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Characterization of a carbon black rubber Poisson's ratio based on optimization technique applied in FEA data fit

  • Lalo, Debora Francisco (Graduate Program in Structural Engineering, Department of Structural Engineering, School of Engineering, Universidade Federal de Minas Gerais) ;
  • Greco, Marcelo (Graduate Program in Structural Engineering, Department of Structural Engineering, School of Engineering, Universidade Federal de Minas Gerais) ;
  • Meroniuc, Matias (Fluid Mechanics Laboratory, Railway Engineering, National Technological University)
  • Received : 2019.07.11
  • Accepted : 2020.08.13
  • Published : 2020.12.10

Abstract

The paper presents a study regarding rubber compressibility behavior. The objective is to analyze the effect of compression degree of rubber on its mechanical properties and propose a new methodology based on reverse engineering to predict compressibility degree based on uniaxial stretching test and Finite Element Analysis (FEA). In general, rubbers are considered to be almost incompressible and Poisson's ratio is close to 0.5. Since this property is intimately related to the rubber packing density, little changes in Poisson's ratio can lead to significant changes regarding mechanical behavior. The deviatory hyperelastic constants were obtained through experimental data fitting by least squares method for the most relevant constitutive models implemented in commercial software Abaqus, such as: Neo-Hooke, Mooney-Rivlin, Ogden, Yeoh and Arruda-Boyce, whereas the hydrostatic part was determined through an optimization algorithm implemented in the Abaqus environment by Python scripting. The simulation results presented great influence of the Poisson's ratio in the rubber specimen mechanical behavior mainly for high strain levels. A conventional pure volumetric compression test was also carried out in order to compare the results obtained by the proposed methodology.

Keywords

Acknowledgement

The authors are grateful for the financial support granted by Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Programa de Pós-Graduação em Engenharia de Estruturas (PROPEEs-UFMG) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), under grant numbers TEC-PPM-00444-18, 302597/2019-0 and 405183/2018-6. The authors also acknowledge UFMG (Universidade Federal de Minas Gerais) and University Center of FEI supports. Authors also acknowledge the valuable contributions of the reviewers that considerably improve the paper.

References

  1. Al-anany, Y.M. and Tait, M.J. (2017), "Experimental assessment of utilizing fiber reinforced elastomeric isolators as bearings for bridge applications", Compos. Part B Eng., 114, 373-385. https://doi.org/10.1016/j.compositesb.2017.01.060
  2. Al Akhrass, D., Bruchon, J., Drapier, S. and Fayolle, S. (2014), "Integrating a logarithmic-strain based hyperelastic formulation into a three-field mixed finite element formulation to deal with incompressibility in finite-strain elastoplasticity", Finite Element Anal. Design, 86, 61-70. https://doi.org/10.1016/j.finel.2014.04.004
  3. ANSYS Inc. (2014), "ANSYS Mechanical User's Guide", ANSYS Manual, ANSYS Inc., Canonsburg, PA. https://148.204.81.206/Ansys/readme.html
  4. Arruda, E.M. and Boyce, M.C. (1993), "A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials", J. Mech. Phys. Solid, 41(2), 389-412. https://doi.org/10.1016/0022-5096(93)90013-6
  5. Asgari, M. and Hashemi, S.S. (2016), "Dynamic visco-hyperelastic behavior of elastomeric hollow cylinder by developing a constitutive equation", Struct. Eng. Mech., 59(4), 601-619. https://doi.org/10.12989/sem.2016.59.4.601
  6. ASTM D412-16. (2016), Standard Test Methods for Vulcanized Rubber and Thermoplastic Elastomers-Tension, ASTM International, West Conshohocken, USA.
  7. Beda, T. (2014), "An approach for hyperelastic model-building and parameters estimation a review of constitutive models", European Polym. J., 50(1), 97-108. https://doi.org/10.1016/j.eurpolymj.2013.10.006
  8. Borst, R. de, Crisfield, M.A., Eindhoven, J.J.C.R. and Verhoosel, C.V. (2012), Non-linear Finite Element Analysis of Solids and Structures (2nd ed.), John Wiley & Sons, NJ, USA.
  9. Bortoli, D.D., Wrubleski, E. and Marczak, R.J. (2011), "Hyperfit - Curve Fitting Software for Incompressible Hyperelastic Material Models", 21st Brazilian Congress of Mechanical Engineering, Natal, Brazil, April. https://doi.org/10.13140/2.1.4055.7448
  10. Cam, J.B. Le. (2010), "A Review of Volume Changes in Rubbers: the Effect of Stretching", Rubber Chem. Technol., 83(3), 247-269. https://doi.org/10.5254/1.3525684
  11. Cam, J. Le and Toussaint, E. (2008), "Volume Variation in Stretched Natural Rubber, Competition between Cavitation and Stress-Induced Crystallization", Macromolecules, 41, 7579-7583. https://doi.org/10.1021/ma801290w.
  12. Cam, J. Le and Toussaint, E. (2009), "Mechanics of Materials Cyclic volume changes in rubber", Mech. Mater., 41(7), 898-901. https://doi.org/10.1016/j.mechmat.2009.02.004
  13. Cao, J., Ding, X.F., Yin, Z.N. and Xiao, H. (2017), "Large elastic deformations of soft solids up to failure: New hyperelastic models with error estimation", Acta Mechanica, 228(3), 1165-1175. https://doi.org/10.1007/s00707-016-1753-8
  14. Cardoso, C., Fernandes, C. S., Lima, R. and Ribeiro, J. (2018), "Biomechanical analysis of PDMS channels using different hyperelastic numerical constitutive models", Mech. Res. Communications, 90, 26-33. https://doi.org/10.1016/j.mechrescom.2018.04.007
  15. Chen, D. L., Chiu, T. C., Chen, T. C., Chung, M. H., Yang, P. F. and Lai, Y. S. (2014), "Using DMA to simultaneously acquire young's relaxation modulus and time-dependent Poisson's ratio of a viscoelastic material", Procedia Eng., 79, 153-159. https://doi.org/10.1016/j.proeng.2014.06.324
  16. Chenal, J., Gauthier, C., Chazeau, L., Guy, L. and Bomal, Y. (2007), "Parameters governing strain induced crystallization in filled natural rubber", Polymer, 48(23), 6893-6901. https://doi.org/10.1016/j.polymer.2007.09.023
  17. Crisfield, M. A. (2000), Nonlinear Finite Element Analysis of Solids and Structures - Volume 2: Advanced Topics, John Wiley and Sons, London, United Kingdom. https://doi.org/10.1017/CBO9781107415324.004
  18. Crocker, L. and Duncan, B. (2001), "Measurement Methods for Obtaining Volumetric Coefficients for Hyperelastic Modelling of Flexible Adhesives", National Phys. Lab., (3),
  19. Destrade, M., Saccomandi, G. and Sgura, I. (2017), "Methodical fitting for mathematical models of rubber-like materials", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2198), https://doi.org/10.1098/rspa.2016.0811
  20. Gauron, O., Saidou, A., Busson, A., Henrique, G. and Paultre, P. (2018), "Experimental determination of the lateral stability and shear failure limit states of bridge rubber bearings", Eng. Struct., 174, 39-48. https://doi.org/10.1016/j.engstruct.2018.07.039
  21. Gehrmann, O., Kroger, N.H., Erren, P. and Juhre, D. (2017), "Estimation of the Compression Modulus of a Technical Rubber via Cyclic Volumetric Compression Tests", Technische Mechanik, 37(1), 28-36. https://doi.org/10.24352/UB.OVGU-2017-048
  22. Hooke, R. and Jeeves, T.A. (1961), "Direct Search, Solution of Numerical and Statistical Problems", J. ACM, 8(2), 212-229. https://doi.org/10.1145/321062.321069
  23. Hwang, Y., Jin, S., Jung, H.Y., Kim, S., Lee, J.J. and Jung, H.J. (2018), "Experimental validation of FE model updating based on multi-objective optimization using the surrogate model", Struct. Eng. Mech., 65(2), https://doi.org/10.12989/sem.2018.65.2.173
  24. Ilseng, A., Skallerud, B. H. and Clausen, A. H. (2015), "Volumetric compression of HNBR and FKM elastomers", Constitutive Models for Rubber IX-Proceedings of the 9th European Conference on Constitutive Models for Rubbers, 19, 235-241.
