Quasi-static behavior identification of polyurethane foam using a memory integer model and the difference-forces method

Abstract

Flexible polyurethane foam is widely used in numerous comfort applications such as automotive seat cushions and mattresses. It would be interesting to design a mechanical model which describes the behavior of this material in a series of test conditions. This study is devoted to the modeling of the quasi-static behavior of polyurethane foam using a memory integer model. Polyurethane foam undergoing large compressive deformation exhibits highly nonlinear elasticity and a viscoelastic behavior. The memory integer model describes the nonlinearity in a polynomial function and the viscoelasticity through a convolution function. Uniaxial compression tests help to identify the mechanical parameters of the model. The difference between the force responses of foam in load and unload phases constitute the base element of the method used in this article. Numerous precautions are taken into account to obtain accurate results which verify the thermodynamic conditions. Finally, the reliability as well as the limits of the memory integer model are discussed.

Keywords

flexible polyurethane foam quasi-static behavior linear viscoelasticity thermodynamic conditions of model memory integer model identification parameters

Get full access to this article

View all access options for this article.

References

Gibson LJ and Ashby MF Cellular solids: structure and properties. 2nd ed. Cambridge: Cambridge University Press , 1997.

American Society for Testing Material. Plastics (II): ASTM D3574-05 standard test methods for flexible cellular materials and molded urethane foams. Philadelphia: ASTM, 2010.

Goangseup Zi , Byeong MK , Yoon KH and Young HL An experimental study on static behaviour of a GFRP bridge deck filled with a polyurethane foam. Compos Struct 2008; 82(2): 257-268.

Tu ZH , Shim VPW and Lim CT Plastic deformation modes in rigid polyurethane foam under static loading . Int J Solids Struct 2001; 38(50-51): 9267-9279.

Deng R. , Davies P. and Bajaj AK A nonlinear fractional derivative model for large uni-axial deformation behaviour of polyurethane foam. Signal Process 2006; 86(10): 2728-2743.

Dupuis LR and Aubry E. Development and comparison of foam comprehensive law in great deformation . In: SEM XI International Congerss, Orlando, Florida, USA, 2008.

Njeugna N. , Schacher L. , Adolphe CD , Dupuis LR and Aubry E. Comparison of compression behaviour of PU foam and 3D nonwoven. In: Fiber Society 2008 Fall Annual Meeting and Technical Conference , Boucherville, Canada, 2008.

Ouellet S. , Cronin D. and Worswick M. Compressive response of polymeric foams under quasi-static, medium and high strain rate conditions. Polym Test 2006; 25(6): 731-743.

Ippili RK , Davies P. , Bajaj AK and Hagenmeyer L. Nonlinear multi-body dynamic modelling of seat-occupant system with polyurethane seat and H-point prediction. Int J Ind Ergon 2008; 38(5-6): 368-383.

10.

Deng R. Modeling and characterization of flexible polyurethane foam. PhD Thesis, School of Mechanical Engineering, Purdue University , Indiana, USA, 2004.

11.

Singh R. , Davies P. and Bajaj AK Initial condition response of a viscoelastic dynamical system in the presence of dry friction and identification of system parameters. J Sound Vib 2001; 239(5): 1086-1095.

12.

Singh R. , Davies P. and Bajaj AK Estimation of the dynamical properties of polyurethane foam through use of Prony series. J Sound Vib 2003; 264(5): 1005-1043.

13.

Singh R. , Davies P. and Bajaj AK Identification of nonlinear and viscoelastic properties of flexible polyurethane foam. Nonlinear Dyn 2003; 34(3): 319-346.

14.

White SW Dynamic modelling and mesurement of occupied car seats and seating foam. PhD Thesis, School of Mechanical Engineering, Purdue University, Indiana, USA, 1998.

15.

Bezazi A. and Scarpa F. Tensile fatigue of conventional and negative Poisson’s ratio open cell PU foams. Int J Fatigue 2009; 31(3): 488-494.

16.

Rizov V. and Mladensky A. ModeI fatigue fracture behaviour of Divinucell H-30 structural foam - A non-linear approach. Comput Mater Sci 2009; 46(1): 255-260.

17.

Warren WE and Kraynik AM The linear elastic propreties of open-cell foams. J Appl Mech 1988; 55: 341-346.

18.

Warren WE and Kraynik AM The nonlinear elastic behaviour of open-cell foam. J Appl Mech 1991; 58: 376-381.

19.

Song Y. , Wang Z. , Zhao L. and Luo J. Dynamic crushing behaviour of 3D closed-cell foams based on Voronoi random model. Mater Des 2010; 31(9): 4281-4289.

20.

Zhu HX , Thorpe SM and Windle AH The effect of cell irregularity on the high strain compression of 2D Voronoi honeycombs. Int J Solids Struct 2006; 43(5): 1061-1078.

21.

Yeoh OH Some forms of the strain energy function for rubber. Rubber Chem Technol 1993; 66: 754-771.

22.

Arruda EM and Boyce MC A three-dimensional constitutive model for the large stretch behaviour of rubber elastic materials. J Mech Phys Solids 1993; 41(2): 389-412.

23.

Treloar LRG. The physics of rubber elasticity. 3rd ed. Oxford: Clarendon Press, 1975.

24.

Storåkers B. On material representation and constitutive branching in finite compressible elasticity. J Mech Phys Solids 1986; 34(2): 125-145.

25.

Ogden RW Large deformation istropic elasticity: on the correlation of theory and experiment for compressible rubber like solids. Proc R Soc Lond Ser A, Math Phys Sci 1972; 328(1575): 567-583.