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Numerical Methods for Differential Equations, Optimization, and Technological Problems pp 431–444Cite as

Failure Simulations with a Strain Rate Dependent Ductile-to-Brittle Transition Model

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Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 27))

Abstract

In this paper, simulations with a phenomenological model to describe the ductile-to-brittle transition of rate-dependent solids are presented. The model is based on consistent thermodynamic formulation using proper expressions for the Helmholtz free energy and the dissipation potential. In the model, the dissipation potential is additively split into damage and visco-plastic parts and the transition behaviour is obtained using a stress dependent damage potential. The damage is described by using a vectorial variable.

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Notes

  1. 1.

    The symbols Δ and δ refer to incremental and iterative values, , , where the sub- and superscripts refer to step and iteration numbers, respectively.

  2. 2.

    This corresponds to the same case as in [5], where the damage potential (24.9) was in the scalar case was defined in a slightly different way.

References

  1. Askes H, Hartikainen J, Kolari K, Kouhia R (2009) Dispersion analysis of a strain-rate dependent ductile-to-brittle transition model. In: Mäkinen R, Neittaanmäki P, Tuovinen T, Valpe K (eds) Proceedings of the 10th finnish mechanics days, University of Jyväskylä, Jyväskylä, pp 478–489

    Google Scholar 

  2. Duvault G, Lions L (1972) Inequalities in mechanics and physics. Springer, Berlin

    Google Scholar 

  3. Eirola T, Hartikainen J, Kouhia R, Manninen T (2006) Some observations on the integration of inelastic constitutive models with damage. In: Dahlblom O, Fuchs L, Persson K, Ristinmaa M, Sandberg G, Svensson I (eds) Proceedings of the 19th nordic seminar on computational mechanics, Division of Structural Mechanics, LTH, Lund University, pp 23–32

    Google Scholar 

  4. Eriksson K, Estep PHD, Johnsson C (1996) Computational differential equations. Studentlitteratur

    MATH  Google Scholar 

  5. Fortino S, Hartikainen J, Kolari K, Kouhia R, Manninen T (2006) A constitutive model for strain-rate dependent ductile-to brittle-transition. In: von Hertzen R, Halme T (eds) The IX finnish mechanics days, Lappeenranta University of Technology, Lappeenranta, pp 652–662

    Google Scholar 

  6. Frémond M (2002) Non-smooth thermomechanics. Springer, Berlin

    MATH  Google Scholar 

  7. Hughes T (1987) The finite element method. Linear static and dynamic finite element analysis. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  8. Kolari K (2007) Damage mechanics model for brittle failure of transversely isotropic solids—finite element implementation. Tech rep 628, VTT Publications, Espoo

    Google Scholar 

  9. Kouhia R (2004) A time discontinuous Petrov-Galerkin method for the integration of inelastic constitutive equations. In: Neittaanmäki P, Rossi T, Majava K, Pironneau O (eds) ECCOMAS 2004 CD-ROM proceedings

    Google Scholar 

  10. Kouhia R, Marjamäki P, Kivilahti J (2005) On the implicit integration of rate-dependent inelastic constitutive models. Int J Numer Methods Eng 62(13):1832–1856

    Article  MATH  Google Scholar 

  11. Lemaitre J (1992) A course on damage mechanics. Springer, Berlin

    MATH  Google Scholar 

  12. Lemaitre J, Chaboche J-L (1990) Mechanics of solid materials. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  13. Perzyna P (1966) Fundamental problems in viscoplasticity. Advances in Applied Mechanics, vol 9. Academic Press, London

    Google Scholar 

  14. Ristinmaa M, Ottosen N (2000) Consequences of dynamic yield surface in viscoplasticity. Int J Solids Struct 37:4601–4622

    Article  MATH  Google Scholar 

  15. Runesson K, Sture S, Willam K (1988) Integration in computational plasticity. Comput Struct 30:119–130

    Article  MATH  Google Scholar 

  16. Simo J, Hughes T (1998) Computational inelasticity, 1st edn. Springer, New York

    MATH  Google Scholar 

  17. Wallin M, Ristinmaa M (2001) Accurate stress updating algorithm based on constant strain rate assumption. Comput Methods Appl Mech Eng 190:5583–5601

    Article  MATH  Google Scholar 

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Acknowledgements

This research has been supported in part by the Academy of Finland, decision number 121778.

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Authors and Affiliations

  1. Aalto University, P.O. Box 12100, 00076, Aalto, Finland

    Juha Hartikainen

  2. VTT, P.O. Box 1000, 02044, VTT, Finland

    Kari Kolari

  3. Tampere University of Technology, P.O. Box 589, 33101, Tampere, Finland

    Reijo Kouhia

Authors
  1. Juha Hartikainen
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  2. Kari Kolari
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  3. Reijo Kouhia
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Corresponding author

Correspondence to Juha Hartikainen .

Editor information

Editors and Affiliations

  1. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Sergey Repin

  2. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Timo Tiihonen

  3. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Tero Tuovinen

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Hartikainen, J., Kolari, K., Kouhia, R. (2013). Failure Simulations with a Strain Rate Dependent Ductile-to-Brittle Transition Model. In: Repin, S., Tiihonen, T., Tuovinen, T. (eds) Numerical Methods for Differential Equations, Optimization, and Technological Problems. Computational Methods in Applied Sciences, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5288-7_24

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  • DOI: https://doi.org/10.1007/978-94-007-5288-7_24

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5287-0

  • Online ISBN: 978-94-007-5288-7

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