  25. Kaya, N., Erkek, M.Y. and Guven, C. (2016), "Hyperelastic modelling and shape optimisation of vehicle rubber bushings", J. Vehicle Design, 71(1-4), 212-225. https://doi.org/10.1504/IJVD.2016.078778.
  26. Keerthiwansa, R., Javorik, J., Kledrowetz, J. and Nekoksa, P. (2018), "Elastomer testing: The risk of using only uniaxial data for fitting the Mooney-Rivlin hyperelastic-material model", Materiali in Tehnologije, 52(1), 3-8. https://doi.org/10.17222/mit.2017.085
  27. Lalo, D.F., Greco, M. and Meroniuc, M. (2019), "Numerical Modeling and Experimental Characterization of Elastomeric Pads Bonded in a Conical Spring under Multiaxial Loads and Pre-Compression", Math. Problems Eng., (2019), 1-14. https://doi.org/10.1155/2019/5182629
  28. Lalo, D. and Greco, M. (2017), "Rubber bushing hyperelastic behavior based on shore hardness and uniaxial extension", Procceedings of the 24th ABCM International Congress of Mechanical Engineering, Curitiba, Brazil, December. https://doi.org/10.26678/ABCM.COBEM2017.COB17-5280
  29. Lee, H.S., Shin, J.K., Msolli, S. and Kim, H.S. (2017), "Prediction of the dynamic equivalent stiffness for a rubber bushing using the finite element method and empirical modeling", J. Mech. Mater. Design, 15(1) 1-15. https://doi.org/10.1007/s10999-017-9400-7
  30. Madsen, K. and Nielsen, H. (2010), Introduction to Optimization and Data Fitting, Technical University of Denmark.
  31. Mansouri, M. R., Darijani, H. and Baghani, M. (2017), "On the Correlation of FEM and Experiments for Hyperelastic Elastomers", Exp. Mech., 57(2), 195-206. https://doi.org/10.1007/s11340-016-0236-0.
  32. Marckmann, G. and Verron, E. (2006), "Comparison of Hyperelastic Models for Rubber-Like Materials", Rubber Chem. Technol., 79(5), 835-858. https://doi.org/10.5254/1.3547969
  33. Miller, K. (2002), Testing Elastomers for Finite Element Analysis. 2002 International ANSYS Conference Proceedings, 1-13.
  34. Miller, K. (2004), Testing Elastomers for Hyperelastic Material Models in Finite Element Analysis (Testing and Analysis Testing), Michigan.
  35. Mott, P.H., Dorgan, J.R. and Roland, C.M. (2008), "The bulk modulus and Poisson's ratio of 'incompressible' materials", J. Sound Vib., 312(4-5), 572-575. https://doi.org/10.1016/j.jsv.2008.01.026
  36. MSC Software Corporation. (2016), MSC Marc Theory and User Information.
  37. Musa, I.A. (2016), "Buckling of plates including effect of shear deformations: A hyperelastic formulation", Struct. Eng. Mech., 57(6), 1107-1124. https://doi.org/10.12989/sem.2016.57.6.1107
  38. Ogden, R.W. (1972), "Large deformation isotropic elasticity on the correlation of theory and experiment for incompressible rubber-like solids", Philosophical Transactions of the Royal Society of London - Series A, 326(1567), 565-584.
  39. Kumar, P., Fukahori, Y., Thomas, A.G. and Busfield, J.J.C. (2007), "Recycled Rubber: The Rubber Granulate - Virgin Rubber Interface", Rubber Chem. Technol., 80(1), 24-39. https://doi.org/10.5254/1.3548167
  40. Ramier, J., Chazeau, L., Gauthier, C., Stelandre, L., Guy, L. and Peuvrel-Disdier, E. (2007), "In situ SALS and volume variation measurements during deformation of treated silica filled SBR", J. Mater. Sci., 42, 8130-8138. https://doi.org/10.1007/s10853-007-1728-1
  41. Rivlin, R.S. and Saunders, D.W. (1951), "Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber", Philosophical Transac. Royal Society A Math., Phys. Eng. Sci., 243(865), 251-288. https://doi.org/10.1098/rsta.1951.0004
  42. Shahzad, M., Kamran, A., Siddiqui, M. Z. and Farhan, M. (2015), "Mechanical characterization and fe modelling of a hyperelastic material", Mater. Res., 18(5), 918-924. https://doi.org/10.1590/1516-1439.320414
  43. Simulia (2016), Abaqus Analysis User's Manual, Version 6.13. Dassault Systems, Vélizy-Villacoublay.
  44. Tommernes, V. (2014), Implementation of the Arruda-Boyce Material Model for Polymers in Abaqus, (June), https://doi.org/10.1016/j.jadohealth.2014.02.002.
  45. Williams, K.C. and Partheeban, P. (2018), "An experimental and numerical approach in strength prediction of reclaimed rubber concrete", Adv. Concrete Construct., 1, 87-102. http://dx.doi.org/10.12989/acc.2018.6.1.087.
  46. Yeoh, O.H. (1990), "Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates", Rubber Chem. Technol., 63(5), 792-805. https://doi.org/10.5254/1.3538289.
  47. Zhang, Q. and Yang, Q.S. (2017), "Effects of large deformation and material nonlinearity on spherical indentation of hyperelastic soft materials", Mech. Res. Communications, 84, 55-59. https://doi.org/10.1016/j.mechrescom.2017.06.003.
  48. Zimmermann, J. and Stommel, M. (2013a), "Influence of the mechanical stress and the filler content on the hydrostatic compression behaviour of natural rubber", IOP Conference Series: Mater. Sci. Eng., 48(1), https://doi.org/10.1088/1757-899X/48/1/012006.
  49. Zimmermann, J. and Stommel, M. (2013b), "The mechanical behaviour of rubber under hydrostatic compression and the effect on the results of finite element", Arch Appl Mech, 83(2), 293-302. https://doi.org/10.1007/s00419-012-0655-z