Skip to main content
SpringerLink
Log in
Book cover

Very Slow Flows of Solids pp 411–444Cite as

Viscoelasticity and transient creep

  • Chapter

  • 168 Accesses

Part of the book series: Mechanics of Fluids and Transport Processes ((MFTP,volume 7))

Abstract

For non-perfect plastic behavior under varying loads, as well as in creep flow when the stress field has large gradients, memory effects have to be introduced. The principle of local action (Section 5.1) will always be assumed. Therefore, the constitutive relationship involves the values at some material point of the diverse variables and of their space derivatives of low order only. Nevertheless, it may include not only the actual values, but the past ones, for the same material particle.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   329.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Zahorski: Mechanics of viscoelastic fluids, Martinus Nijhoff, The Hague (1982).

    Google Scholar 

  2. M. Reiner: Rheology. In Encyclopedia of Physics (S. Flügge ed.) Vol. 6: Elasticity and plasticity, Springer Verlag, Berlin (1958) pp. 434–550.

    Google Scholar 

  3. A. M. Freundenthal and H. Geiringer: The mathematical theories of the inelastic continuum. B. Stress-strain relations, ibid. pp. 256–293.

    Google Scholar 

  4. I. M. Longman: A Green’s function for determining the deformation of the Earth under surface mass loads. 1. Theory, J. Geophys. Res., 67 (1962) pp. 845–850. 2. Computations and numerical methods, ibid., 68 (1963) pp. 485–496.

    Article  Google Scholar 

  5. W. E. Farrell: Deformation of the Earth by surface loads, Rev. Geophys. Space Phys., 10 (1972) pp. 761–797.

    Article  Google Scholar 

  6. W. R. Peltier: The impulse response of a Maxwell Earth, Rev. Geophys. Space Phys., 12 (1974) pp. 649–669.

    Article  Google Scholar 

  7. W. E. Farrell and J. A. Clark: On post-glacial sea level, Geophys. J. Roy Astron. Soc., 46 (1976) pp. 647–667.

    Article  Google Scholar 

  8. W. R. Peltier and J. T. Andrews: Glacial isostatic adjustment. I. The forward problem. Geophys. j: Roy. Astron. Soc., 46 (1976) pp. 605–646.

    Article  Google Scholar 

  9. W. R. Peltier: Glacial isostatic adjustment. II. The inverse problem, ibid. pp. 669–705.

    Google Scholar 

  10. P. Wu and W. R. Peltier: Viscous gravitational relaxation, Geophys. J. Roy. Astron. Soc., 70 (1982) pp. 435–485.

    Google Scholar 

  11. R. Peltier: Dynamics of the Ice Age Earth. In Advances in Geophysics (B. Saltzman ed.), Academic Press, New York, 24 (1982) pp. 1–146.

    Google Scholar 

  12. J. Weertman: Creep laws for the mantle of the Earth, Phil. Trans. Roy. Soc. London A, 288 (1978) pp. 9–26.

    Article  Google Scholar 

  13. W. R. Peltier: New constraints on transient lower mantle rheology and internal mantle buoyancy from glacial rebound data, Nature, 318 (1985) pp. 614–617.

    Article  Google Scholar 

  14. W. Findley and G. Khosla: Application of the superposition principle and theories of mechanical equations of state, strain and time hardening to creep of plastics under changing loads, J. Appl. Phys., 26 (1955) pp. 821–832.

    Article  Google Scholar 

  15. P. E. Senseny: Specimen size and history effects on creep of salt. In [27], pp. 369–379.

    Google Scholar 

  16. N. L. Carter and S. H. Kirby: Transient creep and semibrittle behavior of crystalline rocks, Pure Appl. Geophys., 116 (1978) pp. 807–839.

    Article  Google Scholar 

  17. P. Duval: Lois du fluage transitoire ou permanent de la glace polycristalline pour divers états de contrainte, Ann. Géophys., 32 (1976) pp. 335–350.

    Google Scholar 

  18. C. Goetze and W. F. Brace: Laboratory observations of high-temperature rheology of rocks, Tectonophysics, 13 (1972) pp. 583–600.

    Article  Google Scholar 

  19. S. A. F. Murrell: Rheology of the lithosphère: experimental indications, Tectonophysics, 36 (1976) pp. 5–24.

    Article  Google Scholar 

  20. P. Duval: Anelastic behaviour of polycrystalline ice, J. Glaciol., 21 (1978) pp. 621–628.

    Google Scholar 

  21. F. Thouvenot: Frequency dependence of the quality factor in the upper crust: a deep seismic sounding approach, Geophys. J. Roy. Astron. Soc., 73 (1983) pp. 427–447.

