Skip to main content Accessibility help

Large Deformation Analysis for Soft Foams Based on Hyperelasticity

  • G. Silber (a1), M. Alizadeh (a2) and M. Salimi (a2)


In Elastomeric foam materials find wide applications for their excellent energy absorption properties. The mechanical property of elastomeric foams is highly nonlinear and it is essential to implement mathematical constitutive models capable of accurate representation of the stress-strain responses of foams. A constitutive modeling method of defining hyperfoam strain energy function by a Simplex Strategy is presented in this work. This study will demonstrate that a strain energy function of finite hyperelasticity for compressible media is applicable to describe the elastic properties of open cell soft foams. This strain energy function is implemented in the FE-tool ABAQUS and proposed for high compressible soft foams. To determine this constitutive equation, experimental data from a uniaxial compression test are used. As the parameters in the constitutive equation are linked in a non-linear way, non-linear optimization routines are adopted. Moreover due to the in homogeneities of the deformation field of the uniaxial compression test, the quality function of the optimization routine has to be determined by an FE-tool. The appropriateness of the strain energy function is tested by a complex loading test.

By using the optimized parameters the FE-simulation of this test is in good accordance with the experimental data.


Corresponding author

* Professor, correspondence author
** Assistant Professor
*** M.Sc. student


Hide All
1.Gibson, L. J. and Ashby, M.F, Structure and Properties, University Press (1997).
2.Ben-Dor, G., Cederbaum, G., Mazor, G. and Igra, O., “Well Tailored ompressive Stress-Strain Relations for Elastomeric Foams in Uni-Axial tress Compression,” Journal of Materials Science, 31, pp. 11071113 (1996).
3.Ben-Dor, G., Mazor, G., Cederbaum, G. and Igra, O., “Stress-Strain Relations for Elastomeric Foams in Uni-, Bi-, and Tri-Axial Compression Modes,” Archive of Applied Mechanics, 66, pp. 409418 (1996).
4.Warren, W. E., Kraynik, A. M. and Stone, C. M., “A Constitutive Model for Two Dimensional Nonlinear Elastic Foams,” Journal of Mechanics and Physics of Solids, 37, pp. 717733 (1989).
5.Warren, W. E. and Kraynik, A. M., “Nonlinear Elastic Behavior of Open-Cell Foams,” Journal of Applied Mechanics, 58, pp. 376381 (1991).
6.Full, R., Aspects of invariance in solid mechanics. Advances in Applied Mechanics, 18, pp. 175 (1978).
7.Twizell, E. H. and Ogden, R. W., “Non-Linear Optimization of the Material Constants in Ogden's Stress- Deformation Function for Incompressible Isotropic Elastic Materials,” Journal of the Australian Mathematical Society, Ser. B, 24, pp. 424434 (1983).
8.Storakers, B., “On Material Representation and Constitutive Branching in Finite Compressible Elasticity,” Journal of Mechanics and Physics of Solids, 34, pp. 125145 (1986).
9.Ogden, R. W., “Recent Advances in the Phenomenological Theory of Rubber Elasticity,” Rubber Chemistry and Technology, 59, pp. 361383 (1986).
10. ABAQUS benchmarks manual, Version 6.4. Hibbitt, Karlsson and Sorensen, Inc. (2004).
11.Setyabudhy, R. H., All, A., Hubbard, R P., Beckett, C. and Averill, R. C, “Measuring and Modeling of Human Soft Tissue and Seat Interaction,” SAE World Congress, 970593, pp. 135142 (1997).
12.Mills, N. J. and Gilchrist, A., “Modeling the Indentation of Low Density Polymer Foams,” Cellular Polymers, 19 (2000).
13.Mullins, L., “Softening of Rubber by Deformation,” Rubber Chemistry and Technology, 42, pp. 339362 (1969).
14.Reese, S., Theorie und Numerik des Stabilitdtsverhaltens Hyperelastischer Festkorper, Ph.D. thesis, TH Darmstadt (1994).
15.Green, A. E. and Adkins, J. E, Large Elastic Deformations, 2nd Ed., Oxford University Press, Oxford (1970).
16.Often, R.H.J.M, van Ginneken, L.P.P.P.: The Annealing Algorithm, Kluwer, Boston (1989).
17.Nelder, J.A. and Mead, R., A simplex method for function minimization. Computer Journal, 7, pp. 308313 (1969).
18.Schwefel, H.P., Evolution and Optimum Seeking, Wiley and Sons, New York (1995).
19.James, A.G. and Green, A., “Strain Energy Functions of Rubber. Ii the Characterization of Filled Vilcanisates,” Journal of Applied Polymer Science, 19, pp. 20332058 (1975).
20.Van den Bogert, P.A.J. and de Borst, R., “On the Behavior of Rubberlike Materials in Compression and Shear,” Archives of Applied Mechanics, 64, pp. 136146 (1994).
21.Hartmann, S., Tschope, T., Schreiber, L. and Haupt, P., “Finite Deformations of a Carbonblack-Filled Rubber. Experiment, Optical Measurement and Material Parameter Identification Using Finite Elements,” European Journal of Mechanics A/Solids, 22, pp. 309324 (2003).
22.Lion, A., “A Constitutive Model for Carbon Black Filled Rubber: Experimental Investigations and Mathematical Representation. Continuum,” Mechanics Thermodyn., 8, pp. 153169 (1996).
23.Chagnon, G., Marckmann, G., Verron, E., Gornet, L., Charrier, P. and Ostoja-Kuczynski, E., “A New Modeling of the Mullins Effect and the Viscoelasticity of Elastomer Based on a Physical Approach,” Proceedings of the International Rubber Conference. Prague, Czech Republic (2002).
24.Ehlers, W. and Markert, B., Viscoelastic polyurethane foams at finite deformations. In: Wall, W. A., Bletzinger, K.U. and Schweizerhof, K. Eds., Trends in Computational Structural Mechanics, CIMNE, Barcelona, pp. 249256 (2001).


Large Deformation Analysis for Soft Foams Based on Hyperelasticity

  • G. Silber (a1), M. Alizadeh (a2) and M. Salimi (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed