Skip to main content
SpringerLink
Log in

Asymmetric relaxation and compliance matrices in linear viscoelasticity

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Zusammenfassung

Die Beschränkungen, welche die Symmetrie des Materials den Nachgiebigkeitsmatrizen anisotroper viskoelastischer Stoffe auferlegt, werden ohne Bezug auf thermodynamisch bedingte Symmetrien abgeleitet. Experimente zur Überprüfung der thermodynamischen Theorien lassen sich auf die Unterschiede gründen, die zwischen den mit oder ohne Annahmen über Matrix-Symmetrie erhaltenen Formen bestehen. Transversale Isotropie und kubische Symmetrie werden im Detail behandelt.

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. E. H. Lee,Viscoelastic Stress Analysis, Proc., First Symposium on Naval Structural Mechanics (Pergamon, New York 1960).

    Google Scholar 

  2. D. R. Bland,Theory of Linear Viscoelasticity (Pergamon, London 1960).

    Google Scholar 

  3. M. A. Biot,Theory of Stress-Strain Relations in Anisotropic Viscoelasticity and Relaxation Phenomena, J. Appl. Phys.25 (1954), 1385–1391.

    Google Scholar 

  4. M. A. Biot,Linear Thermodynamics and the Mechanics of Solids, Proc. Third U.S. Nat'l. Cong. of Appl. Mech. (1958), 1–18.

  5. A. J. Staverman andF. Schwarzl,Non-Equilibrium Thermodynamics of Viscoelastic Behavior, Proc. Roy. Ac. Sci. Amsterdam55 (1952), 474–490.

    Google Scholar 

  6. A. J. Staverman,Thermodynamics of Linear Viscoelastic Behavior, Proc. Second Int. Cong. on Rheology (Academic Press, New York 1954), 134–138.

    Google Scholar 

  7. J. Meixner,Die thermodynamische Theorie der Relaxationserscheinungen und ihr Zusammenhang mit der Nachwirkungstheorie, Koll. Zeitsch.134 (1953), 2–16.

    Google Scholar 

  8. J. Meixner,Thermodynamische Theorie der elastischen Relaxation, Z. für Naturforsch., OA,718 (1954), 654–665.

    Google Scholar 

  9. S. R. de Groot,Thermodynamics of Irreversible Processes (Interscience Publishers Inc., New York 1952).

    Google Scholar 

  10. B. D. Coleman andC. Truesdell, J. Chem. Phys.33 (1960), 28.

    Google Scholar 

  11. E. H. Lee,Stress Analysis in Viscoelastic Bodies, Quart. Appl. Math.13 (1955), 183–190.

    Google Scholar 

  12. G. F. Smith andR. S. Rivlin,The Anisotropic Tensors, Quart. Appl. Math.15 (1957), 308–314.

    Google Scholar 

  13. P. R. Pinnock andI. M. Ward,Dynamic Mechanical Measurements on Polyethylene Terephthalate, Proc. Phys. Soc. In press.

Download references

Author information

Author notes

  1. Tryfan G. Rogers

    Present address: Stanford University, Stanford, California

Authors and Affiliations

  1. Providence, R.I., USA

    Tryfan G. Rogers & Allen C. Pipkin

  2. Division of Applied Mathematics, Brown University, Brown, USA

    Allen C. Pipkin

Authors
  1. Tryfan G. Rogers
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Allen C. Pipkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper was prepared under Contract No. 562(10) with the Office of Naval Research.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rogers, T.G., Pipkin, A.C. Asymmetric relaxation and compliance matrices in linear viscoelasticity. Journal of Applied Mathematics and Physics (ZAMP) 14, 334–343 (1963). https://doi.org/10.1007/BF01603090

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01603090

Keywords

Search

Navigation