Skip to main content
SpringerLink
Log in

Discussion of some objections to thermomechanical orthogonality

  • Published:
Ingenieur-Archiv Aims and scope Submit manuscript

Übersicht

Die Untersuchung gewisser Einwände, die gegen die thermomechanische Orthogonalität erhoben worden sind, zeigt, daß (a) Modelle zur Überprüfung der Orthogonalität ungeeignet sind und (b) Orthogonalität im Geschwindigkeitsraum nicht notwendigerweise auch Orthogonalität im Kräfteraum zur Folge hat. Die verschiedenen Einwände sprechen nicht gegen die Orthogonalität im Geschwindigkeitsraum, zeigen aber, daß die in [2] formulierten Regeln leicht präzisiert und genau beachtet werden müssen.

Summary

Investigation of certain objections raised against thermomechanical orthogonality shows that (a) models are not suitable to check orthogonality, and (b) orthogonality in velocity space does not necessarily imply orthogonality in force space. The various objections do not invalidate orthogonality in velocity space but show that the rules stated in [2] must be slightly amended and carefully obeyed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Onsager, L.: Reciprocal relations in irreversible processes. Phys. Rev. 37 (II) (1931) 405, 38 (II) (1931) 2265

    Google Scholar 

  2. Ziegler, H.: An introduction to thermomechanics. Amsterdam—New York—Oxford 1977

  3. v. Mises, R.: Mechanik der plastischen Formänderungen von Kristallen. Z. Angew. Math. Mech. 8 (1928) 161

    Google Scholar 

  4. Prager, W.: An introduction to plasticity. Reading, Mass.—London 1959, 13

  5. Houlsby, G. T.: Some implications of the derivation of the small-strain incremental theory of plasticity from thermomechanics. Report CUED/D Soils TR 74 (1979), Cambridge University to appear in J. of Non-Linear Mech.

  6. Michałowski, R.; Mróz, Z.: Associated and non-associated sliding rules in contact friction problems. Arch. Mech. Stosowanej 30, 3 (1978) 259

    Google Scholar 

  7. Moszyński, W.: Frottement des corps solides dans le cas de l'anisotropie naturelle et artificielle. Bull. Acad. Polon. Sci. Lettres, Sèrie 7, Suppl. 4 (1951) 447

    Google Scholar 

  8. Drucker, D. C.; Prager, W.: Soil mechanics and plastic analysis or limit design. Quart. Appl. Math. 10 (1952) 157

    Google Scholar 

  9. Salençon, J.: Theorie de la plasticité pour les applications à la mécanique des sols. Paris 1974, p. 17

  10. Drucker, D. C.; Greenberg, H. J.; Prager, W.: The safety factor of an elastic-plastic body in plane stress. J. Appl. Mech. 18 (1951) 371

    Google Scholar 

  11. Drucker, D. C.; Prager, W.; Greenberg, H. J.: Extended limit design theorems for continuous media. Quart. Appl. Math. 9 (1952) 381

    Google Scholar 

  12. Drucker, D. C.: Limit analysis of two and three dimensional soil mechanics problems. J. Mech. Phys Solids 1 (1952) 217

    Google Scholar 

  13. Shield, R. T.: On Coulomb's law of failure in soils. J. Math. Phys. Solids 4 (1955) 10

    Google Scholar 

  14. Shield, R. T.: Mixed boundary value problems in soil mechanics. Quart. Appl. Math. 11 (1953) 61

    Google Scholar 

  15. Shield, R. T.: Plastic potential theory and Prandtl bearing capacity solution. J. Appl. Mech. 21 (1954) 193

    Google Scholar 

  16. Ziegler, H.: Zum plastischen Potential in der Bodenmechanik. Z. Angew. Math. Phys. 20 (1969) 659

    Google Scholar 

  17. Kupper, W.: Der plastische Grenzzustand in der schiefen ebenen Erd- oder Schneeschicht. Z. Angew. Math. Phys. 18 (1967) 705

    Google Scholar 

  18. Balke, H.: Zum Zieglerschen Dissipationsprinzip in der nichtlinearen Viskoelastizitätstheorie. Z. Angew. Math. Mech. 56 (1976) H 247

    Google Scholar 

  19. Drucker, D. C.: Stress-strain-time-relations and irreversible thermodynamics. In Reiner, M. and Abir, D., ed.: Second-order effects in elasticity, plasticity, and fluid dynamics. Oxford and Jerusalem 1964, p. 331

Download references

Author information

Authors and Affiliations

  1. Weiherweg 6, CH-8803, Rüschlikon, Switzerland

    H. Ziegler

Authors
  1. H. Ziegler
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ziegler, H. Discussion of some objections to thermomechanical orthogonality. Ing. arch 50, 149–164 (1981). https://doi.org/10.1007/BF00536486

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00536486

Keywords

Search

Navigation