    Google Scholar 

  22. H. Berckhemer, W. Kampfmann, E. Aulbach and H. Schmeling: Shear modulus and Q of forsterite and dunite near partial melting from forced-oscillation experiments, Phys. Earth Planet. Int., 29 (1982) pp. 30–41.

    Article  Google Scholar 

  23. A. Ulug and H. Berckhemer: Frequency dependence of Q for seismic body waves in the Earth’s mantle, J. Geophys., 56 (1984) pp. 9–19.

    Google Scholar 

  24. R. Bass: A theoretical analysis of the mechanical relaxation of single-crystalline ice, Proc Roy. Soc. A, 247 (1958) pp. 462–464.

    Article  Google Scholar 

  25. J. W. Glen: The mechanics of ice, Corps of Engineers, U.S. Army, Cold Regions Science and Engineering Monograph II-C2b (1975).

    Google Scholar 

  26. R. Vassoille: Comportement anélastique et microplastique de la glace lh à basse fréquence, Thèse, Université de Lyon I (1978).

    Google Scholar 

  27. H. R. Hardy Jr. and M. Langer (eds.): The mechanical behavior of salt, Trans Tech Publ., D-3392 Clausthal-Zellerfeld (1984).

    Google Scholar 

  28. E. N. Lindner and B. H. G. Brady: Memory aspects of salt creep. In [27], pp. 241–273.

    Google Scholar 

  29. S. Horseman and E. Passaris: Creep tests for storage cavity closure prediction. In [27], pp. 119–157.

    Google Scholar 

  30. T. F. Lomenick: Accelerated deformation of rock salt at elevated temperature and pressure and its implications for high level radioactive waste disposal, ORNL-TM-2102, Oak Ridge Nat. Lab. Also Ph.D. Dissertation, Univ. of Tennessee.

    Google Scholar 

  31. J. E. Russell and T. F. Lomenick: Analysis of long term creep tests on model pillars. In [27], pp. 355–366.

    Google Scholar 

  32. A. Fossum: Viscoplastic behaviour during the excavation phase of a salt cavity, Int. J. num. anal, meth. in Geomech., 1 (1977) pp. 45–55.

    Article  Google Scholar 

  33. D. E. Munson and P. R. Dawson: Salt constitutive modeling using mechanisms maps. In [27], pp. 717–737.

    Google Scholar 

  34. E. H. Lee: The use of plastic strain as a state variable. In Plasticity to-day, (A. Sawczuk and G. Bianchi, eds.), Elsevier Applied Sci. Publ., London (1985) pp. 175–177.

    Google Scholar 

  35. K. -M. Borchert, H. Hebner and T. Richter: Creep calculation on salt by using an endochronic material law compared to other creep formulations. In [27], pp. 573–587.

    Google Scholar 

  36. H. Le Gac: Contribution à la détermination des lois de comportement de la glace polycristalline. Thèse de 3e cycle, Univ. of Grenoble I (1980).

    Google Scholar 

  37. H. Jacka: The time and strain required for the development of minimum strain rates in ice, Cold Regions Sci. Techn., 5 (1984) pp. 261–268.

    Article  Google Scholar 

  38. M. F. Ashby and P. Duval: The creep of polycrystalline ice, Cold Regions Sci. and Techn., 11 (1985) pp. 285–300.

    Article  Google Scholar 

  39. J. W. Glen: The creep of polycrystalline ice, Proc. Roy. Soc. A, 228 (1955) pp. 519–538.

    Article  Google Scholar 

  40. G. J. Lloyd and R. J. McElroy: On the anelastic contribution to creep, Acta Metall, 22 (1974) pp. 339–347.

    Article  Google Scholar 

  41. S. K. Mitra and D. McLean: Work hardening and recovery in creep, Proc. Roy. Soc. A, 295 (1961) pp. 288–299.

    Google Scholar 

  42. H. Le Gac and P. Duval: Constitutive relations for the non-elastic deformation of polycrystalline ice. In Physics and mechanics of ice, IUTAM Symp., Copenhagen 1979 (P. Tryde, ed.), Springer Verlag, Berlin (1980) pp. 51–59.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Grenoble I, Grenoble, France

    Louis A. Lliboutry (Professor of Geophysics)

Authors
  1. Louis A. Lliboutry
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Martinus Nijhoff Publishers, Dordrecht

About this chapter

Cite this chapter

Lliboutry, L.A. (1987). Viscoelasticity and transient creep. In: Very Slow Flows of Solids. Mechanics of Fluids and Transport Processes, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3563-1_15

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3563-1_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8094-1

  • Online ISBN: 978-94-009-3563-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation