Other Applications: Engineering

  • L. A. GraciaEmail author
  • J. M. Bielsa
  • F. J. Martínez
  • J. M. Royo
  • J. L. Pelegay
  • B. Calvo
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 12)


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.


Fatigue Life Energy Release Rate Natural Rubber Finite Element Simulation Strain Energy Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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.


  1. 1.
    Hamed, G.R., Hatfield, S.: On the role of bound rubber in carbon black reinforcement. Rubber Chem. Technol. 62, 143–156 (1989)CrossRefGoogle Scholar
  2. 2.
    Meinecke, E.A., Taftaf, M.I.: Effect of carbon black on the mechanical properties of elastomers. Rubber Chem. Technol. 61, 534–547 (1988)CrossRefGoogle Scholar
  3. 3.
    So, H., Chen, U.D.: A nonlinear mechanical model for solid filled polymers. Polym. Eng. Sci. 6, 410–416 (1991)Google Scholar
  4. 4.
    Zienkiewicz, O.C., Taylor, R.L.: The FE Method, vol. 1: Basic Formulation and Linear Problems. McGraw-Hill, London (1989)Google Scholar
  5. 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. 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)CrossRefGoogle Scholar
  7. 7.
    Govindjee, S., Simo, J.: Mullins effect and the strain amplitude dependence of the storage modulus. Int. J. Solids Struct. 29, 1737–1751 (1992)CrossRefGoogle Scholar
  8. 8.
    Lion, A.: A constitutive model for carbon black filled rubber: experimental investigations and mathematical representation. Continuum Mech. Thermodyn. 8, 153–169 (1996)CrossRefGoogle Scholar
  9. 9.
    Lion, A.: Thixotropic behaviour of rubber Ander dynamic loading histories: Experiments and theory. J. Mech. Phys. Solids 46(5), 895–930 (1998)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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)CrossRefGoogle Scholar
  12. 12.
    Bergström, J.S., Boyce, M.C.: Large strain time-dependent behavior of filled elastomers. Mech. Mater. 32, 627–644 (2000)CrossRefGoogle Scholar
  13. 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)CrossRefGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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. 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)CrossRefGoogle Scholar
  17. 17.
    Treolar, L.R.G.: The Physics of Rubber Elasticity. Oxford University Press, Oxford (1975)Google Scholar
  18. 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)CrossRefGoogle Scholar
  19. 19.
    Yeoh, O.H.: Characterisation of elastic properties of carbon-black filled rubber vulcanizates. Rubber Chem. Technol. 63, 792–805 (1990)CrossRefGoogle Scholar
  20. 20.
    Mooney, M.: A theory of large elastic deformation. J. Appl. Phys. 11, 582–592 (1940)CrossRefGoogle Scholar
  21. 21.
    James, H.M., Guth, E.: Theory of the elastic properties of rubber. J. Chem. Phys. 11(10), 455–481 (1943)CrossRefGoogle Scholar
  22. 22.
    Wall, F.T., Flory, P.J.: Statistical thermodynamics of rubber elasticity. J. Chem. Phys. 19(12), 1435–1439 (1951)CrossRefGoogle Scholar
  23. 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)CrossRefGoogle Scholar
  24. 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)CrossRefGoogle Scholar
  25. 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)CrossRefGoogle Scholar
  26. 26.
    Ogden, R.W.: Non-linear Elastic Deformations. Dover Publications, Ellis Harwood Ltd, New York (1984)Google Scholar
  27. 27.
    Yeoh, O.H.: Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66, 754–771 (1993)CrossRefGoogle Scholar
  28. 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)CrossRefGoogle Scholar
  29. 29.
    Gent, A.N., Thomas, A.G.: Forms of the stored (strain) energy function for vulcanized rubber. J. Polym. Sci. 28, 625–637 (1958)CrossRefGoogle Scholar
  30. 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)CrossRefGoogle Scholar
  31. 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)CrossRefGoogle Scholar
  32. 32.
