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Cohesive Zone Models—Theory, Numerics and Usage in High-Temperature Applications to Describe Cracking and Delamination

  • Joachim NordmannEmail author
  • Konstantin Naumenko
  • Holm Altenbach
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 117)

Abstract

This treatise deals with Cohesive Zone Models which were developed around 1960 through Barenblatt and Dugdale. At first, we present an overview about these models and the numerical treatment of these models in the sense of the Finite Element Method. Further on, a rate-dependent Cohesive Zone Model is presented and tested through a simulation of a Four-Point-Bend-Test with a metal compound. The required material parameters are determined through numerical optimisation by using a neural network which is explained, as well.

Notes

Acknowledgements

The financial support rendered by the German Research Foundation (DFG) in context of the research training group ‘Micro-Macro-Interactions of Structured Media and Particle Systems’ (RTG 1554) is gratefully acknowledged.

References

  1. 1.
    Papazafeiropoulos, G., Muñiz-Calvente, M., Martínez-Pañeda, E.: Adv. Eng. Softw. 105, 9 (2017).  https://doi.org/10.1016/j.advengsoft.2017.01.006CrossRefGoogle Scholar
  2. 2.
    Altenbach, H.: Kontinuumsmechanik: Einführung in die materialunabhängigen und materialabhängigen Gleichungen, 4th edn. Springer, Berlin (2018).  https://doi.org/10.1007/978-3-662-57504-8CrossRefGoogle Scholar
  3. 3.
    Lai, W., Rubin, D., Krempl, E.: Introduction to Continuum Mechanics, 4th edn. Butterworth-Heinemann, Oxford (2009)zbMATHGoogle Scholar
  4. 4.
    Bertram, A.: Elasticity and Plasticity of Large Deformations: An Introduction, 3rd edn. Springer, Berlin (2012).  https://doi.org/10.1007/978-3-642-24615-9CrossRefGoogle Scholar
  5. 5.
    Lebedev, L.P., Cloud, M.J., Eremeyev, V.A.: Tensor Analysis with Applications in Mechanics. World Scientific, Singapore (2010).  https://doi.org/10.1142/9789814313995
  6. 6.
    Schwalbe, K.H., Scheider, I., Cornec, A.: Guidelines for Applying Cohesive Models to the Damage Behaviour of Engineering Materials and Structures. Springer, Berlin (2013).  https://doi.org/10.1007/978-3-642-29494-5CrossRefGoogle Scholar
  7. 7.
    Barenblatt, G.: J. Appl. Math. Mech. 23(3), 622 (1959).  https://doi.org/10.1016/0021-8928(59)90157-1MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dugdale, D.: J. Mech. Phys. Solids 8(2), 100 (1960).  https://doi.org/10.1016/0022-5096(60)90013-2CrossRefGoogle Scholar
  9. 9.
    Needleman, A.: Procedia IUTAM 10, 221 (2014).  https://doi.org/10.1016/j.piutam.2014.01.020CrossRefGoogle Scholar
  10. 10.
    Hillerborg, A., Modéer, M., Petersson, P.E.: Cem. Concr. Res. 6(6), 773 (1976)Google Scholar
  11. 11.
    Bažant, Z.P.: Eng. Fract. Mech. 69(2), 165 (2002).  https://doi.org/10.1016/s0013-7944(01)00084-4CrossRefGoogle Scholar
  12. 12.
    Needleman, A.: J. Mech. Phys. Solids 38(3), 289 (1990)Google Scholar
  13. 13.
    Needleman, A.: Non-linear Fracture, pp. 21–40. Springer, Netherlands (1990).  https://doi.org/10.1007/978-94-017-2444-9_2CrossRefGoogle Scholar
  14. 14.
