Skip to main content
SpringerLink
Log in

Other Applications: Engineering

  • Chapter
  • First Online:
Advances in Elastomers II

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 12))

  • 2014 Accesses

Abstract

This chapter describes how the finite element technique can be used for the design of elastomeric components for automotive and railway applications. In the first section a description of the industrial needs regarding the design with these types of materials and the reasons why they arouse so much interest for engineering applications is given. Also, a complete literature review and explanation of fundamentals are included concerning different features these materials exhibit from the mechanical point of view: elasticity, inelasticity, fatigue, and tribology behavior. The second section includes several details about constitutive models used for the finite element (FE) modelling of elastomeric materials. Among them, some basic kinematics of finite elastic deformations are explained as well as details about constitutive behavior for rubbers and rubber-like materials such as strain energy potentials usually implemented in FE codes for modelling hyperelasticity, time and frequency domain viscoelasticity, constitutive models for modelling inelastic effects, and available approaches for modeling fatigue behavior. In the third section, a methodology for the design of elastomeric components by means of the FE method is explained, including valuable information about experimental testing for material characterization focused on the calibration of former explained constitutive models. In the fourth and last section, four examples are presented, related to the application of FE techniques for the analysis and the design of components for automotive and railway applications. These examples cover the modelling of different aspects and features of elastomeric materials and demonstrate the advantages provided by FE techniques in comparison to the experimental design procedures used until the recent past in the industry.

“Use of finite element (FE) techniques for the design of elastomeric components for automotive and railway applications”.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Hamed, G.R., Hatfield, S.: On the role of bound rubber in carbon black reinforcement. Rubber Chem. Technol. 62, 143–156 (1989)

    Article  CAS  Google Scholar 

  2. Meinecke, E.A., Taftaf, M.I.: Effect of carbon black on the mechanical properties of elastomers. Rubber Chem. Technol. 61, 534–547 (1988)

    Article  CAS  Google Scholar 

  3. So, H., Chen, U.D.: A nonlinear mechanical model for solid filled polymers. Polym. Eng. Sci. 6, 410–416 (1991)

    Google Scholar 

  4. Zienkiewicz, O.C., Taylor, R.L.: The FE Method, vol. 1: Basic Formulation and Linear Problems. McGraw-Hill, London (1989)

    Google Scholar 

  5. Zienkiewicz, O.C., Taylor, R.L.: The FE Method, vol. 2: Solid and Fluid Mechanics, Dynamics and Non-Linearity. McGraw-Hill, London (1991)

    Google Scholar 

  6. Govindjee, S., Simo, J.: Transition from micro-mechanics to computationally efficient phenomenology: carbon black filled rubbers incorporating Mullins effect. J. Mech. Phys. Solids 40, 213–233 (1992)

    Article  CAS  Google Scholar 

  7. Govindjee, S., Simo, J.: Mullins effect and the strain amplitude dependence of the storage modulus. Int. J. Solids Struct. 29, 1737–1751 (1992)

    Article  Google Scholar 

  8. Lion, A.: A constitutive model for carbon black filled rubber: experimental investigations and mathematical representation. Continuum Mech. Thermodyn. 8, 153–169 (1996)

    Article  Google Scholar 

  9. Lion, A.: Thixotropic behaviour of rubber Ander dynamic loading histories: Experiments and theory. J. Mech. Phys. Solids 46(5), 895–930 (1998)

    Article  CAS  Google Scholar 

  10. Kim, S.J., Kim, K.S., Cho, J.Y.: Viscoelastic model of finitely deforming rubber and its FE anlysis. J. Appl. Mech. 64, 835–841 (1997)

    Article  CAS  Google Scholar 

  11. Bergström, J.S., Boyce, M.C.: Constitutive modelling of the large strain time-dependent behaviour of elastomers. J. Mech. Phys. Solids 46, 931–954 (1998)

    Article  Google Scholar 

  12. Bergström, J.S., Boyce, M.C.: Large strain time-dependent behavior of filled elastomers. Mech. Mater. 32, 627–644 (2000)

    Article  Google Scholar 

  13. Miehe, C., Keck, J.: Superimposed finite elastic-viscoelastic-plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic Implementation. J. Mech. Phys. Solids 48, 323–365 (2000)

    Article  Google Scholar 

  14. Mars, W.V., Fatemi, A.: Observations of the constitutive response and characterization of filled natural rubber under monotonic and cyclic multiaxial stress states. J. Eng. Mater. Technol. 126(1), 19–28 (2004)

    Article  CAS  Google Scholar 

  15. Paige, R.E., Mars, W.V.: Implications of the Mullins effect on the Stiffness of a Pre-loaded Rubber Component. In: Proceedings of the 17th Abaqus User’s Conference, Boston, Massachusetts, USA (2004)

    Google Scholar 

  16. Rivlin, R.S., Saunders, D.W.: Large elastic deformations of isotropic materials. VII. Experiments on the deformation of rubber. Philos. Trans. R. Soc. Lond., Ser. A 243, 251–288 (1951)

    Article  Google Scholar 

  17. Treolar, L.R.G.: The Physics of Rubber Elasticity. Oxford University Press, Oxford (1975)

    Google Scholar 

  18. James, A.G., Green, A., Simpson, G.M.: Strain energy functions of rubber. I. Characterization of gum vulcanizates. J. Appl. Polym. Sci. 19, 2033–2058 (1975)

    Article  CAS  Google Scholar 

  19. Yeoh, O.H.: Characterisation of elastic properties of carbon-black filled rubber vulcanizates. Rubber Chem. Technol. 63, 792–805 (1990)

    Article  CAS  Google Scholar 

  20. Mooney, M.: A theory of large elastic deformation. J. Appl. Phys. 11, 582–592 (1940)

    Article  Google Scholar 

  21. James, H.M., Guth, E.: Theory of the elastic properties of rubber. J. Chem. Phys. 11(10), 455–481 (1943)

    Article  CAS  Google Scholar 

  22. Wall, F.T., Flory, P.J.: Statistical thermodynamics of rubber elasticity. J. Chem. Phys. 19(12), 1435–1439 (1951)

    Article  CAS  Google Scholar 

  23. Flory, P.J.: Theory of elasticity of polymer networks. The effect of local constraints on junctions. J. Chem. Phys. 66(12), 5720–5729 (1977)

    Article  CAS  Google Scholar 

  24. Ogden, R.W.: Large deformation isotropic elasticity I: on the correlation of theory and experiment for incompressible rubber-like materials. Proc. R. Soc. Lond. Ser. A 326, 565–584 (1972)

    Article  CAS  Google Scholar 

  25. Blatz, P.J., Ko, W.L.: Application of finite elastic theory to the deformation of rubbery materials. Trans. Soc. Rheol. 6, 223–251 (1962)

    Article  CAS  Google Scholar 

  26. Ogden, R.W.: Non-linear Elastic Deformations. Dover Publications, Ellis Harwood Ltd, New York (1984)

    Google Scholar 

  27. Yeoh, O.H.: Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66, 754–771 (1993)

    Article  CAS  Google Scholar 

  28. Arruda, E., Boyce, M.C.: A three-dimensional constitutive model for the large stretch behaviour of rubber elastic materials. J. Mech. Phys. Solids 41(2), 389–412 (1993)

    Article  CAS  Google Scholar 

  29. Gent, A.N., Thomas, A.G.: Forms of the stored (strain) energy function for vulcanized rubber. J. Polym. Sci. 28, 625–637 (1958)

    Article  CAS  Google Scholar 

  30. Valanis, K.C., Landel, R.F.: The strain-energy function of a hyperelastic material in terms of the extension ratios. J. Appl. Phys. 38, 2997–3002 (1967)

    Article  CAS  Google Scholar 

  31. James, A.G., Green, A.: Strain energy functions of rubber. II. The characterization of filled vulcanizates. J. Appl. Polym. Sci. 19, 2319–2330 (1975)

    Article  CAS  Google Scholar 

  32. Ferry, J.D.: Viscoelastic Properties of Polymers. John Wiley & Sons, Inc., New York (1980)

    Google Scholar 

  33. Hausler, K., Sayir, M.B.: Nonlinear viscoelastic response of carbon black reinforced rubber derived from moderately large deformations in torsion. J. Mech. Phys. Solids 43(2), 295–318 (1995)

    Article  CAS  Google Scholar 

  34. Johnson, A.R., Quigley, C.J., Freese, C.E.: A viscohyperelastic FE model for rubber. Comput. Methods Appl. Mech. Eng. 127, 163–180 (1995)

    Article  Google Scholar 

  35. Simo, J.: On a fully thee-dimensional finite-strain viscoelastic damage model: formulation and computational aspects. Comput. Methods Appl. Mech. Eng. 60, 153–173 (1987)

    Article  Google Scholar 

  36. Kaliske, M.: Zur Theorie und Numerik von Polymerstrukturen unter statischen un dynamischen Einwirkungen. Mitteilung Nr. 41-95 des Instituts für Statik der Universität Hannover (1995)

    Google Scholar 

  37. Holzapfel, G.A., Stadler, M., Ogden, R.W.: Aspects of stress softening in filled rubbers incorporating residual strains. In: Dorfman, A., Muhr, A. (eds.) Constitutive Models for Rubber I, pp. 189–193. ©1999 Balkema, Rotterdam, ISBN 90 5809 113 9 (1999)

    Google Scholar 

  38. Besdo, D., Ihlemann, J.: Zur Modellierung des Stoffverhaltens von Elastomeren. Kautschuck un Gummi Kunstoffe 49, 495–503 (1996)

    Google Scholar 

  39. Dannenberg, E.M.: The effect of surface chemical interactions on the properties of filler reinforced rubbers. Rubber Chem. Technol. 44, 440–478 (1975)

    Google Scholar 

  40. Vidal, A., Donnet, J.B.: Carbon black: surface properties and interactions with elastomers. Adv. Polym. Sci. 76, 104–106 (1996)

    Google Scholar 

  41. Mullins, L.: Effect of stretching on the properties of rubber. Rubber Chem. Technol. 21, 281–300 (1948)

    Article  CAS  Google Scholar 

  42. Mullins, L., Tobin, N.R.: Stress softening in rubber vulcanizates. Part I. J. Appl. Polym. Sci. 9, 2993 (1965)

    Article  CAS  Google Scholar 

  43. Harwood, J.A.C., Mullins, L., Payne, A.R.: Stress softening in natural rubber vulcanizantes. Part II. Stress softening in pure gum and filler loaded rubbers. J. Appl. Polym. Sci. 9, 3011–3021 (1965)

    Article  CAS  Google Scholar 

  44. Harwood, J.A.C., Payne, A.R.: Stress softening in natural rubber vulcanizates. Part II. Carbon black-filled vulcanizates. J. Appl. Polym. Sci. 10, 315–324 (1966)

    Article  CAS  Google Scholar 

  45. Harwood, J.A.C., Payne, A.R.: Stress softening in natural rubber vulcanizates. Part IV. Unfilled vulcanizates. J. Appl. Polym. Sci. 10, 1203–1211 (1966)

    Article  CAS  Google Scholar 

  46. Bueche, F.: Molecular basis for the Mullins effect. J. Appl. Polym. Sci. 4(10), 107–114 (1960)

    Article  CAS  Google Scholar 

  47. Bueche, F.: Mullins effect and rubber-filler interaction. J. Appl. Polym. Sci. 5(15), 271–281 (1961)

    Article  CAS  Google Scholar 

  48. Marigo, J.J.: Modelling of brittle and fatigue damage for elastic material by growth of microvoids. Eng. Fract. Mech. 21(4), 861–874 (1985)

    Article  Google Scholar 

  49. Kachanov, L.M.: Introduction to Continuum Damage Mechanics. Martinus Nijhoff Publishers, Dordrecht (1986)

    Book  Google Scholar 

  50. Lemaitre, J.: A Course on Damage Mechanics. Springer, Berlin (1992)

    Google Scholar 

  51. Ogden, R.W., Roxburgh, D.G.: A pseudo-elastic model for the Mullins effect in filled rubber. Proc. R. Soc. Lond. Ser. A 455, 2861–2877 (1999)

    Article  Google Scholar 

  52. Ogden, R.W., Roxburgh, D.G.: An energy based model of the Mullins effect. In: Dorfmann, A., Muhr, A. (eds.) Constitutive Models for Rubber I, pp. 23–28. ©1999 Balkema, Rotterdam, ISBN 90 5809 113 9

    Google Scholar 

  53. Austrell, P.E.: Modelling of elasticity and damping for filled elastomers. Ph.D. Dissertation, Report TVSN-1009, Lund University, Division of Structural Mechanics, Sweden (1997)

    Google Scholar 

  54. Austrell, P.E., Olsson, A.K., Jönsson, M.: A method to analyse the non-linear dynamic behaviour of carbon-black-filled rubber components using standard FE-codes. In: Besdo, D., Shuster, R.H., Ihlemann, J. (eds.) Constitutive Models for Rubber II, pp. 231–235. ©2001 Swets & Zeitlinger, ISBN 90 2651 847 1

    Google Scholar 

  55. Besseling, J.F.: A theory of elastic, plastic and creep deformation of an initially isotropic material. J. Appl. Mech. 25, 529–536 (1998)

    Google Scholar 

  56. Fletcher, W.P., Gent, A.N.: Non-linearity in the dynamic properties of vulcanised rubber compounds. I.R.I. Trans. 29, 266–280 (1953)

    Google Scholar 

  57. Payne, A.R.: The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I. J. Appl. Polym. Sci. VI, 57–63 (1962)

    Google Scholar 

  58. Olsson, A.K.: Austrell, P.E.: A fitting procedure for a viscoelastic-elastoplastic material model. In: Besdo, D., Shuster, R.H., Ihlemann, J. (eds.) Constitutive Models for Rubber II, pp. 261–266. ©2001 Swets & Zeitlinger, ISBN 90 2651 847 1

    Google Scholar 

  59. Ahmadi, H.R, Kingston, J.G.R., Muhr, A.H., Gracia, L.A., Gómez, B.: Interpretation of the high low-strain modulus of filled rubbers as an inelastic effect. In: Busfield, J., Muhr, A. (eds.) Constitutive Models for Rubber III, pp. 357–364. ©2003 Swets & Zeitlinger, Lisse, ISBN 90 5809 566 5

    Google Scholar 

  60. Morman, K.N., Nagtegaal, J.C.: FE analysis of sinusoidal small-amplitude vibrations in deformed viscoelastic solids. Part I. Theoretical development. Int. J. Num. Methods Eng. 19, 1079–1103 (1983)

    Article  Google Scholar 

  61. MSC MARC User’s manual (2005)

    Google Scholar 

  62. Miller, K.: Testing and Analysis. Measuring the Dynamic Properties of Elastomers for Analysis. Dynamic Review. Axel Products, Ann Arbor (2000)

    Google Scholar 

  63. Gómez, J., Royo, J.M.: Prediction of dynamic stiffness of filled rubber mounts. III European Conference on Computational Mechanics, Lisbon, Portugal, 5–8 June 2006

    Google Scholar 

  64. Ellul, M.D.: Mechanical fatigue. Engineering with Rubber: How to Design Rubber Components (Chap. 6), pp. 130–167. Hanser, New York (1992)

    Google Scholar 

  65. Lake, G.J.: Mechanical fatigue of rubber. Rubber Chem. Technol. 45, 309 (1972)

    Article  CAS  Google Scholar 

  66. Lake, G.J.: Fatigue and fracture of elastomers. Rubber Chem. Technol. 68, 435–460 (1995)

    Article  CAS  Google Scholar 

  67. Cadwell, S.M., Merrill, R.A., Sloman, C.M., Yost, F.L.: Dynamic fatigue life of rubber. Ind. Eng. Chem. (Anal. Ed.) 12, 19–23 (1940) (reprinted in Rubber Chem. Technol. 13, 304–315)

    Google Scholar 

  68. Roach, J.F.: Crack growth in elastomers under biaxial stress. Ph.D. dissertation, University of Akron (1982)

    Google Scholar 

  69. Lake, G.J.: Aspects of fatigue and fracture of rubber. Prog. Rubber Technol. 45, 89 (1983)

    Google Scholar 

  70. Lake, G.J., Yeoh, O.H.: Effect of crack tip sharpness on the strength of vulcanized rubbers. J. Polym. Sci.: Polym. Phys. Ed. 25, 1157 (1987)

    Article  CAS  Google Scholar 

  71. Lake,G.J., Lindley, P.B.: The mechanical fatigue limit for rubber. J. Appl. Polym. Sci. 9, 1233–1251 (1965) (reprinted in Rubber Chem. Technol. 39, 348–364 (1966))

    Google Scholar 

  72. Gent, A.N., Lindley, P.B., Thomas, A.G.: Cut growth and fatigue of rubbers. I. The relationship between cut growth and fatigue. J. Appl. Polym. Sci. 8, 455–466 (1964) (reprinted in Rubber Chem. Technol. 38, 292–300 (1965))

    Google Scholar 

  73. Mars, W.V.: Multiaxial fatigue on rubber. Ph.D. thesis, University of Toledo (2001)

    Google Scholar 

  74. Flamm, M., Steinweger, T., Weltin, U.: Schadeakkumulation bei Elastomeren. Kautschuk Gummi Kunststoffe 55(12), 665–668 (2002)

    CAS  Google Scholar 

  75. Mars, W.V., Fatemi, A.: Multiaxial fatigue of rubber—part I: Equivalence criteria and theoretical aspects. Fatigue Fract. Eng. Mater. Struct. 28, 515–522 (2005)

    Article  CAS  Google Scholar 

  76. Mars, W.V., Fatemi, A.: Multiaxial fatigue of rubber: Part II: Experimental observations and life predictions. Fatigue Fract. Eng. Mater. Struct. 28, 523–538 (2005)

    Article  CAS  Google Scholar 

  77. Mars, W.V., Kingston, J.G.R., Muhr, A.: Fatigue analysis of an exhaust mount. In: Austrell, P.E., Kari, L. (eds.) Constitutive Models for Rubber IV, pp. 23–29. ©2005 Taylor & Francis Group, London, ISBN 0 415 38346 3

    Google Scholar 

  78. Thomas, A.G.: Rupture of rubber. VI. Further experiments on the tear criterion. J. Polym. Sci. 31, 467 (1958)

    Article  Google Scholar 

  79. Lindley, P.B.: Relation between hysteresis and the dynamic crack growth resistance of natural rubber. Int. J. Fract. 9–4, 449–462 (1973)

    Google Scholar 

  80. Lindley, P.B.: Non-relaxing crack growth and fatigue in a non-crystallizing rubber. Rubber Chem. Technol. 47, 1253–1264 (1974)

    Article  CAS  Google Scholar 

  81. Rabinowicz, E.: Friction and Wear of Materials, 2nd edn. Wiley-Interscience, New York (1995)

    Google Scholar 

  82. Stachowiak, G.W., Batchelor A.W.: Engineering Tribology, 3rd edn. Elsevier (2011)

    Google Scholar 

  83. Zhang, S.W.: State-of-the-art of polymer tribology. Tribol. Int. 31, 49–60 (1998)

    Article  CAS  Google Scholar 

  84. Persson, B.N.J.: Sliding Friction: Physical Principles and Applications, 2nd edn. Springer, Heidelberg (2000)

    Google Scholar 

  85. Thirion, P.: Les coefficients d’adhérence du caoutchouc. Rubber Chem. Technol. 21, 505–515 (1948)

    Article  CAS  Google Scholar 

  86. Persson, B.N.J.: Theory of rubber friction and contact mechanics. J. Chem. Phys. 115–118, 3840–3861 (2001)

    Article  CAS  Google Scholar 

  87. Mofidi, M., Prakash, B., Persson, B.N.J.: Albohr O. Rubber friction on (apparently) smooth lubricated surfaces. J. Phys.: Condens. Matter 20(8), 085223 (2008)

    Article  CAS  Google Scholar 

  88. Kragelskii, I.V.: Friction and Wear, p. 458. Pergamon Press, Elmsford (1982)

    Google Scholar 

  89. Blau, P.J.: Friction and wear transitions of materials. Noyes Publication, New York (1989)

    Google Scholar 

  90. Zhang, S.W.: Tribology of elastomers. In: Briscoe, B.J. (ed.) Tribology and Interface Engineering, Series no. 47, pp. 37–177. Elsevier, Amsterdam (2004)

    Google Scholar 

  91. Myshkin, N.K., Petrokovets, M.I., Kovalev, A.V.: Tribology of polymers: adhesion, friction, wear and mass-transfer. Tribol. Int. 38, 910–921 (2005)

    Article  CAS  Google Scholar 

  92. Je, J.H., Gyarmati, E., Naoumidis, A.: Scratch adhesion test of reactively sputtered TiN coatings on a soft substrate. Thin Solid Films 136, 57–67 (1986)

    Article  CAS  Google Scholar 

  93. Viswanath, V., Bellow, D.G.: Development of an equation for the wear of polymers. Wear 181–183(1), 42–49 (1995)

    Google Scholar 

  94. Nah, C.: Ph.D. dissertation, Wear mechanisms of rubber compounds, The University of Akron (1995)

    Google Scholar 

  95. Meng, H.C., Ludema, K.C.: Wear models and predictive equations: their form and content. Wear 181–183, 443–457 (1995)

    Article  Google Scholar 

  96. Muhr, A.H.: Dynamic properties of rubber. In: Proceedings, ACEM, NR in Engineering Workshop. Kulalumpur, Sept. 1991

    Google Scholar 

  97. Hibbitt, Karlsson and Sorensen. Abaqus Standard Theory and User’s Manual v6.5 (2005)

    Google Scholar 

  98. Freakly, P.K., Payne, A.R.: Theory and Practise of Engineering with Rubber. Applied Science Publishers, London (1978)

    Google Scholar 

  99. Layouni, K., Laiaridrasana, L., Piques, R.: Compressibility induced by damage in carbon black reinforced natural rubber. In: Busfield, A., Muhr, A. (eds.) Constitutive Models for Rubber III, pp. 273–281. ©2003 Swets & Zeitlinger, Lisse, ISBN 90 5809 566 5

    Google Scholar 

  100. Muhr, A.H.: Properties of rubber compounds for engineering applications. J. Nat. Rubber Res. 7(1), 14–37 (1992)

    CAS  Google Scholar 

  101. Ahmadi, H.R., Muhr, A.H.: Modelling dynamic properties of filled rubber. Plast. Rubber Compos. Process. Appl. 26, 451–461 (1997)

    CAS  Google Scholar 

  102. Harris, J.A.: Dynamic testing under non-sinusoidal conditions and the consequences of nonlinearities for service performance. In: Proceedings of the Rubber Division Meeting. American Chemical Society, Montreal, Quebec, Canada, 26–29 May 1987

    Google Scholar 

  103. Harris, J., Stevenson, A.: On the role of non-linearity in the dynamic behaviour of rubber components. Rubber Chem. Technol. 59, 741–764 (1986)

    Article  Google Scholar 

  104. Mullins, L.: Softening of rubber by deformation. Rubber Chem. Technol. 42, 339–362 (1969)

    Article  CAS  Google Scholar 

  105. Mullins, L., Tobin, N.R.: Theoretical model for the elastic behaviour of filler-reinforced vulcanized rubber. Rubber Chem. Technol. 30, 555–571 (1957)

    Article  Google Scholar 

  106. Spencer, A.J.M.: Constitutive theory for strongly anisotropic solids. In: Continuum Theory of the Mechanics of Fiber-Reinforced Composites, pp. 1–32. Springer, Wien (1984)

    Google Scholar 

  107. Holzapfel, G.A., Eberlein, R., Wriggers, P., Weizsäcker, H.W.: A new axisymmetrical membrane element for anisotropic, finite strain analysis of arteries. Commun. Numer. Methods Eng. 12, 507–517 (1996)

    Article  Google Scholar 

  108. Weiss, J.A., Maker, B.N., Govindjee, S.: FE implementation of incompressible, transversely isotropic hyperelasticity. Comput. Methods Appl. Mech. Eng. 135, 107–128 (1996)

    Article  Google Scholar 

  109. Alastrué, V., Calvo, B., Peña, E., Doblaré, M.: Biomechanical modelling of refractive corneal surgery. J. Biomech. Eng. T ASME 128(1), 150–160 (2006)

    Article  Google Scholar 

  110. Roland, C.M.: Dynamic mechanical behaviour of filled rubber at small strains. J. Rheol. 34, 25 (1990)

    Article  Google Scholar 

  111. Medalia, A.I.: Effects of carbon-black on dynamic properties of rubber. Rubber Chem. Technol. 51, 437 (1978)

    Article  CAS  Google Scholar 

  112. Brown, M.W., Miller, K.J.: A theory for fatigue under multi-axial stress-strain condition. Proc. Inst. Mech. Eng. 187, 745–755 (1973)

    Google Scholar 

  113. Fatemi, A., Socie, D.F.: A critical plane approach to multiaxial fatigue damage including out-of-plane loading. Fatigue Fract. Eng. Mater. Struct. 14, 149–166 (1988)

    Google Scholar 

  114. Smith, R.N., Watson, P., Topper, T.H.: A stress-strain parameter for the fatigue of metals. J. Mater. 5, 767–778 (1970)

    Google Scholar 

  115. Wang, C.H., Brown, M.W.: A path-independent parameter for fatigue under proportional and non-proportional loading. Fatigue Fract. Eng. Mater. Struct. 16, 1285–1298 (1993)

    Article  CAS  Google Scholar 

  116. Wang, C.H., Brown, M.W.: Life prediction techniques for variable amplitude multiaxial fatigue, Part 1: Theories. J. Eng. Mater. Technol. 118, 367–370 (1996)

    Article  Google Scholar 

  117. Wang, C.H., Brown, M.W.: Life prediction techniques for variable amplitude multiaxial fatigue, Part 2, comparison with experimental results. J. Eng. Mater. Technol. 118, 371–374 (1996)

    Article  Google Scholar 

  118. Chen, X., Xu, S.-Y., Huang, D.-X.: Critical plane-strain energy density criterion of multiaxial low-cycle fatigue life. Fatigue Fract. Eng. Mater. Struct. 22, 679–686 (1999)

    CAS  Google Scholar 

  119. Saintier, N., Cailletaud, G., Piques, R.: Crack initiation and propagation under multiaxial fatigue. Int. J. Fatigue 28, 61–72 (2006)

    Article  CAS  Google Scholar 

  120. Saintier, N., Cailletaud, G., Piques, R.: Multiaxial fatigue life prediction for a natural rubber. Int. J. Fatigue 28, 530–539 (2006)

    Article  CAS  Google Scholar 

  121. Findley, W.M., Mathur, P.N., Szczepanski, E., et al.: Energy versus stress theories for combined stress—a fatigue experiment using a rotating disk. ASME Trans. J. Basic Eng. 83, 10–14 (1961)

    Article  Google Scholar 

  122. Rivlin, R.S., Thomas, A.G.: Rupture of rubber. I. Characteristic energy for tearing. J. Polym. Sci. 10, 291–318 (1953)

    Article  CAS  Google Scholar 

  123. Ro, H.S.: Modeling and interpretation of fatigue failure initiation in rubber related to pneumatic tires. Ph.D. dissertation, Purdue University, USA (1989)

    Google Scholar 

  124. Yamashita, S.: Selecting damping materials (service environment, strain and endurance). Int. Polym. Sci. Technol. 19(4), T/41–T/56 (1992)

    Google Scholar 

  125. Andre, N., Cailletaud, G., Piques, R.: Haigh diagram for fatigue crack initiation prediction of natural rubber components. Kautschuk Und Gummi Kunstoffe 52, 120–123 (1999)

    CAS  Google Scholar 

  126. Lindley, P.B., Stevenson, A.: Fatigue resístanse of natural rubber in compression. Rubber Chem. Technol. 55, 337–351 (1982)

    Article  CAS  Google Scholar 

  127. Gent, A.N., Wang, C.: Strain energy release rate for crack growth in an elastic cylinder subjected to axial shear. Rubber Chem. Technol. 66, 712 (1993)

    Google Scholar 

  128. Fielding-Russell, G.S., Rongone, R.L.: Fatiguing of rubber–rubber interfaces. Rubber Chem. Technol. 56, 838–844 (1983)

    Article  CAS  Google Scholar 

  129. Verron, E., Le Cam, J.B., Gournet, L.: A multiaxial criterion for crack nucleation in rubber. Mech. Re. Commun. 33, 493–498 (2006)

    Article  Google Scholar 

  130. Verron E., Andriyana, A.: Definition of a new predictor for multiaxial fatigue crack nucleation in rubber. J. Mech. Phys. Solids 56(2), 417–443 (2008)

    Google Scholar 

  131. Andriyana, A., Verron, E.: Prediction of fatigue life improvement in natural rubber using configurational stress. Int. J. Solids Struct. 44, 2079–2092 (2007)

    Article  CAS  Google Scholar 

  132. Wang, B., Lu, H., Kim, G.: A damage model for the fatigue life of elastomeric materials. Mech. Mater. 34, 475–483 (2002)

    Article  CAS  Google Scholar 

  133. Schallamach, A.: Friction and abrasion of rubber. Wear 1, 384–417 (1958)

    Article  Google Scholar 

  134. Rymuza, Z.: Wear in polymer micro-pairs. Proceedings of the 3rd International Conference on Wear of Materials, pp. 125–132 (1981)

    Google Scholar 

  135. Buckley, D.H.: Surface effects in adhesion, friction, wear and lubrication. Elsevier, Amsterdam (1981)

    Google Scholar 

  136. Makinson, K.R., Tabor, D.: The friction and transfer of polytetrafluoroethylene. Proc. R. Soc. Lond. Ser. A 281, 49–61 (1964)

    Article  CAS  Google Scholar 

  137. Tanaka, K., Uchiyama, Y., Toyooka, S.: The mechanism of wear of PTFE. Wear 23, 153–172 (1973)

    Article  CAS  Google Scholar 

  138. Thorpe, J.M.: Tribological properties of selected polymer matrix composites against steel surfaces. In: Friedrich, K. (ed.) Friction and Wear of Polymer Composites, Vol. 1, Composite Materials Science, pp. 137–174. Elsevier, Amsterdam (1986)

    Google Scholar 

  139. Jain, V.K., Bahadur, S.: Material transfer in polymer–polymer sliding. Wear 46, 177–198 (1978)

    Article  CAS  Google Scholar 

  140. Birkett, A., Lancaster, J.K.: Counterface effects on the wear of a composite dry-bearing liner. In: Proceedings of the JSLE International Tribology Conference, Tokyo, pp. 465–470. Elservier, Amsterdam (1985)

    Google Scholar 

  141. Dowson, D., Challen, J.M., Holmes, K., Atkinson, J.R.: The influence of counterface roughness on the wear rate of polyethylene. In: Proceedings of the 3rd Leeds-Lyon Symposium on Tribology, Wear of Non-Metallic Materials, Sept. 1976, pp. 99–102. University of Leeds, London (1978)

    Google Scholar 

  142. Barrett, T.S., Stachowiak, G.W., Batchelor, A.W.: Effect of roughness and sliding speed on the wear and friction of ultra-high molecular weight polyethylene. Wear 153, 331–350 (1992)

    Article  CAS  Google Scholar 

  143. Play, D.F.: Counterface roughness effect on the dry steady state wear of self-lubricating polyimide composites. Trans. ASME, J. Lubr. Technol. 106, 177–184 (1984)

    Google Scholar 

  144. Blanchett, T.A., Kennedy, F.E.: The development of transfer films in ultra-high molecular weight polyethiylene/stainless steel oscillatory sliding. Tribol. Trans. 32, 371–379 (1982)

    Article  Google Scholar 

  145. Tanaka, K., Uchiyama, Y.: Friction, wear and surface melting of crystalline polymers. In: Lee, L.H. (ed.) Advances in Polymer Friction and Wear, Vol. 5B, pp. 499–531. Plenum Press, New York (1974)

    Google Scholar 

  146. Kar, M.K., Bahadur, S.: Micromechanism of wear at polymer-metal sliding interface. Wear 46, 189–202 (1978)

    Article  CAS  Google Scholar 

  147. Ettles, Mc C., C.M., : Polymer and elastomer friction in the thermal control regime. ASLE Trans. 30, 149–159 (1987)

    Article  CAS  Google Scholar 

  148. Mizutani, Y., Kato, K., Shimura, Y.: Friction and wear of phenolic resin up to 200 °C. In: Proceedings of the JSLE International Tribology Conference, Tokyo, pp. 489–494. Elsevier (1985)

    Google Scholar 

  149. Watanabe, M., Yamaguchi, H.: The friction and wear properties of nylon. Proceedings of the JSLE International Tribology Conference, Tokyo, pp. 483-488. Elsevier (1985)

    Google Scholar 

  150. Southern, E., Thomas, A.G.: Studies of rubber abrasion. Plast. Rubber Mater. Appl. 3, 133–138 (1978)

    CAS  Google Scholar 

  151. Cohen, S.C., Tabor, D.: The friction and lubrication of polymers. Proc. Roy. Soc. Lond. Series A 291, 186–207 (1966)

    Google Scholar 

  152. Evans, D.C. (1978) Polymer-fluid interactions in relation to wear. In: Proceedings of the 3rd Leeds-Lyon Symposium on Tribology, Wear of Non-Metallic Materials, Sept. 1976. University of Leeds, London, pp. 47–71 (1978)

    Google Scholar 

  153. Batchelor, A.W., Tan, B.P.: Effect of an oxidizing agent on the friction and wear of nylon 6 against a steel counterface, vol. I, pp. 175–180. In: Proceedings of the 4th International Tribology Conference, AUSTRIB’94. Uniprint UWA (1994)

    Google Scholar 

  154. Scott, N.W., Stachowiak, G.W.: Long-term behaviour of UHMWPE in hydrogen peroxide solutions, vol. I, pp. 169–174. In: Proceedings of the 4th International Tribology Conference, AUSTRIB´94. Uniprint UWA (1994)

    Google Scholar 

  155. Bartenevev, G.M., Lavrentev, V.V.: Friction and wear of polymers. Tribology, Tribology Series, no. 6, p. 10-260. Elsevier Scientific Publishing Company, Amsterdam (1981)

    Google Scholar 

  156. Burris, D.L., Sawyer, W.G.: A low friction and ultra low wear rate PEEK/PTFE composite. Wear 261, 410–418 (2006)

    Article  CAS  Google Scholar 

  157. Zhang, S.W., Deguo, W., Yin, W.: Investigation of abrasive erosion of polymers. J. Mater. Sci. 30, 4561–4566 (1995)

    Article  CAS  Google Scholar 

  158. Zhang, S.W., Deguo, W., He, R., Fan, Q.: Abrasive erosion of polyurethane. J. Mater. Sci. 36, 5037–5043 (2001)

    Article  CAS  Google Scholar 

  159. Arnold, J.C., Hutchings, I.M.: The mechanisms of erosion of unfilled elastomers by solid particle impact. Wear 138, 33–46 (1990)

    Article  CAS  Google Scholar 

  160. Bely, V.A., Sviridenok, A.I., Petrokovets, M.I., Savkin, V.G.: Friction and wear in polymer-based materials, p. 416. Pergamon Press, Oxford (1982)

    Google Scholar 

  161. Andrew, W.: Fatigue and Tribological Properties of Plastics and Elastomers, vol. VI. Plastics Design Library, New York (1995)

    Google Scholar 

  162. Swain, M.V.: Microscopic observation of abrasive wear of polycrystalline alumina. Wear 35, 185–189 (1975)

    Article  CAS  Google Scholar 

  163. Bhowmick, A.K., Basu, S., De, S.K.: Scanning electron microscopy studies of abraded rubber surfaces. J. Mater. Sci. 16(6), 1654 (1981)

    Article  CAS  Google Scholar 

  164. Kayaba, T.: The latest investigations of wear by the microscopic observations. JSLE Trans. 29, 9–14 (1984)

    Google Scholar 

  165. Kuriakose, B., De, S.K.: Scanning electron microscopy studies on tensile, tear and abrasion of thermoplastic elastomers. J. Mater. Sci. 20–5, 1864–1872 (1985)

    Article  Google Scholar 

  166. Thomas, S.: Scanning electron microscopy studies on wear properties of blends of plasticized poly(vinyl chloride) and thermoplastic copolyester elastomer. Wear 116, 201–209 (1987)

    Article  CAS  Google Scholar 

  167. Singer, I.L., Wahl, K.J.: Role of third bodies in friction and wear. J. Vac. Sci. Tech. A. Vac. Surf. Films 21(5), 232–240 (2003)

    Google Scholar 

  168. Zum Gahr K.H.: Wear by hard particles. Tribol. Int. 31(10), 587–596 (1998)

    Google Scholar 

  169. Harsha, A.P., Tewari, U.S.: Two-body and three-body abrasive wear behaviour of polyaryletherketone composites. Polym. Tests 22, 403 (2003)

    Google Scholar 

  170. Johnson, R.W.: The use of the scanning electron microscope to study the deterioration of abrasive papers. Wear 12, 213–216 (1968)

    Article  Google Scholar 

  171. Misra, A., Finnie, I.: A classification of three-body abrasive wear and design of a new tester. ASTM International Conference On Wear of Materials, 1979

    Google Scholar 

  172. Jain, V.K., Bahadur, S.: Surface topography changes in polymer-metal sliding. In: Proceedings of International Conference on Wear of Materials, Dearborn, p. 581 (1979)

    Google Scholar 

  173. Neale, M.J., Gee, M.: Guide to Wear Problems and Testing for Industry. William Andrew Publishing, New York (2001)

    Google Scholar 

  174. Jia, X., Ling, R.: Two-body free-abrasive wear of polyethylene, nylon 1010, epoxy and polyurethane coatings. Tribol. Int. 40(8), 1276–1283 (2007)

    Article  CAS  Google Scholar 

  175. Liu J.J., Zhou P.A., Sun, X.T., Liao, Q.C.: Adhesive Wear and Fatigue Wear of Materials, pp. 234–323. Machinery Industry Press, Beijing (1989)

    Google Scholar 

  176. Marchenko, E.A.: Essentials of Friction Breakage for Metals Surface, pp. 1–8. National Defence Industry Press, Beijing (1990)

    Google Scholar 

  177. Johnson, K.L.: Contact mechanics and the wear of metals. Wear 190, 162–170 (1995)

    Article  CAS  Google Scholar 

  178. Suh, N.P., Mosleh, M., Arinez, J.: Tribology of polyethylene homocomposites. Wear 214, 231–236 (1998)

    Article  CAS  Google Scholar 

  179. Da Silva, R.C.L., Da Silva, C.H., Medeiros, J.T.N.: Is there delamination wear in polyurethane? Wear 263(7–12), 974–983 (2007)

    Article  CAS  Google Scholar 

  180. Holzapfel, G.A.: Nonlinear Solid Mechanics. A Continuum Approach for Engineering. John Wiley & Sons, Chichester (2000)

    Google Scholar 

  181. Marlow, R.S.: A general first-invariant hyperelastic constitutive model. In: Busfield, A., Muhr, A. (eds.) Constitutive Models for Rubber III, pp. 157–160. ©2003 Swets & Zeitlinger, Lisse, ISBN 90 5809 566 5

    Google Scholar 

  182. Chaboche, J.L.: Continuum damage mechanics: present state and future trends. Nucl. Eng. Des. 105, 19–33 (1987)

    Article  Google Scholar 

  183. Kaliske, M., Rothert, H.: Viscoelastic and elastoplastic damage formulations. In: Dorfmann, A., Muhr, A. (eds.) Constitutive Models for Rubber I, pp. 159–167. ©1999 Balkema, Rotterdam, ISBN 90 5809 113 9

    Google Scholar 

  184. Miehe, C.: Discontinuous and continuous damage evolution in Ogden-type large strain elastic materials. Eur. J. Mech. A/Solids 14, 697–724 (1995)

    Google Scholar 

  185. Desmorat, R., Cantournet, S.: Thermodynamics modelling of internal friction and hysteresis of elastomers. In: Besdo, D., Shuster, R.H., Ihlemann, J. (eds.) Constitutive Models for Rubber II, pp. 37–43. ©2001 Swets & Zeitlinger, ISBN 90 2651 847 1

    Google Scholar 

  186. De Souza Neto, E.A., et al.: A phenomenological three-dimensional rate-independent continuum damage model for highly filled polymers: formulation and computational aspects. J. Mech. Phys. Solids 42, 1533–1550 (1994)

    Google Scholar 

  187. Aubard, X., et al.: Modelling and simulation of damage in elastomer structures at high strains. Comput. Struct. 80, 2289–2298 (2002)

    Article  Google Scholar 

  188. Reese, S., Wriggers, P.: Modelling of the thermo-mechanical material behaviour of rubber-like polymers—micromechanical motivation and numerical simulation. In: Dorfmann, A., Muhr, A. (eds.) Constitutive Models for Rubber I, pp. 13–21. ©1999 Balkema, Rotterdam, ISBN 90 5809 113 9

    Google Scholar 

  189. Klüppel, M., Schramm, J.: Advanced micro-mechanical model of hyperelasticity and stress softening of reinforced rubbers. In: Dorfmann, A., Muhr, A. (eds.) Constitutive Models for Rubber I, pp. 211–218. ©1999 Balkema, Rotterdam, ISBN 90 5809 113 9

    Google Scholar 

  190. Heinrich, G.: Statistical-mechanical basis of constitutive models for heterogeous rubber materials. In: Besdo, D., Shuster, R.H., Ihlemann, J. (eds.) Constitutive Models for Rubber II, pp. 3–10. ©2001 Swets & Zeitlinger, ISBN 90 2651 847 1

    Google Scholar 

  191. Achenbach, M.: A model to describe filler effects in rubber. In: Besdo, D., Shuster, R.H., Ihlemann, J. (eds.) Constitutive Models for Rubber II, pp. 21–26. ©2001 Swets & Zeitlinger, ISBN 90 2651 847 1

    Google Scholar 

  192. Govindjee, S., Simo, J.: A Micro-mechanically based continuum damage model for carbon black-filled rubber incorporating Mullins’ effect. J. Mech. Phys. Solids 39, 87–112 (1991)

    Article  Google Scholar 

  193. Lubliner, J.: A model of rubber viscoelasticity. Mech. Res. Comm. 12, 93–99 (1985)

    Article  Google Scholar 

  194. Lianis, G.: Small deformations superposed on large deformation in viscoelastic bodies. In: Proceedings of the Fourth International Congress on Rheology, pt. 2, pp. 104–119. Interscience, New York (1965)

    Google Scholar 

  195. Coleman, B.D., Noll, W.: An approximation theorem for functional with applications to continuum mechanics. Arch. Ratl. Mech. Anal. 6, 355–370 (1960)

    Google Scholar 

  196. Besdo, D., Ihlemann, J.: A phenomenological constitutive model for rubber like materials and its numerical applications. Int. J. Plast. 19, 1019–1036 (2003)

    Article  CAS  Google Scholar 

  197. Qi, H., Boyce, M.C.: Constitutive model for stretch-induced softening of the stress-strain behavior of elastomeric materials. J. Mech. Phys. Solids 52, 2187–2205 (2004)

    Article  CAS  Google Scholar 

  198. Marckmann, G., Verron, E., Gornet, L., Chagnon, G., Charrier, P., Fort, P.: A theory of network alteration for the Mullins effect. J. Mech. Phys. Solids 50, 2011–2028 (2002)

    Article  CAS  Google Scholar 

  199. Gracia, L.A.: Simulación por Elementos Finitos de efectos inelásticos en materiales elastómeros. Ph.D. Thesis, Universidad de Zaragoza (2006)

    Google Scholar 

  200. Fielding, J.H.: Flex life and crystallization of synthetic rubber. Ind. Eng. Chem. 35, 1259–1261 (1943)

    Article  CAS  Google Scholar 

  201. Standard test method for rubber property—extension cycling fatigue, ASTM D 4482-85 (1994)

    Google Scholar 

  202. Klenke, D., Beste, A.: Ensurance of the fatigue-life of metal–rubber components. Kautschuk und Gummi Kunstoffe 40, 1067–1071 (1987)

    CAS  Google Scholar 

  203. Grosch, K.: Rolling resistance and fatigue life of tires. Rubber Chem. Technol. 61, 42–63 (1988)

    Article  CAS  Google Scholar 

  204. DeEskinazi, J., Ishihara, K., Volk, H., Warholic, T.C.: Towards predicting relative belt edge endurance with the FE method. Tire Sci. Technol. 18, 216–235 (1990)