    Ferry, J.D.: Viscoelastic Properties of Polymers. John Wiley & Sons, Inc., New York (1980)Google Scholar
  33. 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)CrossRefGoogle Scholar
  34. 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)CrossRefGoogle Scholar
  35. 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)CrossRefGoogle Scholar
  36. 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. 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. 38.
    Besdo, D., Ihlemann, J.: Zur Modellierung des Stoffverhaltens von Elastomeren. Kautschuck un Gummi Kunstoffe 49, 495–503 (1996)Google Scholar
  39. 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. 40.
    Vidal, A., Donnet, J.B.: Carbon black: surface properties and interactions with elastomers. Adv. Polym. Sci. 76, 104–106 (1996)Google Scholar
  41. 41.
    Mullins, L.: Effect of stretching on the properties of rubber. Rubber Chem. Technol. 21, 281–300 (1948)CrossRefGoogle Scholar
  42. 42.
    Mullins, L., Tobin, N.R.: Stress softening in rubber vulcanizates. Part I. J. Appl. Polym. Sci. 9, 2993 (1965)CrossRefGoogle Scholar
  43. 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)CrossRefGoogle Scholar
  44. 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)CrossRefGoogle Scholar
  45. 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)CrossRefGoogle Scholar
  46. 46.
    Bueche, F.: Molecular basis for the Mullins effect. J. Appl. Polym. Sci. 4(10), 107–114 (1960)CrossRefGoogle Scholar
  47. 47.
    Bueche, F.: Mullins effect and rubber-filler interaction. J. Appl. Polym. Sci. 5(15), 271–281 (1961)CrossRefGoogle Scholar
  48. 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)CrossRefGoogle Scholar
  49. 49.
    Kachanov, L.M.: Introduction to Continuum Damage Mechanics. Martinus Nijhoff Publishers, Dordrecht (1986)CrossRefGoogle Scholar
  50. 50.
    Lemaitre, J.: A Course on Damage Mechanics. Springer, Berlin (1992)Google Scholar
  51. 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)CrossRefGoogle Scholar
  52. 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 9Google Scholar
  53. 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. 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 1Google Scholar
  55. 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. 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. 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. 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 1Google Scholar
  59. 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 5Google Scholar
  60. 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)CrossRefGoogle Scholar
  61. 61.
    MSC MARC User’s manual (2005)Google Scholar
  62. 62.
    Miller, K.: Testing and Analysis. Measuring the Dynamic Properties of Elastomers for Analysis. Dynamic Review. Axel Products, Ann Arbor (2000)Google Scholar
  63. 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 2006Google Scholar
  64. 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. 65.
    Lake, G.J.: Mechanical fatigue of rubber. Rubber Chem. Technol. 45, 309 (1972)CrossRefGoogle Scholar
  66. 66.
    Lake, G.J.: Fatigue and fracture of elastomers. Rubber Chem. Technol. 68, 435–460 (1995)CrossRefGoogle Scholar
  67. 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. 68.
    Roach, J.F.: Crack growth in elastomers under biaxial stress. Ph.D. dissertation, University of Akron (1982)Google Scholar
  69. 69.
    Lake, G.J.: Aspects of fatigue and fracture of rubber. Prog. Rubber Technol. 45, 89 (1983)Google Scholar
  70. 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)CrossRefGoogle Scholar
  71. 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. 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. 73.
    Mars, W.V.: Multiaxial fatigue on rubber. Ph.D. thesis, University of Toledo (2001)Google Scholar
  74. 74.
    Flamm, M., Steinweger, T., Weltin, U.: Schadeakkumulation bei Elastomeren. Kautschuk Gummi Kunststoffe 55(12), 665–668 (2002)Google Scholar
  75. 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)CrossRefGoogle Scholar
  76. 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)CrossRefGoogle Scholar
  77. 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 3Google Scholar
  78. 78.
    Thomas, A.G.: Rupture of rubber. VI. Further experiments on the tear criterion. J. Polym. Sci. 31, 467 (1958)CrossRefGoogle Scholar
  79. 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. 80.
    Lindley, P.B.: Non-relaxing crack growth and fatigue in a non-crystallizing rubber. Rubber Chem. Technol. 47, 1253–1264 (1974)CrossRefGoogle Scholar
  81. 81.