    Scheider, I., Brocks, W.: Eng. Fract. Mech. 70(14), 1943 (2003).  https://doi.org/10.1016/s0013-7944(03)00133-4CrossRefGoogle Scholar
  15. 15.
    Tvergaard, V., Hutchinson, J.W.: J. Mech. Phys. Solids 40(6), 1377 (1992).  https://doi.org/10.1016/0022-5096(92)90020-3CrossRefGoogle Scholar
  16. 16.
    Dassault Systèmes, SIMULIA Corp., ABAQUS version 2017 documentation (2017)Google Scholar
  17. 17.
    Gurtin, M.E.: J. Appl. Math. Phys. (ZAMP) 30(6), 991 (1979).  https://doi.org/10.1007/BF01590496CrossRefGoogle Scholar
  18. 18.
    Rice, J.R., Wang, J.S.: Mater. Sci. Eng.: A 107, 23 (1989)Google Scholar
  19. 19.
    Bouvard, J., Chaboche, J., Feyel, F., Gallerneau, F.: Int. J. Fatigue 31(5), 868 (2009).  https://doi.org/10.1016/j.ijfatigue.2008.11.002CrossRefGoogle Scholar
  20. 20.
    Nase, M., Rennert, M., Naumenko, K., Eremeyev, V.A.: J. Mech. Phys. Solids 91, 40 (2016).  https://doi.org/10.1016/j.jmps.2016.03.001MathSciNetCrossRefGoogle Scholar
  21. 21.
    Chandra, N., Li, H., Shet, C., Ghonem, H.: Int. J. Solids Struct. 39(10), 2827 (2002).  https://doi.org/10.1016/s0020-7683(02)00149-xCrossRefGoogle Scholar
  22. 22.
    Naumenko, K., Altenbach, H.: Modeling High Temperature Materials Behavior for Structural Analysis. Springer International Publishing, New York (2016).  https://doi.org/10.1007/978-3-319-31629-1CrossRefGoogle Scholar
  23. 23.
    Fagerström, M., Larsson, R.: J. Mech. Phys. Solids 56(10), 3037 (2008).  https://doi.org/10.1016/j.jmps.2008.06.002MathSciNetCrossRefGoogle Scholar
  24. 24.
    Helmholtz, H.: Physical Memoirs Selected and Translated from Foreign Sources. Physical Society of London, vol. 1, pp. 43–97. Taylor & Francis, London (1882) (1888)Google Scholar
  25. 25.
    Clausius, R.: The Mechanical Theory of Heat. Macmillan, London (1879)Google Scholar
  26. 26.
    Duhem, P.: Mixture and Chemical Combination, pp. 291–309. Springer, Netherlands (1901) (2002).  https://doi.org/10.1007/978-94-017-2292-6_22CrossRefGoogle Scholar
  27. 27.
    Truesdell, C.: J. Ration. Mech. Anal. 1, 125 (1952)Google Scholar
  28. 28.
    Coleman, B.D.: The Rational Spirit in Modern Continuum Mechanics, pp. 1–13. Kluwer Academic Publishers, New York (2003).  https://doi.org/10.1007/1-4020-2308-1_1
  29. 29.
    Musto, M.: On the formulation of hereditary cohesive-zone models. Ph.D. thesis, Brunel University School of Engineering and Design (2014)Google Scholar
  30. 30.
    Gao, Y.F., Bower, A.F.: Model. Simul. Mater. Sci. Eng. 12(3), 453 (2004).  https://doi.org/10.1088/0965-0393/12/3/007CrossRefGoogle Scholar
  31. 31.
    Needleman, A.: Comput. Methods Appl. Mech. Eng. 67(1), 69 (1988).  https://doi.org/10.1016/0045-7825(88)90069-2CrossRefGoogle Scholar
  32. 32.
    Lemaitre, J., Desmorat, R.: Engineering Damage Mechanics. Springer, Berlin (2005).  https://doi.org/10.1007/b138882
  33. 33.
    Miehe, C., Hofacker, M., Welschinger, F.: Comput. Methods Appl. Mech. Eng. 199(45–48), 2765 (2010).  https://doi.org/10.1016/j.cma.2010.04.011MathSciNetCrossRefGoogle Scholar
  34. 34.
    Abu-Eishah, S., Haddad, Y., Solieman, A., Bajbouj, A.: J. Lat. Am. Appl. Res. (LAAR) 34, 257 (2004)Google Scholar
  35. 35.
    Narender, K., Rao, A.S.M., Rao, K.G.K., Krishna, N.G.: J. Mod. Phys. 04(03), 331 (2013).  https://doi.org/10.4236/jmp.2013.43045CrossRefGoogle Scholar
  36. 36.
    Leckie, F., Hayhurst, D.: Acta Metall. 25(9), 1059 (1977).  https://doi.org/10.1016/0001-6160(77)90135-3CrossRefGoogle Scholar
  37. 37.
    Cocks, A., Ashby, M.: Prog. Mater. Sci. 27(3–4), 189 (1982).  https://doi.org/10.1016/0079-6425(82)90001-9CrossRefGoogle Scholar
  38. 38.
    Fourier, J.B.J.: Théorie Analytique de la Chaleur. Cambridge University Press, Cambridge (2009).  https://doi.org/10.1017/cbo9780511693229
  39. 39.
    Holzapfel, G.A.: Nonlinear Solid Mechanics. Wiley, New York (2000)Google Scholar
  40. 40.
    Wriggers, P.: Nonlinear Finite Element Methods. Springer, Berlin (2008).  https://doi.org/10.1007/978-3-540-71001-1
  41. 41.
    Allix, O., Corigliano, A.: Int. J. Solids Struct. 36(15), 2189 (1999).  https://doi.org/10.1016/s0020-7683(98)00079-1CrossRefGoogle Scholar
  42. 42.
    Dhondt, G.: The Finite Element Method for Three-Dimensional Thermomechanical Applications. Wiley-Blackwell, Hoboken (2004)CrossRefGoogle Scholar
  43. 43.
    Park, K., Paulino, G.H.: Eng. Fract. Mech. 93, 239 (2012).  https://doi.org/10.1016/j.engfracmech.2012.02.007CrossRefGoogle Scholar
  44. 44.
    Musto, M., Alfano, G.: Comput. Struct. 118, 126 (2013).  https://doi.org/10.1016/j.compstruc.2012.12.020CrossRefGoogle Scholar
  45. 45.
    de Borst, R., Sluys, L., Mühlhaus, H.B., Pamin, J.: Eng. Comput. 10(2), 99 (1993).  https://doi.org/10.1108/eb023897CrossRefGoogle Scholar
  46. 46.
    Gens, A., Carol, I., Alonso, E.: Comput. Geotech. 7(1–2), 133 (1989).  https://doi.org/10.1016/0266-352x(89)90011-6CrossRefGoogle Scholar
  47. 47.
    Schellekens, J.C.J., Borst, R.D.: Int. J. Numer. Methods Eng. 36(1), 43 (1993).  https://doi.org/10.1002/nme.1620360104CrossRefGoogle Scholar
  48. 48.
    Svenning, E.: Comput. Methods Appl. Mech. Eng. 310, 460 (2016).  https://doi.org/10.1016/j.cma.2016.07.031MathSciNetCrossRefGoogle Scholar
  49. 49.
    Vignollet, J., May, S., de Borst, R.: Int. J. Numer. Methods Eng. 102(11), 1733 (2015).  https://doi.org/10.1002/nme.4867MathSciNetCrossRefGoogle Scholar
  50. 50.
    Yu, H., Olsen, J.S., Olden, V., Alvaro, A., He, J., Zhang, Z.: Eng. Fract. Mech. 166, 23 (2016).  https://doi.org/10.1016/j.engfracmech.2016.08.019CrossRefGoogle Scholar
  51. 51.
    Nordmann, J., Thiem, P., Cinca, N., Naumenko, K., Krüger, M.: J. Strain Anal. Eng. Des. 53(4), 255 (2018).  https://doi.org/10.1177/0309324718761305CrossRefGoogle Scholar
  52. 52.
    Alfano, G., Crisfield, M.A.: Int. J. Numer. Methods Eng. 50(7), 1701 (2001).  https://doi.org/10.1002/nme.93CrossRefGoogle Scholar
  53. 53.
    Turon, A., Dávila, C., Camanho, P., Costa, J.: Eng. Fract. Mech. 74(10), 1665 (2007).  https://doi.org/10.1016/j.engfracmech.2006.08.025CrossRefGoogle Scholar
  54. 54.
    Ersoy, N., Ahmadvashaghbash, S., Engül, M., Öz, F.E.: Eur. Conf. Compos. Mater. (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Joachim Nordmann
    • 1
    Email author
  • Konstantin Naumenko
    • 1
  • Holm Altenbach
    • 1
  1. 1.Chair of Engineering Mechanics, Faculty of Mechanical Engineering, Institute of MechanicsOtto von Guericke University MagdeburgMagdeburgGermany

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