Skip to main content

Some Remarks on the Phenomenological Description of Anisotropic Behaviour of Elastic-Plastic Solids

  • Chapter
Advances in Continuum Mechanics
  • 161 Accesses

Abstract

Considering deformation processes of polycrystalline solid bodies from a phenomenological (macroscopic) point of view we may observe different phenomena giving rise to an anisotropic behaviour of the material. The main reasons for the existence of an anisotropy of polycrystalline materials are:

  1. a)

    anisotropic distribution of lattice defects (like dislocations etc.) inside the single crystal grains

  2. b)

    occurrence of a crystallographic texture which is characterized by a non-random distribution of the orientation of the crystal axes of the grains, and

  3. c)

    appearance of a morphological texture due to an oriented distribution of the shape of the grains.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Muschik, W.: Thermodynamical Constitutive Laws - Outlines -; in: Constitutive Laws and Microstructure (Axelrad, D.R. and Muschik, W. eds.), Springer-Verlag Berlin etc. (1988), 3/25

    Google Scholar 

  2. Lehmann, Th.: Thermodynamical Considerations on Plastic and Viscoplastic Behaviour of Solid Bodies; in: Constitutive Laws and Microstructure (Axelrad, D.R. and Muschik, W. eds.), Springer-Verlag Berlin etc. (1988), 27/42

    Google Scholar 

  3. Müller, I.: Thermodynamik, Grundlagen der Materialtheorie, Bertelsmann Univ.Verl. Düsseldorf (1973)

    Google Scholar 

  4. Müller, I.: ThermodynamiCS; Pitman. London (1985)

    Google Scholar 

  5. Lehmann, Th. On Thermodynamically Consistent Constitutive Laws in Plasticity and Viscoplasticity; Arch. Mech. 40 (1988), 415/431

    MathSciNet  MATH  Google Scholar 

  6. Lehmann, Th.: Internal Variables in Thermoplasticity, in: Advances in Constitutive Laws for Engineering Materials (Fan Jinghong and Murakami, S. eds.), Pergamon Press/Int. Acad. Publ. 1989, 934/950

    Google Scholar 

  7. Lehmann, Th.: On the Balance of Energy and Entropy at Inelastic Deformations of Solid Bodies; Europ. J. Mech., A./Solids 8 (1989), 235/251

    MathSciNet  MATH  Google Scholar 

  8. Lehmann, Th.: Some Remarks on the Description of the Elastic Part Involved in Inelastic Deformations of Solid Bodies (submitted)

    Google Scholar 

  9. Lehmann, Th.: Formänderungen eines klassischen Kontinuums in vierdimensionaler Darstellung; in: Proc. Xl. Int. Congr. Appl. Mech. München 1964 (Görtler, H. ed.), Springer-Verlag Berlin etc. (1966), 376/382

    Google Scholar 

  10. Lehmann, Th., Guo, Zhong-heng, Liang, Haoyun: The Conjugacy between Cauchy Stress and Logarithm of the Left Stretch Tensor; Europ. J. Mech., A/Solids 9 (1990) (in print)

    Google Scholar 

  11. Haupt, P. and Tsakmakis, Ch.: On the Application of Dual Variables in Continuum Mechanics; Cont. Mech. Thermod. 1 (1989), 165/196

    Article  MathSciNet  MATH  Google Scholar 

  12. Lehmann, Th.: Some Thermodynamical Considerations on Inelastic Deformations Including Damage Processes; Acta Mech. 79 (1989), 1/24

    Article  MATH  Google Scholar 

  13. Lehmann, Th.: Thermodynamical Foundations of Large Inelastic Deformations of Solid Bodies Including Damage; Int. J. Plasticity, 6 (1990) (in print)

    Google Scholar 

  14. Seth, B.-R.: Generalized Strain Measure with Application to Physical Problems; in: Second Order Effects in Elasticity, Plasticity and Fluid Dynamic (Reiner, M. and Abir, D. eds.), Mc Milian, New York (1964), 162/171

    Google Scholar 

  15. Armstrong, P.J. and Frederick, C.O.: A Mathematical Representation of the Multiaxial Bauschinger Effect; G.E.G.B. report RDIBIN 731 (1966), 369/389