    Rabinowicz, E.: Friction and Wear of Materials, 2nd edn. Wiley-Interscience, New York (1995)Google Scholar
  82. 82.
    Stachowiak, G.W., Batchelor A.W.: Engineering Tribology, 3rd edn. Elsevier (2011) Google Scholar
  83. 83.
    Zhang, S.W.: State-of-the-art of polymer tribology. Tribol. Int. 31, 49–60 (1998)CrossRefGoogle Scholar
  84. 84.
    Persson, B.N.J.: Sliding Friction: Physical Principles and Applications, 2nd edn. Springer, Heidelberg (2000)Google Scholar
  85. 85.
    Thirion, P.: Les coefficients d’adhérence du caoutchouc. Rubber Chem. Technol. 21, 505–515 (1948)CrossRefGoogle Scholar
  86. 86.
    Persson, B.N.J.: Theory of rubber friction and contact mechanics. J. Chem. Phys. 115–118, 3840–3861 (2001)CrossRefGoogle Scholar
  87. 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)CrossRefGoogle Scholar
  88. 88.
    Kragelskii, I.V.: Friction and Wear, p. 458. Pergamon Press, Elmsford (1982)Google Scholar
  89. 89.
    Blau, P.J.: Friction and wear transitions of materials. Noyes Publication, New York (1989)Google Scholar
  90. 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. 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)CrossRefGoogle Scholar
  92. 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)CrossRefGoogle Scholar
  93. 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. 94.
    Nah, C.: Ph.D. dissertation, Wear mechanisms of rubber compounds, The University of Akron (1995) Google Scholar
  95. 95.
    Meng, H.C., Ludema, K.C.: Wear models and predictive equations: their form and content. Wear 181–183, 443–457 (1995)CrossRefGoogle Scholar
  96. 96.
    Muhr, A.H.: Dynamic properties of rubber. In: Proceedings, ACEM, NR in Engineering Workshop. Kulalumpur, Sept. 1991Google Scholar
  97. 97.
    Hibbitt, Karlsson and Sorensen. Abaqus Standard Theory and User’s Manual v6.5 (2005)Google Scholar
  98. 98.
    Freakly, P.K., Payne, A.R.: Theory and Practise of Engineering with Rubber. Applied Science Publishers, London (1978)Google Scholar
  99. 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 5Google Scholar
  100. 100.
    Muhr, A.H.: Properties of rubber compounds for engineering applications. J. Nat. Rubber Res. 7(1), 14–37 (1992)Google Scholar
  101. 101.
    Ahmadi, H.R., Muhr, A.H.: Modelling dynamic properties of filled rubber. Plast. Rubber Compos. Process. Appl. 26, 451–461 (1997)Google Scholar
  102. 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 1987Google Scholar
  103. 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)CrossRefGoogle Scholar
  104. 104.
    Mullins, L.: Softening of rubber by deformation. Rubber Chem. Technol. 42, 339–362 (1969)CrossRefGoogle Scholar
  105. 105.
    Mullins, L., Tobin, N.R.: Theoretical model for the elastic behaviour of filler-reinforced vulcanized rubber. Rubber Chem. Technol. 30, 555–571 (1957)CrossRefGoogle Scholar
  106. 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. 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)CrossRefGoogle Scholar
  108. 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)CrossRefGoogle Scholar
  109. 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)CrossRefGoogle Scholar
  110. 110.
    Roland, C.M.: Dynamic mechanical behaviour of filled rubber at small strains. J. Rheol. 34, 25 (1990)CrossRefGoogle Scholar
  111. 111.
    Medalia, A.I.: Effects of carbon-black on dynamic properties of rubber. Rubber Chem. Technol. 51, 437 (1978)CrossRefGoogle Scholar
  112. 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. 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. 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. 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)CrossRefGoogle Scholar
  116. 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)CrossRefGoogle Scholar
  117. 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)CrossRefGoogle Scholar
  118. 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)Google Scholar
  119. 119.
