Simulated optimisation of disordered structures with negative Poisson's ratios

Mechanics of Materials

Volumn 41, Issue 8, 2009, Pages 919-927

  Horrigan, E J ^a   Smith, C W ^a   Scarpa, F L ^b   Gaspar, N ^a   Javadi, A A ^a   Berger, M A ^a   Evans, K E ^a  

^a UNIVERSITY OF EXETER   (United Kingdom)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DISORDERED STRUCTURES; HETEROGENEOUS MATERIALS; MANUFACTURING PROCESS; MATERIAL PROPERTY; NEGATIVE POISSON'S RATIOS; OPTIMISATION; REAL-WORLD; THREE DIMENSIONS; TWO-DIMENSION; UNIT CELLS;

HETEROGENEOUS NETWORKS; MECHANICAL PROPERTIES; POISSON DISTRIBUTION; POISSON EQUATION; STRUCTURAL OPTIMIZATION; TWO DIMENSIONAL;

POISSON RATIO;

EID: 65649084499     PISSN: 01676636     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmat.2009.04.008     Document Type: Article

References (48)

1. ABAQUS 6.5-5, 2007. Dassault Systems, Providence, RI, USA.
2. Alderson A., and Evans K.E. Rotation and dilation deformation mechanisms for auxetic behaviour in the α-cristobalite tetrahedral framework structure. Physics and Chemistry of Minerals 28 (2001) 711-718
3. Alderson K.L., and Evans K.E. The fabrication of microporous polyethylene having a negative Poisson's ratio. Polymer 33 20 (1992) 4435-4438
4. ANSYS 11.0, 2007. ANSYS Inc, Canonsburg, PA, USA.
5. Baughman R.H., Shacklette J.M., Zakhidov A.A., and Stafstrom S. Negative Poisson's ratios as a common feature of cubic metals. Nature 392 (1998) 362-365
6. Bezazi A., and Scarpa F. Mechanical behaviour of conventional and negative Poisson's ratio thermoplastic polyurethane foam under compressive cyclic loading. International Journal of Fatigue 29 5 (2007) 922-930
7. Caddock B.D., and Evans K.E. Microporous materials with negative Poisson's ratios 1: microstructure and mechanical properties. Journal of Physics D: Applied Physics 22 12 (1989) 1877-1882
8. Davis L. Handbook of Genetic Algorithms (1991), Van Nostrand Reinhold, USA
9. Evans K.E., Nkansah M.A., and Hutchinson I.J. Molecular network design. Nature 353 (1991) 124
10. Evans K.E., and Alderson A. Auxetic materials: functional materials and structures from lateral thinking. Advanced Materials 9 12 (2000) 617-627
11. Evans K.E., and Grima J.N. Auxetic behaviour from rotating squares. Journal of Material Science Letters 19 (2000) 1563-1565
12. Friis E.A., Lakes R.S., and Park J.B. Negative Poisson's ratio polymeric and metallic foams. Journal of Materials Science 23 12 (1988) 4406-4414
13. Gaspar N., and Koenders M.A. Micromechanic formulation of macroscopic structures in a granular medium. Journal of Engineering Mechanics 127 10 (2001) 987-993
14. Gaspar, N., Koenders, M.A. 2001b. Estimates of the shear modulus of a granular assembly using heterogeneous media techniques. In: Powders and Grains Conference, July 1993, Birmingham, UK, pp. 165-168.
15. Gaspar N., Smith C.W., and Evans K.E. The effect of heterogeneity on the elastic properties of auxetic materials. Journal of Applied Physics 94 9 (2003) 6143-6149
16. Gaspar N., Ren X.J., Smith C.W., Grima J.N., and Evans K.E. Novel honeycombs with auxetic behaviour. Acta Materialia 53 8 (2005) 2439-2445
17. Gaspar N., Smith C.W., Behne E.A., Seidler G.T., and Evans K.E. Quantitative analysis of the microscale of auxetic foams. Physica Status Solidi B 242 3 (2005) 550-560
18. Gibson L.J., Ashby M.F., and Schajer G.S. The mechanics of two-dimensional cellular materials. Proceedings of the Royal Society of London A 382 (1982) 22-45
19. Gibson L.J., and Ashby M.F. Cellular Solids: Structure and Properties (1997), Cambridge University Press, Cambridge pp. 105
20. Gunton D.J., and Saunders G.A. Young's modulus and Poisson's ratio of arsenic, antimony and bismuth. Journal of Materials Science 7 9 (1972) 1061
21. Guo X.E., and Gibson L.J. Behaviour of intact and damaged honeycombs: a finite element study. International Journal of Mechanical Sciences 41 (1999) 85-105
22. Javadi A.A., Farmani R., and Tan T.P. A hybrid intelligent genetic algorithm. Advanced Engineering Informatics 19 (2005) 255-262
23. Koenders M.A. Evolution of spatially structured elastic materials using a harmonic density function. Physical Review E 56 (1997) 5585-5593
24. Koenders M.A. Constitutive properties of contacting materials with a finite-sized microstructure. Molecular Simulation 13 13 (2005) 837-882
25. Koenders M.A., and Gaspar N. The auxetic properties of a network of bending beams. Physica Status Solidi B 245 3 (2008) 539-544
26. Kuhn M.R. Heterogeneity and patterning in the quasi-static behaviour of granular materials. Granular Matter 4 4 (2003) 155-166
27. Lakes R. Foam structures with a negative Poisson's ratio. Science 235 (1987) 1038-1040
28. Lakes R., 1987b. Patent Application PCT/US87/01148 Polyhedron Cell Structure and Making of the Same.
29. Lakes R., Rosakis P., and Ruina A. Microbuckling instability in elastomeric cellular solids. Journal of Material Science 28 17 (1993) 4667-4672
30. Lees C., Vincent J.F.V., and Hillerton J.E. Poisson's ratio in skin. BioMedical Materials and Engineering 19 (1991) 19-23
31. Lew T.L., Spencer A.B., Scarpa F., Worden K., Rutherford A., and Hemez F. Identification of response surface models using genetic programming. Mechanical Systems and Signal Processing 20 (2006) 1819-1831
32. Masters I.G., and Evans K.E. Models for the elastic deformation of honeycombs. Composite Structures 35 4 (1996) 403-422
33. Mayer D.G., Kinghorn B.P., and Archer A.A. Differential evolution - an easy and efficient evolutionary algorithm for model optimisation. Agricultural Systems 83 3 (2005) 315-328
34. Mitchell M. An Introduction to Genetic Algorithms (1996), MIT Press, USA
35. Nye JF. Physical Properties of Crystals (1957), Oxford University Press, Oxford (Chapter 8)
36. Pathria D., and Morris J.L. A variable spectral collocation algorithm for the solution of non-linear evolutionary equations. Applied Numerical Mathematics 8 3 (1991) 243-256
37. Sanders W.S., and Gibson L.J. Mechanics of BCC and FCC hollow sphere foams. Materials Science and Engineering A 383 (2003) 150-161
38. Sanders W.S., and Gibson L.J. Mechanics of hollow sphere foams. Materials Science and Engineering A 347 (2003) 70-85
39. Scarpa F., Blain S., Lew T., Perrott D., Ruzzene M., and Yates J.R. Elastic buckling of hexagonal chiral cell honeycombs. Composites Part A (Applied Science and Manufacturing) 38 2 (2007) 280-289
40. Silva M.J., Hayes W.C., and Gibson L.J. The effects of non-periodic microstructure on the elastic properties of two-dimensional cellular solids. International Journal of Mechanical Sciences 37 11 (1995) 1161-1177
41. Silva M.J., and Gibson L.J. The effects of non-periodic microstructure and defects on the compressive strength of three-dimensional cellular solids. International Journal of Mechanical Sciences 39 5 (1997) 549-563
42. Storn, R., 1996. On the use of differential evolution for function optimisation. NAPHIS.
43. Veronda D.R., and Westmann R.A. Mechanical characterization of skin-finite deformations. Journal of Biomechanics 3 1 (1970) 111
44. Warren W.E., and Kraynik A.M. The linear elastic properties of open-cell foams. Journal of Applied Mechanics 55 (1988) 341-346
45. Warren W.E., and Kraynik A.M. The nonlinear elastic properties of open-cell foams. Journal of Applied Mechanics 58 (1991) 376-381
46. Williams J.L., and Lewis J.L. Properties and an anisotropic mode of cancellous bone from the proximal tibial epiphysis. Journal of Biomechanical Engineering-Transactions of the ASME 104 (1982) 50-56
47. Williams J.R., and Rege N. The development of circulation cell structures in granular materials undergoing compression. Powder Technology 90 (1997) 187-194
48. Yang S., Gokhale A.M., and Shan Z. Utility of microstructure modelling for simulation of micro-mechanical response of composites containing non-uniformly distributed fibres. Acta Materialia 48 (1999) 2307-2322