On the distribution of elastic forces in disordered structures and materials. I Computer simulation

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

Volumn 461, Issue 2054, 2005, Pages 433-458

  Ngan, A H W ^a  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Cellular materials; Disordered materials; Granular materials; Linear elasticity

Indexed keywords

ARTICLE; CHEMICAL ENGINEERING; COMPUTER SIMULATION; ELASTICITY; FORCE; MATERIALS TESTING; MECHANICS; STATISTICAL ANALYSIS; THEORETICAL STUDY;

EID: 14544269683     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2004.1346     Document Type: Article

References (44)

1. Ashby, M. F., Evans, A. G., Fleck, N. A., Gibson, L. J., Hutchinson, J. W. & Wadley, H. N. G. 2000 Metal foams: a design guide. Boston, MA: Butterworth-Heinemann.
2. Blair, D. L., Mueggenburg, N. W., Marshall, A. H., Jaeger, H. M. & Nagel, S. R. 2001 Force distributions in three-dimensional granular assemblies: effects of packing order and interparticle friction. Phys. Rev. E 63, 041304.
3. Chan, S. H. & Ngan, A. H. W. 2005 Statistical distribution of contact forces in packings of deformable spheres. Mech. Mater. (In the press.)
4. Chao, L. P., Huang, J. H. & Huang, Y. S. 1999 The influence of aspect ratio of voids on the effective elastic moduli of foamed metals. J. Compos. Mater. 33, 2002-2016.
5. Chen, C., Lu, T. J. & Fleck, N. A. 1999 Effect of imperfections on the yielding of two-dimensional foams. J. Mech. Phys. Solids 47, 2235-2272.
6. Cheng, X., Sastry, A. M. & Layton, B. E. 2001 Transport in stochastic fibrous networks. ASME J. Engng Mater. Technol. 123, 12-19.
7. Chuang, C. H. & Huang, J. S. 2002a Yield surfaces for hexagonal honeycombs with plateau borders under in-plane biaxial loads. Acta Mech. 159, 157-172.
8. Chuang, C. H. & Huang, J. S. 2002b Elastic moduli and plastic collapse strength of hexagonal honeycombs with plateau borders. Int. J. Mech. Sci. 44, 1827-1844.
9. Claudin, P., Bouchaud, J.-P., Cates, M. E. & Wittmer, J. P. 1998 Models of stress fluctuations in granular media. Phys. Rev. E 57, 4441-4457.
10. Coppersmith, S. N., Liu, C., Majumdar, S., Narayan, O. & Witten, T. A. 1996 Model for force fluctuations in bead packs. Phys. Rev. E 53, 4673-4685.
11. Erikson, J. M., Mueggenburg, N. W., Jaeger, H. M. & Nagel, S. R. 2002 Force distributions in three-dimensional compressible granular packs. Phys. Rev. E 66, 040301(R).
12. Gao, P. & Gleiter, H. 1987 High-resolution electron-microscope observation of small gold crystals. Acta Metall. 35, 1571-1575.
13. Gibson, L. J. 1989 Modelling the mechanical behaviour of cellular materials. Mater. Sci. Engng A 110, 1-36.
14. Gibson, L. J. & Ashby, M. F. 1997 Cellular solids: structure and properties. Cambridge University Press.
15. Gibson, L. J., Ashby, M. F., Zhang, J. & Triantafillou, T. C. 1989 Failure surfaces for cellular materials under multiaxial loads. 1. Modelling. Int. J. Mech. Sci. 31, 635-663.
16. Johnson, K. L. 1985 Contact mechanics. Cambridge University Press.
17. Ke, M., Hackney, S. A., Milligan, W. W. & Aifantis, E. C. 1995 Observation and measurement of grain rotation and plastic strain in nanostructured metal thin-films. Nanostruct. Mater. 5, 689-697.
18. Kim, H. S. & Al-Hassani, S. T. S. 2001 Plastic collapse of cellular structures comprised of doubly tapered struts. Int. J. Mech. Sci. 43, 2453-2478.
19. Kim, H. S. & Al-Hassani, S. T. S. 2002 A morphological model of vertebral trabecular bone. J. Biomech. 35, 1101-1114.
20. Lewandowska, M., Mathur, H. & Yu, Y. 2001 Dynamics and critical behaviour of the q model. Phys. Rev. E 64, 026107.
21. Liu, C. H., Nagel, S. R., Schecter, D. A., Coppersmith, S. N., Majumdar, S., Narayan, O. & Witten, T. A. 1995 Force fluctuations in bead packs. Science 269, 513-515.
22. Makse, N. A., Johnson, D. L. & Schwartz, L. M. 2000 Packing of compressible granular materials. Phys. Rev. Lett. 84, 4160-4163.
23. Masters, I. G. & Evans, K. E. 1996 Models for the elastic deformation of honeycombs. Compos. Struct. 35, 403-422.
24. Moukarzel, C. F. 1999 Granular matter instability: a structural rigidity point of view. In Rigidity theory and applications (ed. M. F. Thorpe & P. M. Duxbury), pp. 125-142. New York: Kluwer Academic/Plenum.
25. Mueth, D. M., Jaeger, H. M. & Nagel, S. R. 1998 Force distribution in a granular medium. Phys. Rev. E 57, 3164-3169.
26. Narayan, O. 2000 Vector lattice model for stresses in granular materials. Phys. Rev. E 63, 010301R
27. Ngan, A. H. W. 2005 On the distribution of elastic forces in disordered structures and materials. II. A statistical mechanics theory. Proc. R Soc. Lond. A 363. (doi:10.1098/rspa.2004.1417.)
28. Nguyen, M. L. & Coppersmith, S. N. 1999 Properties of layer-by-layer vector stochastic models for force fluctuations in granular materials. Phys. Rev. E 59, 5870-5880.
29. Nguyen, M. L. & Coppersmith, S. N. 2000 Scalar model of inhomogeneous elastic and granular media. Phys. Rev. E 62, 5248-5262.
30. O'Hern, C. S., Langer, S. A., Lin, A. J. & Nagel, S. R. 2002 Random packings of frictionless particles. Phys. Rev. Lett. 88, 075507.
31. Onck, P. R., Andrews, E. W. & Gibson, L. J. 2001 Size effects in ductile cellular solids. I. Modelling. Int. J. Mech. Sci. 43, 681-699.
32. Overaker, D. W., Cuitino, A. M. & Langrana, N. A. 1998 Elastoplastic micromechanical modeling of two-dimensional irregular convex and nonconvex (re-entrant) hexagonal foams. ASME J. Appl. Mech. 65, 748-757.
33. Overaker, D. W., Langrana, N. A. & Cuitino, A. M. 1999 Finite element analysis of vertebral body mechanics with a nonlinear microstructural model for the trabecular core. ASME J. Biomech. Engng 121, 542-550.
34. Papka, S. D. & Kyriakides, S. 1994 In-plane compressive response and crushing of honeycomb. J. Mech. Phys. Solids 42, 1499-1532.
35. Radjai, F., Jean, M., Moreau, J.-J. & Roux, S. 1996 Force distributions in dense two-dimensional granular systems. Phys. Rev. Lett. 77, 274-277.
36. Rajchenbach, J. 2001 Stress transmission through textured granular packings. Phys. Rev. E 63, 041301.
37. Silbert, L. E., Grest, G. S. & Landry, J. W. 2002 Statistics of the contact network in frictional and frictionless granular packings. Phys. Rev. E 66, 061303.
38. Silva, M. J. & Gibson, L. J. 1997 The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids. Int. J. Mech. Sci. 39, 549-563.
39. Simone, A. E. & Gibson, L. J. 1998 Effects of solid distribution on the stiffness and strength of metallic foams. Acta Mater. 46, 2139-2150.
40. Socolar, J. E. S. 1998 Average stresses and force fluctuations in noncohesive granular materials. Phys. Rev. E 57, 3204-3215.
41. Thomas, G. J., Siegel, R. W. & Eastman, J. A. 1990 Grain-boundaries in nanophase palladium: high-resolution electron-microscopy and image simulation. Scr. Metall. Mater. 24, 201-206.
42. Triantafillou, T. C. & Gibson, L. J. 1990 Constitutive modelling of elastic-plastic open-cell foams. ASME J. Biomech. Engng 116, 2772-2776.
43. Warren, W. E. & Kraynik, A. M. 1987 Foam mechanics: the linear elastic response of two dimensional spatially periodic cellular materials. Mech. Mater. 6, 27-37.
44. Warren, W. E., Kraynik, A. M. & Stone, C. M. 1989 A constitutive model for two-dimensional nonlinear elastic foams. J. Mech. Phys. Solids 37, 717-733.