    Saintier, N., Cailletaud, G., Piques, R.: Crack initiation and propagation under multiaxial fatigue. Int. J. Fatigue 28, 61–72 (2006)CrossRefGoogle Scholar
  120. 120.
    Saintier, N., Cailletaud, G., Piques, R.: Multiaxial fatigue life prediction for a natural rubber. Int. J. Fatigue 28, 530–539 (2006)CrossRefGoogle Scholar
  121. 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)CrossRefGoogle Scholar
  122. 122.
    Rivlin, R.S., Thomas, A.G.: Rupture of rubber. I. Characteristic energy for tearing. J. Polym. Sci. 10, 291–318 (1953)CrossRefGoogle Scholar
  123. 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. 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. 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)Google Scholar
  126. 126.
    Lindley, P.B., Stevenson, A.: Fatigue resístanse of natural rubber in compression. Rubber Chem. Technol. 55, 337–351 (1982)CrossRefGoogle Scholar
  127. 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. 128.
    Fielding-Russell, G.S., Rongone, R.L.: Fatiguing of rubber–rubber interfaces. Rubber Chem. Technol. 56, 838–844 (1983)CrossRefGoogle Scholar
  129. 129.
    Verron, E., Le Cam, J.B., Gournet, L.: A multiaxial criterion for crack nucleation in rubber. Mech. Re. Commun. 33, 493–498 (2006)CrossRefGoogle Scholar
  130. 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. 131.
    Andriyana, A., Verron, E.: Prediction of fatigue life improvement in natural rubber using configurational stress. Int. J. Solids Struct. 44, 2079–2092 (2007)CrossRefGoogle Scholar
  132. 132.
    Wang, B., Lu, H., Kim, G.: A damage model for the fatigue life of elastomeric materials. Mech. Mater. 34, 475–483 (2002)CrossRefGoogle Scholar
  133. 133.
    Schallamach, A.: Friction and abrasion of rubber. Wear 1, 384–417 (1958)CrossRefGoogle Scholar
  134. 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. 135.
    Buckley, D.H.: Surface effects in adhesion, friction, wear and lubrication. Elsevier, Amsterdam (1981)Google Scholar
  136. 136.
    Makinson, K.R., Tabor, D.: The friction and transfer of polytetrafluoroethylene. Proc. R. Soc. Lond. Ser. A 281, 49–61 (1964)CrossRefGoogle Scholar
  137. 137.
    Tanaka, K., Uchiyama, Y., Toyooka, S.: The mechanism of wear of PTFE. Wear 23, 153–172 (1973)CrossRefGoogle Scholar
  138. 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. 139.
    Jain, V.K., Bahadur, S.: Material transfer in polymer–polymer sliding. Wear 46, 177–198 (1978)CrossRefGoogle Scholar
  140. 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. 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. 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)CrossRefGoogle Scholar
  143. 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. 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)CrossRefGoogle Scholar
  145. 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. 146.
    Kar, M.K., Bahadur, S.: Micromechanism of wear at polymer-metal sliding interface. Wear 46, 189–202 (1978)CrossRefGoogle Scholar
  147. 147.
    Ettles, Mc C., C.M., : Polymer and elastomer friction in the thermal control regime. ASLE Trans. 30, 149–159 (1987)CrossRefGoogle Scholar
  148. 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. 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. 150.
    Southern, E., Thomas, A.G.: Studies of rubber abrasion. Plast. Rubber Mater. Appl. 3, 133–138 (1978)Google Scholar
  151. 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. 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. 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. 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. 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. 156.
    Burris, D.L., Sawyer, W.G.: A low friction and ultra low wear rate PEEK/PTFE composite. Wear 261, 410–418 (2006)CrossRefGoogle Scholar
  157. 157.
    Zhang, S.W., Deguo, W., Yin, W.: Investigation of abrasive erosion of polymers. J. Mater. Sci. 30, 4561–4566 (1995)CrossRefGoogle Scholar
  158. 158.
    Zhang, S.W., Deguo, W., He, R., Fan, Q.: Abrasive erosion of polyurethane. J. Mater. Sci. 36, 5037–5043 (2001)CrossRefGoogle Scholar
  159. 159.
    Arnold, J.C., Hutchings, I.M.: The mechanisms of erosion of unfilled elastomers by solid particle impact. Wear 138, 33–46 (1990)CrossRefGoogle Scholar
  160. 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. 161.
    Andrew, W.: Fatigue and Tribological Properties of Plastics and Elastomers, vol. VI. Plastics Design Library, New York (1995)Google Scholar
  162. 162.
    Swain, M.V.: Microscopic observation of abrasive wear of polycrystalline alumina. Wear 35, 185–189 (1975)CrossRefGoogle Scholar
  163. 163.
    Bhowmick, A.K., Basu, S., De, S.K.: Scanning electron microscopy studies of abraded rubber surfaces. J. Mater. Sci. 16(6), 1654 (1981)CrossRefGoogle Scholar
  164. 164.
    Kayaba, T.: The latest investigations of wear by the microscopic observations. JSLE Trans. 29, 9–14 (1984)Google Scholar
  165. 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)CrossRefGoogle Scholar
  166. 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)CrossRefGoogle Scholar
  167. 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. 168.
    Zum Gahr K.H.: Wear by hard particles. Tribol. Int. 31(10), 587–596 (1998) Google Scholar
  169. 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. 170.
    Johnson, R.W.: The use of the scanning electron microscope to study the deterioration of abrasive papers. Wear 12, 213–216 (1968)CrossRefGoogle Scholar
  171. 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, 1979Google Scholar
  172. 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. 173.
    Neale, M.J., Gee, M.: Guide to Wear Problems and Testing for Industry. William Andrew Publishing, New York (2001)Google Scholar
  174. 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)CrossRefGoogle Scholar
  175. 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. 176.
    Marchenko, E.A.: Essentials of Friction Breakage for Metals Surface, pp. 1–8. National Defence Industry Press, Beijing (1990)Google Scholar
  177. 177.
    Johnson, K.L.: Contact mechanics and the wear of metals. Wear 190, 162–170 (1995)CrossRefGoogle Scholar
  178. 178.
    Suh, N.P., Mosleh, M., Arinez, J.: Tribology of polyethylene homocomposites. Wear 214, 231–236 (1998)CrossRefGoogle Scholar
  179. 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)CrossRefGoogle Scholar
  180. 180.
    Holzapfel, G.A.: Nonlinear Solid Mechanics. A Continuum Approach for Engineering. John Wiley & Sons, Chichester (2000)Google Scholar
  181. 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 5Google Scholar
  182. 182.
    Chaboche, J.L.: Continuum damage mechanics: present state and future trends. Nucl. Eng. Des. 105, 19–33 (1987)CrossRefGoogle Scholar
  183. 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 9Google Scholar
  184. 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. 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 1Google Scholar
  186. 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. 187.
    Aubard, X., et al.: Modelling and simulation of damage in elastomer structures at high strains. Comput. Struct. 80, 2289–2298 (2002)CrossRefGoogle Scholar
  188. 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 9Google Scholar
  189. 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 9Google Scholar
  190. 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 1Google Scholar
  191. 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 1Google Scholar
  192. 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)CrossRefGoogle Scholar
  193. 193.
    Lubliner, J.: A model of rubber viscoelasticity. Mech. Res. Comm. 12, 93–99 (1985)CrossRefGoogle Scholar
  194. 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. 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. 196.
    Besdo, D., Ihlemann, J.: A phenomenological constitutive model for rubber like materials and its numerical applications. Int. J. Plast. 19, 1019–1036 (2003)CrossRefGoogle Scholar
  197. 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)CrossRefGoogle Scholar
  198. 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)CrossRefGoogle Scholar
  199. 199.
    Gracia, L.A.: Simulación por Elementos Finitos de efectos inelásticos en materiales elastómeros. Ph.D. Thesis, Universidad de Zaragoza (2006)Google Scholar
  200. 200.
    Fielding, J.H.: Flex life and crystallization of synthetic rubber. Ind. Eng. Chem. 35, 1259–1261 (1943)CrossRefGoogle Scholar
  201. 201.
    Standard test method for rubber property—extension cycling fatigue, ASTM D 4482-85 (1994)Google Scholar
  202. 202.
    Klenke, D., Beste, A.: Ensurance of the fatigue-life of metal–rubber components. Kautschuk und Gummi Kunstoffe 40, 1067–1071 (1987)Google Scholar
  203. 203.
    Grosch, K.: Rolling resistance and fatigue life of tires. Rubber Chem. Technol. 61, 42–63 (1988)CrossRefGoogle Scholar
  204. 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)CrossRefGoogle Scholar
  205. 205.
    Oh, H.L.: A fatigue-life model of a rubber bushing. Rubber Chem. Technol. 53, 1226–1238 (1980)CrossRefGoogle Scholar
  206. 206.
    Griffith, A.: The phenomenon of rupture and flow in solids. Phil. Trans. Real Soc. Lond. Ser. A 221, 163–198 (1920)CrossRefGoogle Scholar
  207. 207.
    Lindley, P.B.: Ozone attack at a rubber–metal bond. J. Inst. Rubber Ind. 5, 243–248 (1971)Google Scholar
  208. 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)CrossRefGoogle Scholar
  209. 209.
    Pereña, J.M., Benavente, R., Cerrada, M.L.: Ciencia y Tecnología de materiales polímeros. Ed. CSIC I, 233–248 (2004)Google Scholar
  210. 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)CrossRefGoogle Scholar
  211. 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)CrossRefGoogle Scholar
  212. 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)CrossRefGoogle Scholar
  213. 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)CrossRefGoogle Scholar
  214. 214.
    Plint, A.G., Plint, M.A.: A new technique or the investigation of stick-slip. Tribol. Int. 18(4), 247–249 (1985)CrossRefGoogle Scholar
  215. 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)CrossRefGoogle Scholar
  216. 216.
    Franklin, S.E.: Wear experiments with selected engineering polymers and polymer composites under dry reciprocating sliding conditions. Wear 251, 1591–1598 (2001)CrossRefGoogle Scholar
  217. 217.
    Barwell, F.T.: Wear of metals. Wear 1, 317–332, 1957–1958 (1958)Google Scholar
  218. 218.
    Rhee, S.K.: Wear equation for polymers sliding against metal surfaces. Wear 16, 431–445 (1970)CrossRefGoogle Scholar
  219. 219.
    Cantizano, A., Carnicero, A., Zavarise, G.: Numerical simulation of wear-mechanism maps. Comput. Mater. Sci. 25, 54–60 (2002)CrossRefGoogle Scholar
  220. 220.
    Torrance, A.A.: A method for calculating boundary friction and wear. Wear 258, 924–934 (2005)CrossRefGoogle Scholar
  221. 221.
    Archard, J.F.: Contact and rubbing of flat surfaces. J. Appl. Phys. 24, 981–988 (1953)CrossRefGoogle Scholar
  222. 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. 223.
    Sarkar, A.D.: Friction and Wear. Academic Press, London (1980)Google Scholar
  224. 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)CrossRefGoogle Scholar
  225. 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)CrossRefGoogle Scholar
  226. 226.
    MSC MARC.: Theory and User Information, vol A. MSC Software Corporation, Santa Ana, CA, USA (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • L. A. Gracia
    • 1
    Email author
  • J. M. Bielsa
    • 1
  • F. J. Martínez
    • 1
  • J. M. Royo
    • 1
  • J. L. Pelegay
    • 1
  • B. Calvo
    • 2
    • 3
  1. 1.Grupo de Investigación Aplicada en Simulación, Caracterización, Diseño y Desarrollo de Materiales (SICADDEMA)Instituto Tecnológico de Aragón (ITA)ZaragozaSpain
  2. 2.Aragón Institute of Engineering ResearchUniversity of ZaragozaZaragozaSpain
  3. 3.Centro de Investigación Biomédica en Red en BioingenieríaBiomateriales y Nanomedicina (CIBER-BNN)ZaragozaSpain

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