Skip to main content
SpringerLink
Log in
SpringerLink
Log in

The elastic behavior of low-density cellular plastics

  • Chapter
Low density cellular plastics

Abstract

The mechanical behavior of cellular solids is determined by their structure and the mechanical behavior of their constituents. Cellular plastics in particular are available with a broad range of mechanical response because they can be produced with substantially different cell structure and they can also be produced from substantially different polymers. The practical desire to engineer cellular plastics, which we will also refer to as foams, motivates the investigation of structure-property relations. This chapter focuses on the development of theoretical models to predict and understand the connection between the cellular structure of foamed materials and the mechanical response under a broad range of deformation conditions. The micromechanical theories that will be described provide a complete description of deformation and stress on both the microscopic scale of the cells and the macroscopic scale of the foam. This permits one to identify those features of foam morphology and the corresponding micromechanical mechanisms that control global mechanical behavior.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 279.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Meinecke, E. A. and Clark, R. C. (1973) Mechanical Properties of Polymeric Foams, Technomic, Westport, CT.

    Google Scholar 

  2. Hilyard, N. C. (ed.) (1982) Mechanics of Cellular Plastics, Macmillan, New York.

    Google Scholar 

  3. Gibson, L. J. and Ashby, M. F. (1988) Cellular Solids, Pergamon, Oxford.

    Google Scholar 

  4. Gent, A. N. and Thomas, A. G. (1959) The deformation of foamed elastic materials. J. Appl. Polymer Sci., 1, 107–13.

    Article  CAS  Google Scholar 

  5. Gent, A. N. and Thomas, A. G. (1963) Mechanics of foamed elastic materials. Rubber Chem. Tech., 36, 597–610.

    Article  CAS  Google Scholar 

  6. Lederman, J. M. (1971) The prediction of the tensile properties of flexible foams. J. Appl Polymer Sci., 15, 693–703.

    Article  CAS  Google Scholar 

  7. Kanakkanatt, S. V. (1973) Mechanical anisotropy of open-cell foams. J. Cellular Plastics, 9, 50–3.

    Article  CAS  Google Scholar 

  8. Christensen, R. M. (1986) Mechanics of low density materials. J. Mech. Phys. Solids, 34, 563–78.

    Article  Google Scholar 

  9. Ko, W. L. (1965) Deformations of foamed elastomers. J. Cellular Plastics, 1, 45–50.

    Article  Google Scholar 

  10. Menges, G. & Knipschild, F. (1975) Estimation of mechanical properties for rigid Polyurethane foams. Polymer Eng. Sci., 15, 623–7.

    Article  CAS  Google Scholar 

  11. Menges, G. and Knipschild, F. (1982) Stiffness and strength — Rigid plastic foams, in Mechanics of Cellular Plastics (ed. N. C. Hilyard), Macmillan, New York, pp. 27–72.

    Google Scholar 

  12. Gibson, L. J. and Ashby, M. F. (1982) The mechanics of three-dimensional cellular materials. Proc. Royal Soc. London A, 382, 43–59.

    Article  CAS  Google Scholar 

  13. Gibson, L. J, Ashby, M. F, Schajer, G. S. and Robertson, C. I. (1982) The mechanics of two-dimensional cellular materials. Proc. Royal Soc. London A, 382, 25–42.

    Article  Google Scholar 

  14. Gibson, L. J., Easterling, K. E. and Ashby, M. F. (1981) The structure and mechanics of cork. Proc. Royal Soc. London A, 377, 99–117.

    Article  Google Scholar 

  15. Easterling, K. E., Harrysson, R., Gibson, L. J. and Ashby, M. F. (1982) On the mechanics of balsa and other woods. Proc. Royal Soc. London A, 383, 31–41.

    Article  Google Scholar 

  16. Kraynik, A. M. (1988) Foam flows. Annual Review of Fluid Mechanics, 20, 325–57.

    Article  Google Scholar 

  17. Princen, H. M. (1983) Rheology of foams and highly concentrated emulsions. I. Elastic properties and yield stress of a cylindrical model system. J. Colloid Interface Sci., 91, 160–75.

    Article  CAS  Google Scholar 

  18. Khan, S. A. and Armstrong, R. C. (1986) Rheology of foams: I. Theory for dry foams. J. Non-Newtonian Fluid Mech., 22, 1–22.

    Article  CAS  Google Scholar 

  19. Kraynik, A. M. and Hansen, M. G. (1986) Foam and emulsion rheology: A quasistatic model for large deformations of spatially periodic cells. J. Rheology, 30, 409–39.

    Article  CAS  Google Scholar 

  20. Reinelt, D. A. and Kraynik, A. M. (1989) Viscous effects in the rheology of foams and concentrated emulsions. J. Colloid Interface Sci., 132, 491–503.

    Article  CAS  Google Scholar 

  21. Reinelt, D. A. and Kraynik, A. M. (1990) On the shearing flow of foams and concentrated emulsions. J. Fluid Mech., 215, 431–55.

    Article  CAS  Google Scholar 

  22. Kraynik, A. M., Reinelt, D. A. and Princen, H. M. (1991) The nonlinear elastic behavior of polydisperse hexagonal foams and concentrated emulsions. J. Rheology, 35, 1235–53.

    Article  CAS  Google Scholar 

  23. Warren, W. E. and Kraynik, A. M. (1987) Foam mechanics: the linear elastic response of two-dimensional spatially periodic cellular materials. Mechanics of Materials, 6, 27–37.

    Article  Google Scholar 

  24. Plateau, J. (1873) Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires. Gauthier-Villars, Paris.

    Google Scholar 

  25. Muskhelishvili, N. L (1953) Some Basic Problems of the Mathematical Theory of Elasticity, 3rd edn, Noordhoff, Groningen.

    Google Scholar 

  26. Lekhnitskii, S. G. (1963) Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, San Francisco.

    Google Scholar 

  27. Eubanks, R. A. and Sternberg, E. (1954) On the axisymmetric problem of elasticity theory for a medium with transverse isotropy. J. Rat. Mech. and Analysis, 3, 89–101.

    Google Scholar 

  28. Warren, W. E., Kraynik, A. M. and Stone, C. M. (1989) A constitutive model for two-dimensional nonlinear elastic foams. J. Mech. Phys. Solids, 37, 717–33.

    Article  Google Scholar 

  29. ABAQUS (1984) User’s Manual, Version 4.5, Hibbitt, Karlsson and Sorensen, Providence, RI.

    Google Scholar 

  30. Green, A. E. and Zerna, W. (1954) Theoretical Elasticity, Oxford, London.

    Google Scholar 

  31. Warren, W. E. and Kraynik, A. M. (1988) The linear elastic properties of open-cell foams. J. Appl. Mech., 55, 341–7.

    Article  Google Scholar 

  32. Goldstein, H. (1950) Classical Mechanics, Addison-Wesley, Cambridge, MA.

    Google Scholar 

  33. Jackson, C. L., Shaw, M. T. and Aubert, J. H. (1991) The linear elastic properties of microcellular foams. Polymer, 32, 221–5.

    Article  CAS  Google Scholar 

  34. Williams, J. M. (1988) Compression moduli of some PMP microcellular foams. J. Mat. Sci, 23, 900–4.

    Article  CAS  Google Scholar 

  35. LeMay, J. D., Hopper, R. W., Hrubesh, L. W. and Pekala, R. W. (1990) Low-density Microcellular materials. MRS Bulletin, 15, 19–45.

    CAS  Google Scholar 

  36. Warren, W. E. and Kraynik, A. M. (1991) The nonlinear elastic behavior of open-cell foams. J. Appl. Mech. 58, 376–81.

    Article  Google Scholar 

  37. Green, A. E., and Adkins, J. E. (1960) Large Elastic Deformations, Clarendon, Oxford.

    Google Scholar 

  38. Weaire, D. and Kermode, J. P. (1983) Computer simulation of a two-dimensional soap froth. I. Method and motivation. Phil. Mag. B, 48, 245–59.

    Article  CAS  Google Scholar 

  39. Weaire, D. and Fu, T.-L. (1988) The mechanical behavior of foams and emulsions. J. Rheology, 32, 271–83.

    Article  CAS  Google Scholar 

  40. Herdtle, T. (1991) Numerical studies of foam dynamics. PhD thesis, University of California at San Diego, La Jolla, CA.

    Google Scholar 

  41. Matzke, E. B. (1946) The three-dimensional shape of bubbles in foam — An analysis of the role of surface forces in three-dimensional cell shape determination. Am. J. Botany, 33, 58–80.

    Article  CAS  Google Scholar 

  42. Kelvin, Lord (Thompson, W.) (1887) On the division of space with minimum partitional area. Phil. Mag., 24, 503–14.

    Article  Google Scholar 

  43. Budiansky, B. and Kimmel, E. (1987) Elastic moduli of lungs. J. Appl. Mech., 54, 351–8.

    Article  Google Scholar 

  44. Klintworth, J. W. and Strong, W. J. (1989) Plane punch indentation of a honeycomb. Int. J. Mech. Sci., 31, 359–78.

    Article  Google Scholar 

  45. Strong, W. J. and Shim, V. P. W. (1988) Microdynamics of crushing in cellular solids. ASME J. Engr. Mat. & Tech., 110, 185–90.

    Article  Google Scholar 

  46. Truesdell, C. and Noll, W. (1965) The non-linear field theories of mechanics, in Handbuch der Physik, Band III/3 (ed. S. Flügge), Springer-Verlag, Berlin, pp. 60–6.

    Google Scholar 

  47. Lakes, R. (1987) Foam structures with a negative Poisson’s ratio. Science, 235, 1038–40.

    Article  CAS  Google Scholar 

  48. Friis, E. A., Lakes, R. and Park, J. B. (1988) Negative Poisson’s ratio polymeric and metallic foams. J. Materials Sci., 23, 4406–14.

    Google Scholar 

  49. Wei, G. (1992) Negative and conventional Poisson ratios of polymeric networks with special microstructures. J. Chem. Phys., 96, 3226–33.

    Article  CAS  Google Scholar 

  50. Wei, G. and Edwards, S. F. (1992) Polymer networks with negative Poisson’s ratios. Comput. Polym. Sci., 2(1), 44–54.

    CAS  Google Scholar 

  51. Warren, T. L. (1990) Negative Poisson’s ratio in a transversely isotropic foam, J. Appl. Physics, 67, 7591–4.

    Article  Google Scholar 

Download references

Authors
  1. Andrew M. Kraynik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William E. Warren
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Materials Research Institute, Division of Applied Physics, Sheffield Hallam University, UK

    N. C. Hilyard (Honorary Research Fellow) (Honorary Research Fellow)

  2. Company Science and Technology Associate, International R&T Centre, ICI Polyurethanes, Everberg, Belgium

    A. Cunningham

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Kraynik, A.M., Warren, W.E. (1994). The elastic behavior of low-density cellular plastics. In: Hilyard, N.C., Cunningham, A. (eds) Low density cellular plastics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1256-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-1256-7_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4547-6

  • Online ISBN: 978-94-011-1256-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation