Skip to main content

12. Simulation of the Material Behavior from the Engineering Point of View – Classical Approaches and New Trends

  • Part II Simulation from Nanoscopic Systems to Macroscopic Materials
  • Chapter
  • First Online:
Computational Materials Science

Part of the book series: Lecture Notes in Physics ((LNP,volume 642))

  • 2112 Accesses

Abstract

The analysis of any engineering structure is based on three steps - the choice of a material model, of a structural model and of an analytical or numerical method. All three items are interlinked, and the improvement, for example, of the structural model demands the improvement of the material behavior model and vice versa. In this contribution is reported on the engineering approaches to the material modelling. The models are mostly phenomenologically that means the real structure of the material is ignored. On the other hand, they are much simpler in comparison with micro-mechanically or physically based equations.

In the first part some general remarks on the principles of material modelling will be given. Three approaches to formulate material equations are presented. The main attention is paid to the inductive approach. In the final part some examples showing the application of the engineering models of material behavior to the analysis of thin-walled structures (beams, plates, shells) are given.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • 1. H. Altenbach. Modelling of viscoelastic behaviour of plates. In M. Życzkowski, editor, Creep in Structures, pages 531 – 537. Springer, Berlin, Heidelberg, 1991.

    Google Scholar 

  • 2. H. Altenbach. Creep-damage behaviour in plates and shells. Mechanics of Time-Dependent Materials, 3:103–123, 1999.

    Google Scholar 

  • 3. H. Altenbach. An alternative determination of transverse shear stiffnesses for sandwich and laminated plates. Int. J. Solids & Structures, 37(25):3503 – 3520, 2000.

    Google Scholar 

  • 4. H. Altenbach. On the determination of transverse shear stiffnesses of orthotropic plates. ZAMP, 51:629 – 649, 2000.

    Google Scholar 

  • 5. H. Altenbach. Consideration of stress state influences in the material modelling of creep and damage. In S. Murakami and N. Ohno, editors, IUTAM Symposium on Creep in Structures, pages 141 – 150. Kluwer, Dordrecht, 2001.

    Google Scholar 

  • 6. H. Altenbach, J. Altenbach, and R. Rikards. Einführung in die Mechanik der Laminat- und Sandwichtragwerke. Deutscher Verlag für Grundstoffindustrie, Stuttgart, 1996.

    Google Scholar 

  • 7. H. Altenbach, J. Altenbach, and A. Zolochevsky. Erweiterte Deformationsmodelle und Versagenskriterien der Werkstoffmechanik. Deutscher Verlag für Grundstoffindustrie, Stuttgart, 1995.

    Google Scholar 

  • 8. H. Altenbach, G. Kolarow, O. Morachkovsky, and K. Naumenko. On the accuracy of creep-damage predictions in thinwalled structures using the finite element method. Comp. Mech., 25:87–98, 2000.

    Google Scholar 

  • 9. H. Altenbach, V. Kushnevsky, and K. Naumenko. On the use of solid- and shell-type finite elements in creep-damage predictions of thinwalled structures. Arch. Appl. Mech., 71:164 – 181, 2001.

    Google Scholar 

  • 10. H. Altenbach and K. Naumenko. Shear correction factors in creep-damage analysis of beams, plates and shells. JSME International Journal, Series A, 45(1):77 – 83, 2002.

    Google Scholar 

  • 11. H. Altenbach, P. Schieße, and A.A. Zolochevsky. Zum Kriechen isotroper Werkstoffe mit komplizierten Eigenschaften. Rheol. Acta, 30:388 – 399, 1991.

    Google Scholar 

  • 12. H. Altenbach and J. Skrzypek, editors. Creep and Damage in Materials and Structures. CISM Courses and Lectures Notes No. 399. Springer, Wien, New York, 1999.

    Google Scholar 

  • 13. H. Altenbach and A.A. Zolochevsky. Eine energetische Variante der Theorie des Kriechens und der Langzeitfestigkeit für isotrope Werkstoffe mit komplizierten Eigenschaften. ZAMM, 74(3):189 – 199, 1994.

    Google Scholar 

  • 14. J. Altenbach and H. Altenbach. Einführung in die Kontinuumsmechanik. Teubner Studienbücher Mechanik. Teubner, Stuttgart, 1994.

    Google Scholar 

  • 15. J. Altenbach, H. Altenbach, and K. Naumenko. Lebensdauerabschätzung dünnwandiger flächentragwerke auf der grundlage phänomenologischer materialmodelle für kriechen und schädigung. Technische Mechanik, 17(4):353–364, 1997.

    Google Scholar 

  • 16. Y. Başar and W.B. Krätzig. Mechanik der Flächentragwerke. Vieweg, Braunschweig et al., 1985.

    Google Scholar 

  • 17. A. Bertram. What is the general constitutive equation? In A. Cassius et al., editor, Beiträge zur Mechanik: Festschrift zum 65. Geburtstag Rudolf Trostel, pages 28 – 37. TU Berlin, Berlin, 1993.

    Google Scholar 

  • 18. J. Betten. Anwendungen von Tensorfunktionen in der Kontinuumsmechanik anisotroper Materialien. ZAMM, 78(8):507 – 521, 1998.

    Google Scholar 

  • 19. J.T. Boyle and J. Spence. Stress Analysis for Creep. Butterworth, London, 1983.

    Google Scholar 

  • 20. B.J. Cane. Creep fracture of dispersion strengthened low alloy ferritic steels. Acta Metall., 29:1581–1591, 1981.

    Google Scholar 

  • 21. W.F. Chen and H. Zhang. Structural Plasticity. Springer, Berlin et al., 1991.

    Google Scholar 

  • 22. R.M. Christensen. Theory of Viscoelastiocity. Academic Press, New York et al., 1971.

    Google Scholar 

  • 23. T.J. Chung. Continuum Mechanics. Prentice-Hall, London et al., 1988.

    Google Scholar 

  • 24. B.D. Coleman and M.E. Gurtin. Thermodynamics with internal state variables. J. of Physical Chemics, 47(2):597 – 613, 1967.

    Google Scholar 

  • 25. B.F. Dyson and S. Osgerby. Modelling and analysis of creep deformation and fracture in a 1Cr0.5Mb ferritic steel. Technical Report 116, DMM(A), 1993.

    Google Scholar 

  • 26. A.C. Eringen and G.A. Maugin. Electrodynamics of Continua I - Foundations and Solid Media. Springer, New York et al., 1989.

    Google Scholar 

  • 27. P. Gummert. General constitutive equations for simple and non–simple materials. In H. Altenbach and J. Skrzypek, editors, Creep and Damage in Materials and Structures, CISM Courses and Lectures Notes No. 399, pages 1 – 43. Springer, Wien, New York, 1999.

    Google Scholar 

  • 28. P. Haupt. Konzepte der Materialtheorie. Techn. Mechanik, 16(1):13 – 22, 1996.

    Google Scholar 

  • 29. P. Haupt. Continuum Mechanics and Theory of Materials. Springer, Berlin, 2000.

    Google Scholar 

  • 30. D.R. Hayhurst. Creep rupture under multiaxial states of stress. J. Mech. Phys. Solids, 20:381 – 390, 1972.

    Google Scholar 

  • 31. D.R. Hayhurst. Materials data bases and mechanisms–based constitutive equations for use in design. In H. Altenbach and J. Skrzypek, editors, Creep and Damage in Materials and Structures, CISM Courses and Lectures Notes No. 399, pages 285 – 348. Springer, Wien, New York, 1999.

    Google Scholar 

  • 32. J.R. Hutchinson. Shear coefficients for Timoshenko beam theory. Trans. ASME. J. Appl. Mech., 68(1):87–92, 2001.

    Google Scholar 

  • 33. L.M. Kachanov. O vremeni razrusheniya v usloviyakh polzuchesti (Time of the rupture process under creep conditions, in Russ.). Izv. AN SSSR. Otd. Tekh. Nauk, (8):26 – 31, 1958.

    Google Scholar 

  • 34. L.M. Kachanov. Introduction to Continuum Damage Mechanics. Mechanics of Elastic Stability. Martinus Nijhoff, Dordrecht et al., 1986.

    Google Scholar 

  • 35. Z.L. Kowalewski, D.R. Hayhurst, and B.F. Dyson. Mechanisms-based creep constitutive equations for an aluminium alloy. J. Strain Anal., 29(4):309 – 316, 1994.

    Google Scholar 

  • 36. D. Krajcinovic and J. Lemaitre, editors. Continuum Damage Mechanics - Theory and Application. CISM Courses and Lectures Notes No. 295. Springer, Wien, New York, 1987.

    Google Scholar 

  • 37. A. Krawietz. Materialtheorie. Mathematische Beschreibung des phänomenologischen thermomechanischen Verhalten. Springer, Berlin et al., 1986.

    Google Scholar 

  • 38. F.A. Leckie and D.R. Hayhurst. Constitutive equations for creep rupture. Acta Metallurgica, 25:1059 – 1070, 1977.

    Google Scholar 

  • 39. J. Lemaitre. A Course on Damage Mechanics. Springer, Berlin et al., 1996.

    Google Scholar 

  • 40. J. Lemaitre and J.-L. Chaboche. Mechanics of Solid Materials. Cambridge University Press, Cambridge, 1990.

    Google Scholar 

  • 41. N.N. Malinin. Raschet na polzuchest’ konstrukcionnykh elementov (Creep calculations of structural elements, in Russ.). Mashinostroenie, Moskva, 1981.

    Google Scholar 

  • 42. L.I. Manevitch, I.V. Andrianov, and V.G. Oshmyan. Mechanics of Periodically Heterogeneous Structures. Springer, Berlin et al., 2002.

    Google Scholar 

  • 43. J. Meenen and H. Altenbach. A consistent deduction of von Kármán-type plate theories from threedimensional non-linear continuum mechanics. Acta Mechanica, 147:1 – 17, 2001.