    Article  Google Scholar 

  205. Oh, H.L.: A fatigue-life model of a rubber bushing. Rubber Chem. Technol. 53, 1226–1238 (1980)

    Article  Google Scholar 

  206. Griffith, A.: The phenomenon of rupture and flow in solids. Phil. Trans. Real Soc. Lond. Ser. A 221, 163–198 (1920)

    Article  Google Scholar 

  207. Lindley, P.B.: Ozone attack at a rubber–metal bond. J. Inst. Rubber Ind. 5, 243–248 (1971)

    CAS  Google Scholar 

  208. Mars, W.V., Fatemi, A.: A phenomenological model for the effect of R ratio on fatigue of strain crystallizing rubbers. J. Rubber Chem. Technol. 76(5), 1241–1258 (2003)

    Article  CAS  Google Scholar 

  209. Pereña, J.M., Benavente, R., Cerrada, M.L.: Ciencia y Tecnología de materiales polímeros. Ed. CSIC I, 233–248 (2004)

    Google Scholar 

  210. Williams, M.L., Landel, R.F., Ferry, J.D.: The temperature dependant of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 77(14), 3701–3707 (1955)

    Article  CAS  Google Scholar 

  211. Gracia, L.A., Liarte, E., Pelegay, J.L., Calvo, B.: FE simulation of the hysteretic behavior of an industrial rubber. Application to design of rubber components. Finite Elem. Anal. Des. 46, 357–368 (2010)

    Article  Google Scholar 

  212. Gracia, L.A., Peña, E., Royo, J.M., Pelegay, J.L., Calvo, B.: A comparison between pseudo-elastic and damage models for modelling the Mullins effect in industrial rubber components. Mech. Res. Commun. 36, 769–776 (2009)

    Article  Google Scholar 

  213. Blau, P.J., De Vore, C.E.: Sliding friction and wear behaviour of several nickel aluminide alloys under dry and lubricated conditions. Tribol. Int. 23(4), 226–234 (1990)

    Article  CAS  Google Scholar 

  214. Plint, A.G., Plint, M.A.: A new technique or the investigation of stick-slip. Tribol. Int. 18(4), 247–249 (1985)

    Article  Google Scholar 

  215. Song, J., Liu, P., Cremens, M., Bonutti, P.: Effects of machining on tribological behavior of ultra high molecular weight polyethylene (UHMWPE) under dry reciprocating sliding. Wear 225–229, 716–723 (1999)

    Article  Google Scholar 

  216. Franklin, S.E.: Wear experiments with selected engineering polymers and polymer composites under dry reciprocating sliding conditions. Wear 251, 1591–1598 (2001)

    Article  Google Scholar 

  217. Barwell, F.T.: Wear of metals. Wear 1, 317–332, 1957–1958 (1958)

    Google Scholar 

  218. Rhee, S.K.: Wear equation for polymers sliding against metal surfaces. Wear 16, 431–445 (1970)

    Article  Google Scholar 

  219. Cantizano, A., Carnicero, A., Zavarise, G.: Numerical simulation of wear-mechanism maps. Comput. Mater. Sci. 25, 54–60 (2002)

    Article  CAS  Google Scholar 

  220. Torrance, A.A.: A method for calculating boundary friction and wear. Wear 258, 924–934 (2005)

    Article  CAS  Google Scholar 

  221. Archard, J.F.: Contact and rubbing of flat surfaces. J. Appl. Phys. 24, 981–988 (1953)

    Article  Google Scholar 

  222. Greenwood, J.A., Williamson J.B.P.: Contact of nominally flat surfaces. Proc. R. Soc. Lond. Ser. A 295, 300–319 (1966)

    Google Scholar 

  223. Sarkar, A.D.: Friction and Wear. Academic Press, London (1980)

    Google Scholar 

  224. Liu, R., Li, D.Y.: Modification of Archard’s equation by taking account of elastic/pseudoelastic properties of materials. Wear 251, 956–964 (2001)

    Article  Google Scholar 

  225. Molinari, J.F., Ortiz, M., Radovitzky, R., Repetto, E.A.: FE modeling of dry sliding wear in metals. Eng. Comput. 18, 592–609 (2001)

    Article  Google Scholar 

  226. MSC MARC.: Theory and User Information, vol A. MSC Software Corporation, Santa Ana, CA, USA (2001)

    Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge the financial support from the Spanish Ministry of Science and Technology through Research Projects DPI2001-2406, DPI2004-06747, and DPI2008-02335 as well as the cortesy of the companies Industrias E. Díaz, S. A., Caucho Metal Productos, Construcciones y Auxiliar de Ferrocarril, S. A. and TRW Automotive for allowing to publish their industrial examples.

Author information

Authors and Affiliations

  1. Grupo de Investigación Aplicada en Simulación, Caracterización, Diseño y Desarrollo de Materiales (SICADDEMA), Instituto Tecnológico de Aragón (ITA), Zaragoza, Spain

    L. A. Gracia, J. M. Bielsa, F. J. Martínez, J. M. Royo & J. L. Pelegay

  2. Aragón Institute of Engineering Research, University of Zaragoza, Zaragoza, Spain

    B. Calvo

  3. Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BNN), Zaragoza, Spain

    B. Calvo

Authors
  1. L. A. Gracia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. Bielsa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. J. Martínez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. M. Royo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. L. Pelegay
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. B. Calvo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. A. Gracia .

Editor information

Editors and Affiliations

  1. , Centre for Nanoscience and Nanotech., Mahatma Gandhi University, Priyadarshini Hills P. O., Kottayam, Kerlala, 686 560, India

    P. M. Visakh

  2. , Nanoscience and Nanotechnology, Mahatma Gandhi University, Priyadarshini Hills P. O., Kottayam, Kerala, 686 560, India

    Sabu Thomas

  3. Apollo Tyres Ltd., Gujarat, India

    Arup K. Chandra

  4. , Dept. Applied Physics and Mech. Eng., Lulea University of Technology, Lulea, 97187, Sweden

    Aji. P. Mathew

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gracia, L.A., Bielsa, J.M., Martínez, F.J., Royo, J.M., Pelegay, J.L., Calvo, B. (2013). Other Applications: Engineering. In: Visakh, P., Thomas, S., Chandra, A., Mathew, A. (eds) Advances in Elastomers II. Advanced Structured Materials, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20928-4_9

Download citation

Publish with us

Policies and ethics

Search

Navigation