    Google Scholar 

  16. Lemaitre, J. and Chaboche, J.L.: La mécanique des matériaux solides; Dunod (1985)

    Google Scholar 

  17. Besdo D. Zur Formulierung von Stoffgesetzen für plastisch anisotrope/elastisch isotrope Medien im Dehnungsraum; ZAMM 60 (1980), T 101/103

    Google Scholar 

  18. Lehmann, Th.: On Dissipation Connected with Plastic Anisotropy; ZAMM 69 (1989), T 511/513

    Google Scholar 

  19. Hartung, Ch. and Lehmann, Th.: Vergleich einiger Formänderungsgesetze für plastische Formänderungen, ZAMM 48 (1968), T 138/141

    Google Scholar 

  20. Lehmann, Th.: Einige Bemerkungen zu einer allgemeinen Klasse von Stoffgesetzen für große elasto-plastische Formänderungen; Ing. Arch 41 (1972), 279/310

    Article  Google Scholar 

  21. Dienes, J.K.: On the Analysis of Rotation and Stress Rate in Deforming Bodies; Acta Mech. 32 (1979), 217/232

    Article  MathSciNet  MATH  Google Scholar 

  22. Lee, E.H., Mallet, R.L., Wertheimer, T.B.: Stress Analysis for Anisotropic Hardening in Finite-deformation Plasticity, J. Appl. Mech. 50 (1983), 554/560

    Article  ADS  MATH  Google Scholar 

  23. Dafalias, Y.F.: Corotational Rates for Kinematic Hardening at Large Plastic Deformation; J. Appl. Mech. 50 (1983), 561/565

    Article  ADS  MATH  Google Scholar 

  24. Paulun, J.E. and Pecherski, R.B.: Study of Corotational Rate for Kinematic Hardening in Finite Deformation Plasticitiy; Arch. Mech. 37 (1985), 661/677

    MATH  Google Scholar 

  25. Haupt, P. and Tsakmakis, Ch.: On Kinematic Hardening arid Large Plastic Deformations; Int. J. Plasticity 2 (1986), 279/293

    Article  MATH  Google Scholar 

  26. Lehmann, Th.: Some Remarks on the Evolution of Anisotropic Hardening in Plasticity; ZAMM 66 (1986), T 163/165

    Google Scholar 

  27. Loret. B.: On the Effects of Plastic Rotation in the Finite Deformation of An- isotropic Elastoplastic Material; Mech. Materials 2 (1983), 287/304

    Google Scholar 

  28. Dafalias, Y.F.: A Missing Link in the Macroscopic Constitutive Formulation of Large Plastic Deformations; in: Plasticity Today (Sawczuk, A. and Bianchi, C. eds.) Elsevier Appl. Sci. Publ., London/New York (1985) 135/151

    Google Scholar 

  29. Dafalias, Y.F. and Rashid, M.M.: The effect of Plastic Spin on Anisotropic Material Behaviour; Lit. J. Plasticity 5 (1989), 227/246

    Article  MATH  Google Scholar 

  30. Paulun, J. and Pecherski, R.B.: On the Application of the Plastic Spin Concept for the description of Anisotropic Hardening in Finite Deformation Plasticity; Int. J. Plasticity 3 (1987) 303/314

    Article  MATH  Google Scholar 

  31. Lehmann,Tb.: Some remarks on So-called Plastic spin; ZAMM 71 (1991)(in print)

    Google Scholar 

  32. Mroz, Z.: On the Description of Anisotropic Hardening; J. Mech. Phys. Sol. 15 (1967), 163/175

    Article  ADS  Google Scholar 

  33. Dafalias, Y.F. and Popov. E.P.: A Model of Nonlinearly Hardening Materials for Complex Loading; Acta Mech. 21 (1975), 173/192

    Article  MATH  Google Scholar 

  34. Krieg, R.D.: A Practical Two Surface Plasticity Theory; J. Appl. Mech. 42 (1975), 641/646

    Article  ADS  Google Scholar 

  35. Bruhns, O.T. and Müller, R.: Some Remarks on the Application of a Two-Surface Model in Plasticity; Acta Mech. 53 (1984), 81/100

    Article  MATH  Google Scholar 

  36. Pape, A.: Zur Beschreibung des transienten und stationären Verfestigungsverhal- tens von Stahl mit Hilfe eines nichtlinearen Grenzflächenmodells; Mitt. Inst. Mech. Nr. 57 (1988) Ruhr-Univ. Bochum

    Google Scholar 

  37. Bruhns, O.T., Lehmann, Th. and Pape, A.: On the Description of Transient Cyclic Hardening Behaviour of Mild Steel Ck 15 (submitted)

    Google Scholar 

  38. Raniecki, B. and Mroz, Z.: On the Strain-Induced Anisotropy and Texture at Finite Strain of Rigid-Plastic Solids; (submitted)

    Google Scholar 

  39. van der Giessen, E.: A Model of Anisotropically Hardening Materials Based upon the Concept of a Plastically Induced Orientational Structure; Proc. IUTAM Symp. “Yielding, Damage and Failure of Anisotropic Solids” (in memoriam A. Sawczuk) (Boehler ed.) Grenoble (1987)

    Google Scholar 

  40. Boehler, J.P. and Koss. S.: Decouplage des effects des textures cristallographiques et morpologiques sur l’anisotropie du comportement macroscopique des metaux en grandes deformations; Inst. Mécanique des Grenoble; Raport final. (1989)

    Google Scholar 

  41. Baltov, A. and Sawczuk. A.: A Rule of Anisotropic Hardening; Acta Mech. 1 (1965), 81/92

    Article  Google Scholar 

  42. Lehmann, Th.: Einige Bemerkungen zu einer allgemeinen Klasse von Stoffgesetzen für große elasto-plastische Formänderungen; Ing. Arch. 41 (1972), 297/310

    Article  MATH  Google Scholar 

  43. Lehmann, Th.: Some Considerations Concerning Deformation Induced Anisotropy; in: Proc. IUTAM Symp. “Yielding, Damage, and Failure of Anisotropic Solids” (Boehler, J.P. ed.). Grenoble (1987), 83/96

    Google Scholar 

  44. Cosserat, E. and F.: Sur la théorie de l’élasticité; Ann. Toulouse 10 (1896), 1/116

    Article  MathSciNet  Google Scholar 

  45. Cosserat, E. and F.: Théorie des corps déformables; Herman et fils, Paris (1909)

    Google Scholar 

  46. Lippmann, H.: Eine Cosserat-Theorie des plastischen Fließens; Acta Mech. 8 (1969), 255/284

    Article  MATH  Google Scholar 

  47. Besdo, D.: Ein Beitrag zur nichtlinearen Theorie des Cosserat-Kontinuums; Acta Mech. 20 (1974), 105/131

    Article  MathSciNet  MATH  Google Scholar 

  48. Diepolder, W.: Das Cosserat-Kontinuum als Strukturmodell für plastische Korndrehungen; Diss. TU München (1989)

    Google Scholar 

  49. Diepolder, W., Mannl, V. and Lippmann. H.: The Cosserat-Continuum, a Model for Grain Rotations in Metals; Int. J. Plasticity 6 (1990), (in print)

    Google Scholar 

  50. Kröner, E.: Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen; Arch. Rat. Mech. Anal. 4 (1960), 273/334

    Article  MATH  Google Scholar 

  51. Anthony, K.H.: Die Reduktion von nichteuklidischen geometrischen Projekten in eine euklidische Form und Deutung der Reduktion durch Eigenspannungszustände in Kristallen: Arch. Rat. Mech. Anal. 37 (1970), 161/180

    Article  MathSciNet  MATH  Google Scholar 

  52. Anthony, K.H.: Die Theorie der Disklinationen; Arch. Rat. Mech. Anal..39 (1970), 43/88

    Article  MathSciNet  MATH  Google Scholar 

  53. Anthony, K.H: Theorie der nichtmetrischen Spannungen in Kristallen; Arch. Rat. Mech. Anal. 40 (1971), 50/78

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin, Heidelberg

About this chapter

Cite this chapter

Lehmann, T. (1991). Some Remarks on the Phenomenological Description of Anisotropic Behaviour of Elastic-Plastic Solids. In: Brüller, O.S., Mannl, V., Najar, J. (eds) Advances in Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48890-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-48890-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53988-9

  • Online ISBN: 978-3-642-48890-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics