Modeling of Compression Curves of Flexible Polyurethane Foam with Variable Density, Chemical Formulations and Strain Rates

Document Type : Research Paper


1 Director of Research & Development, All Cell Technologies LLC, Chicago

2 ME Department, Penn State Harrisburg, Middletown


Flexible Polyurethane (PU) foam samples with different densities and chemical formulations were tested in quasi-static stress-strain compression tests. The compression tests were performed using the Lloyd LR5K Plus instrument at fixed compression strain rate of 0.033 s-1 and samples were compressed up to 70% compression strains. All foam samples were tested in the foam rise direction and their compression test stress results were modeled using a constitutive Polymeric or Phenomenological Foam Model (PFM). In this research, a new constitutive PFM model that consists of mechanical systems such as dashpots and springs was formulated to be used for different strain rate experiments. The experimental compression test results for different strain rates were compared to the PFM model results for all foam samples. Both modeling and experimental results showed pretty good agreement. From curve fitting of the experimental tests with the PFM model; different mechanical materials’ coefficients such as elastic and viscous parameters were computed. These mechanical parameters are indeed important characteristics for viscoelastic materials. This model can be used for constant and variable strain rates and for characterizing biomechanical material applications such as bone tissues, muscle tissues and other cellular materials.


[1] Walter Timothy R., Richards Andrew W., Subhash G., 2008, A unified phenomenological model for tensile and compression respoonse of polymeric foams, Journal of Engineering Material Technology 131(1):011009-011015.
[2] Jankowski M., Kotelko M.,2010, Dynamic compression tests of a polyurethane flexible foam as a step in modeling impact of the head to the vehicle seat head restrain, FME Transactions 38:121-127.
[3] Doutres O., Atalla N., Dong K., 2013, A semi-phenomenological model to predict the acoustic behavior of fully and partially reticulated polyurethane foams, Journal of Applied Physics 113: 054901-054912.
[4] Goga V., 2011, Testing and application of new phenomenological materials model for foam materials, Computational Modeling and Advanced Simulations Series:Computational Methods in Applied Sciences 24:67-82.
[5] Jeong K.Y., Cheon S.S., Munshi M. B., 2012, A constitutive model for polyurethane foam with strain rate sensitivity, Journal of Mechanical Science and Technology 26 (7): 2033-2038.
[6] Nagy A., Ko W.L., Lindholm U. S., 1974, Mechanical behavior of foamed materials and dynamic compression, Journal of Cellular Plastics 10:127-134.
[7] Avramescu E.T., Călina M.L., Rusu L., 2009, New approaches to cancellous bone bio-modeling, Romanian Journal of Morphology and Embryology 50(2):229-237.
[8] Saha M.C., Mahfuz H., 2005, Effect of density, microstructure and strain rate on compression behavior of polymeric foams, Journal of Material Science and Engineering A 406: 328-334.
[9] Gibson L.J., Ashby M.F., 1988, Cellular Solids: Structures and Properties, Pergamon Press, Oxford, United Kingdom.
[10] Alzoubi M.F., Tanbour E.Y., Al-Waked R., 2011, Compression and hysteresis curves of nonlinear polyurethane foams under different densities, strain rates and different environmental conditions, Proceeding ASME 9: 101-109.
[11] Rusch K.C., 1969, Load-compression behavior of flexible foams, Journal of Applied Polymer Science 13:2297-2311.
[12] Ashby M.F., 1983, The mechanical properties of cellular solids, Metallurgical Transactions 14:1755-1769.
[13] Gibson L.J., Ashby M.F., 1997, Cellular Solids:Structures and Properties, Cambridge University Press, United Kingdom.
[14] Li K., Gao X.L., Roy A.K.,2003, Micromechanics model for three-dimensional open-cell foams using a tetrakaidecahedral unit cell and castigliano’s second theorem, Composites Science and Technology 63:1769-1781.
[15] Li K., Gao X.L., Roy A.K.,2005, Micromechanics model for three-dimensional open-cell foams using the matrix method for spatial frames, Composites Science and Technology 36: 249-262.
[16] Zhang L., Gurao M., Yang K.H., King A.I., 2011, Material characterization and computer model simulation of low density polyurethane foam used in a rodent traumatic brain injury model, Journal of Neuroscience Methods 198(1):93-98.