    Google Scholar 

  • 44. F.R.N. Nabarro and H.L. de Villiers. The Physics of Creep. Creep and Creep–resistant Alloys. Taylor & Francis, London, 1995.

    Google Scholar 

  • 45. K. Naumenko. Modellierung und Berechnung der Langzeitfestigkeit dünnwandiger Flächentragwerke unter Einbeziehung von Werkstoffkriechen und Schädigung. Diss., Fakultät für Maschinenbau, Otto-von-Guericke-Universität, 1996.

    Google Scholar 

  • 46. K. Naumenko. On the use of the first order shear deformation models of beams, plates and shell in creep lifetime estimations. Technische Mechanik, 20(3):215 – 226, 2000.

    Google Scholar 

  • 47. W. Noll. A new mathematical theory of simple materials. Archive for Rational Mechanics and Analysis, 48:1 – 50, 1972.

    Google Scholar 

  • 48. J.F. Nye. Physical Properties of Crystals. Oxford Science Publications, Oxford, 1992.

    Google Scholar 

  • 49. F.K.G. Odqvist. Mathematical Theory of Creep and Creep Rupture. Clarendon, Oxford, 1974.

    Google Scholar 

  • 50. F.K.G. Odqvist and J. Hult. Kriechfestigkeit metallischer Werkstoffe. Springer, Berlin u.a., 1962.

    Google Scholar 

  • 51. P.R. Onck and E. van der Giessen. Growth of an initially sharp crack by boundary cavitation. J. Mech. Phys. Solids, 47:99 – 139, 1999.

    Google Scholar 

  • 52. E. Sanchez Palancia. Introduction aux méthodes asymptotiques et à l’homogénéisation. Masson, Paris, 1992.

    Google Scholar 

  • 53. V. Palmov. Vibrations in Elasto-Plastic Bodies. Springer, Berlin et al., 1998.

    Google Scholar 

  • 54. P. Paul. Macroscopic criteria of plastic flow and brittle fracture. In H. Liebowitz, editor, Fracture: An advanced treatise, Vol. II (Mathematical Fundamentals). Academic Press, New York, 1968.

    Google Scholar 

  • 55. I.J. Perrin and D.R. Hayhurst. Creep constitutive equations for a 0.5Cr–0.5Mo–0.25V ferritic steel in the temperature range 600–675C. J. Strain Anal., 31(4):299 – 314, 1994.

    Google Scholar 

  • 56. Yu. N. Rabotnov. Creep Problems in Structural Members. North-Holland, Amsterdam, 1969.

    Google Scholar 

  • 57. Yu. N. Rabotnov. Elements of Hereditary Solid Mechanics. Mir, Moscow, 1977.

    Google Scholar 

  • 58. M. Reiner. Deformation and Flow. An Elementary Introduction to Rheology. H.K. Lewis & Co., London, 3rd edition, 1969.

    Google Scholar 

  • 59. E. Reissner. On the theory of bending of elastic plates. J. Math. Phys., 23:184 – 191, 1944.

    Google Scholar 

  • 60. E. Reissner. Variational theorem in elasticity. J. Math. Phys., 29:90 – 95, 1950.

    Google Scholar 

  • 61. H. Riedel. Fracture at High Temperatures. Materials Research and Engineering. Springer, Berlin et al., 1987.

    Google Scholar 

  • 62. H. Rothert. Lineare konstitutive Gleichungen der viskoelastischen Cosseratfläche. ZAMM, 55:647 – 656, 1975.

    Google Scholar 

  • 63. J.J. Skrzypek. Plasticity and Creep. CRC Press, Boca Raton et al., 1993.

    Google Scholar 

  • 64. A. Służalec. Introduction to Nonlinear Thermomechanics. Springer, Berlin et al., 1992.

    Google Scholar 

  • 65. P. Suquet. Plasticité et homogénéisation. Thèse de doctorat d’etat, Université Pierre et Marie Curie, Paris 6, 1982.

    Google Scholar 

  • 66. E. van der Giessen, B.-N. Nguyen, and P.R. Onck. From a microstructural to a continuum model for creep fracture. In A. Benallal, editor, Continuous Damage and Fracture, pages 129 – 136. Elsevier, Paris et al., 2000.

    Google Scholar 

  • 67. E. van der Giessen and V. Tvergaard. Development of final creep failure in polycrystalline aggregates. Acta Metall. Mater., 42:959 – 973, 1994.

    Google Scholar 

  • 68. M. Życzkowski. Combined Loadings in the Theory of Plasticity. PWN-Polish Scientific Publisher, Warszawa, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

W. Hergert M. Däne A. Ernst

Rights and permissions

Reprints and permissions

About this chapter

Cite this chapter

Altenbach, H. 12. Simulation of the Material Behavior from the Engineering Point of View – Classical Approaches and New Trends. In: Hergert, W., Däne, M., Ernst, A. (eds) Computational Materials Science. Lecture Notes in Physics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39915-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-39915-5_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21051-1

  • Online ISBN: 978-3-540-39915-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics