Prediction of the Stress–Strain Behavior of Open-Cell Aluminum Foam under Compressive Loading and the Effects of Various RVE Boundary Conditions

  • Behrang Hamidi Ghaleh Jigh
  • Mohammad Ali Farsi
  • Hossein Hosseini Toudeshky


The prediction of the mechanical behavior of metallic foams with realistic microstructure and the effects of various boundary conditions on the mechanical behavior is an important and challenging issue in modeling representative volume elements (RVEs). A numerical investigation is conducted to determine the effects of various boundary conditions and cell wall cross sections on the compressive mechanical properties of aluminum foam, including the stiffness, plateau stress and onset strain of densification. The open-cell AA6101-T6 aluminum foam Duocel is used in the analyses in this study. Geometrical characteristics including the cell size, foam relative density, and cross-sectional shape and thickness of the cell walls are extracted from images of the foam. Then, the obtained foam microstructure is analyzed as a 2D model. The ligaments are modeled as shear deformable beams with elastic-plastic material behavior. To prevent interpenetration of the nodes and walls inside the cells with large deformations, self-contact-type frictionless interaction is stipulated between the internal surfaces. Sensitivity analyses are performed using several boundary conditions and cells wall cross-sectional shapes. The predicted results from the finite element analyses are compared with the experimental results. Finally, the most appropriate boundary conditions, leading to more consistent results with the experimental data, are introduced.


boundary conditions compression experiment metallic foam microstructure 


Conflict of Interests

The authors declare that they have no conflict of interest.


  1. 1.
    C. Tekoglu and P.R. Onck, Size Effects in the Mechanical Behaviour of Cellular Materials, J. Mater. Sci., 2005, 40, p 5911–5917CrossRefGoogle Scholar
  2. 2.
    M.F. Ashby, A.G. Evans, N.A. Fleck, and L.J. Gibson, Metal Foams: A Design Guide, 1st ed., Butterworth-Heinemann, Boston, 2000Google Scholar
  3. 3.
    I. Sridhar and N.A. Fleck, The Multiaxial Yield Behavior of an Aluminium Alloy Foam, J. Mater. Sci., 2005, 40, p 4005–4008CrossRefGoogle Scholar
  4. 4.
    A. Reyes, O.S. Hopperstad, A.G. Hanssen, and M. Langseth, Modelling of Material Failure in Foam-Based Components, Int. J. Impact. Eng., 2004, 30, p 805–834CrossRefGoogle Scholar
  5. 5.
    L. Maheo, Elastic Behaviour of Multi-Scale, Open-Cell Foams, Compos. Part B, 2013, 44, p 172–183CrossRefGoogle Scholar
  6. 6.
    P. Degischer and B. Kriszt, Handbook of Cellular Metals: Production, Processing, Application, Wiley, New York, 2002CrossRefGoogle Scholar
  7. 7.
    J. Gibson and F. Ashby, Cellular Solids: Structure and Properties, 2nd ed., Oxford shire press, Oxford, 1997CrossRefGoogle Scholar
  8. 8.
    V.S. Deshpande and N.A. Fleck, Isotropic Constitutive Models for Metallic Foams, J. Mech. Phys. Solids, 2000, 48, p 1253–1283CrossRefGoogle Scholar
  9. 9.
    P.R. Onck, Application of A Continuum Constitutive Model to Metallic Foam DEN-Specimens in Compression, Int. J. Mech. Sci., 2001, 43, p 2947–2959CrossRefGoogle Scholar
  10. 10.
    Y. Kim and S. Kang, Development of Experimental Method to Characterize Pressure-Dependent Yield Criteria for Polymeric Foams, Polym. Test, 2003, 22, p 197–202CrossRefGoogle Scholar
  11. 11.
    M. Ghayour, H. Hosseini-Toudeshky, M. Jalalvand, and E.J. Barbero, Micro/Macro Approach for Prediction of Matrix Cracking Evolution in Laminated Composites, J. Compos. Mater., 2015, 50, p 2647–2659CrossRefGoogle Scholar
  12. 12.
    G. Sadeghi, H. Hosseini-Toudeshky, and B. Mohammadi, In-Plane Progressive Matrix Cracking Analysis of Symmetric Cross-Ply Laminates With Holes, Fatigue. Fract. Eng. M, 2014, 37, p 290–305CrossRefGoogle Scholar
  13. 13.
    H. Hosseini-Toudeshky, A. Farrokhabadi, and B. Mohammadi, Implementation of a Micro-Meso Approach for Progressive Damage Analysis of Composite Laminates, Struct. Eng. Mech., 2012, 43, p 657–678CrossRefGoogle Scholar
  14. 14.
    R.M. Christensen, Mechanics of Low Density Materials, J. Mech. Phys. Solids, 1986, 34, p 563–578CrossRefGoogle Scholar
  15. 15.
    J.L. Grenestedt, Influence of Wavy Imperfections in Cell Walls on Elastic Stiffness of Cellular Solids, J. Mech. Phys. Solids, 1998, 46, p 29–50CrossRefGoogle Scholar
  16. 16.
    W.E. Warren and A.M. Kraynik, Foam Mechanics: The Linear Elastic Response of Two-Dimensional Spatially Periodic Cellular Materials, Mech. Mater., 1987, 6, p 27–37CrossRefGoogle Scholar
  17. 17.
    W.E. Warren and A.M. Kraynik, The Linear Elastic Properties of Open-Cell Foams, J. Appl. Mech., 1988, 55, p 341–346CrossRefGoogle Scholar
  18. 18.
    W.E. Warren, A.M. Kraynik, and C.M. Stone, A Constitutive Model For Two-Dimensional Nonlinear Elastic Foams, J. Mech. Phys. Solids, 1989, 37, p 717–733CrossRefGoogle Scholar
  19. 19.
    Y. Wang and A.M. Cuitino, Three-Dimensional Nonlinear Open-Cell Foams With Large Deformations, J. Mech. Phys. Solids, 2000, 48, p 961–988CrossRefGoogle Scholar
  20. 20.
    H. Harders, K. Hupfer, and J. Rosler, Influence of Cell Wall Shape And Density on the Mechanical Behaviour of 2D Foam Structures, Acta Mater., 2005, 53, p 1335–1345CrossRefGoogle Scholar
  21. 21.
    H.S. Kim and S.T.S. Al-Hassani, A Morphological Elastic Model of General Hexagonal Columnar Structures, Int. J. Mech. Sci., 2001, 43, p 1027–1060CrossRefGoogle Scholar
  22. 22.
    H.S. Kim and S.T.S. Al-Hassani, The Effect of Doubly Tapered Strut Morphology on the Plastic Yield Surface of Cellular Materials, Int. J. Mech. Sci., 2002, 44, p 1559CrossRefGoogle Scholar
  23. 23.
    M. Avalle, G. Belingardi, and A. Ibba, Mechanical Models of Cellular Solids: Parameters Identification from Experimental Tests, Int. J. Impact. Eng., 2007, 34, p 3–27CrossRefGoogle Scholar
  24. 24.
    D. Miedzinska, T. Niezgoda, and R. Gieleta, Numerical and Experimental Aluminium Foam Microstructure Testing With the Use of Computed Tomography, Comp. Mater. Sci., 2012, 64, p 90–95CrossRefGoogle Scholar
  25. 25.
    “International Standard” Iso13314, Mechanical Testing Of Metals-Ductility Testing-Compression Test for Porous and Cellular Metals, 1st ed, 2011Google Scholar
  26. 26.
    H. Kanahashi, T. Mukai, T.G. Nieh, T. Aizawa, and K. Higashi, Effect of Cell Size on the Dynamic Compressive Properties of Open-Celled Aluminum Foams, Mater. Trans., 2002, 10, p 2548–2553CrossRefGoogle Scholar

Copyright information

© ASM International 2018

Authors and Affiliations

  • Behrang Hamidi Ghaleh Jigh
    • 1
    • 2
  • Mohammad Ali Farsi
    • 1
  • Hossein Hosseini Toudeshky
    • 2
  1. 1.Aerospace Research Institute, Ministry of Science Research and TechnologyTehranIran
  2. 2.Department of Aerospace EngineeringAmirkabir University of TechnologyTehranIran

Personalised recommendations