. 1984 Fourth rank tensors of the thirty-two crystal classes: multiplication tables. Proc. R. Soc. Lond. A 391, 149-179. (doi:10.1098/rspa.1984.0008)
28. Norris AN. 2006 Poisson's ratio in cubic materials. Proc. R. Soc. A 462, 3385-3405. (doi:10.1098/rspa.2006.1726)
29. Warren WE, Kraynik AM. 1988 The linear elastic properties of open-cell foams. J. Appl. Mech. 55, 341-346. (doi:10.1115/1.3173680)
30. Kim HS, Al-Hassani S. 2003 Effective elastic constants of two-dimensional cellular materials with deep and thick cell walls. Int. J. Mech. Sci. 45, 1999-2016. (doi:10.1016/j. ijmecsci.2004.02.002)