Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T06:06:51.308Z Has data issue: false hasContentIssue false
  • English
  • Français

Large Deformation Analysis for Soft Foams Based on Hyperelasticity

Published online by Cambridge University Press:  05 May 2011

G. Silber ,
M. Alizadeh  and
M. Salimi
G. Silber*
Affiliation:
Department of Computer Science and Engineering, Institute of Material Science, University of Applied Sciences, Frankfurt, Germany
M. Alizadeh*
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
M. Salimi*
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
*
* Professor, correspondence author
** Assistant Professor
*** M.Sc. student
Get access

Abstract

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.

Keywords

HyperelasticityStrain energy functionConstitutive equation.
Type
Articles
Information
Journal of Mechanics , Volume 26 , Issue 3 , September 2010 , pp. 327 - 334
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Gibson, L. J. and Ashby, M.F, Structure and Properties, University Press (1997).Google Scholar
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. 1107–1113 (1996).CrossRefGoogle Scholar
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. 409–418 (1996).CrossRefGoogle Scholar
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. 717–733 (1989).CrossRefGoogle Scholar
5.Warren, W. E. and Kraynik, A. M., “Nonlinear Elastic Behavior of Open-Cell Foams,” Journal of Applied Mechanics, 58, pp. 376–381 (1991).CrossRefGoogle Scholar
6.Full, R., Aspects of invariance in solid mechanics. Advances in Applied Mechanics, 18, pp. 1–75 (1978).Google Scholar
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. 424–434 (1983).CrossRefGoogle Scholar
8.Storakers, B., “On Material Representation and Constitutive Branching in Finite Compressible Elasticity,” Journal of Mechanics and Physics of Solids, 34, pp. 125–145 (1986).CrossRefGoogle Scholar
9.Ogden, R. W., “Recent Advances in the Phenomenological Theory of Rubber Elasticity,” Rubber Chemistry and Technology, 59, pp. 361–383 (1986).CrossRefGoogle Scholar
10. ABAQUS benchmarks manual, Version 6.4. Hibbitt, Karlsson and Sorensen, Inc. (2004).Google Scholar
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. 135–142 (1997).Google Scholar
12.Mills, N. J. and Gilchrist, A., “Modeling the Indentation of Low Density Polymer Foams,” Cellular Polymers, 19 (2000).Google Scholar
13.Mullins, L., “Softening of Rubber by Deformation,” Rubber Chemistry and Technology, 42, pp. 339–362 (1969).CrossRefGoogle Scholar
14.Reese, S., Theorie und Numerik des Stabilitdtsverhaltens Hyperelastischer Festkorper, Ph.D. thesis, TH Darmstadt (1994).Google Scholar
15.Green, A. E. and Adkins, J. E, Large Elastic Deformations, 2nd Ed., Oxford University Press, Oxford (1970).Google Scholar
16.Often, R.H.J.M, van Ginneken, L.P.P.P.: The Annealing Algorithm, Kluwer, Boston (1989).Google Scholar
17.Nelder, J.A. and Mead, R., A simplex method for function minimization. Computer Journal, 7, pp. 308–313 (1969).Google Scholar
18.Schwefel, H.P., Evolution and Optimum Seeking, Wiley and Sons, New York (1995).Google Scholar
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. 2033–2058 (1975).CrossRefGoogle Scholar
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. 136–146 (1994).CrossRefGoogle Scholar
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. 309–324 (2003).CrossRefGoogle Scholar
22.Lion, A., “A Constitutive Model for Carbon Black Filled Rubber: Experimental Investigations and Mathematical Representation. Continuum,” Mechanics Thermodyn., 8, pp. 153–169 (1996).CrossRefGoogle Scholar
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).Google Scholar
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. 249–256 (2001).Google Scholar