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Acta Mechanica Sinica

, Volume 34, Issue 5, pp 896–901 | Cite as

Effect of integrating memory on the performance of the fractional plasticity model for geomaterials

  • Yifei Sun
  • Yufeng Gao
  • Shunxiang Song
Research Paper
  • 75 Downloads

Abstract

A fractional plasticity model for geomaterials is proposed by using the fractional derivative. Due to the integral definition of the fractional derivative, the range of load memory for calculating the flow direction may influence the subsequent model performance. Therefore, an investigation on the memory dependence of the model was conducted. It was found that the load memory affected the stress–dilatancy behavior of the geomaterial. Due to the loss of memory from zero- to confining-stress states, slightly higher strain is reported, whereas an insignificant difference in the predicted deviator stress is observed. Thus, for engineering applications, starting the memory from the zero-stress state, which avoids mathematical complexity, is suggested.

Keywords

Plasticity Fractional calculus Memory 

Notes

Acknowledgements

Financial support provided by the National Natural Science Foundation of China (Grant 41630638), the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the Fundamental Research Funds for the Central Universities (Grant 2017B05214) are appreciated.

References

  1. 1.
    Khalili, N., Habte, M.A., Valliappan, S.: A bounding surface plasticity model for cyclic loading of granular soils. Int. J. Numer. Methods Eng. 63, 1939–1960 (2005)CrossRefGoogle Scholar
  2. 2.
    Liu, H.B., Zou, D.G., Liu, J.M.: Constitutive modeling of dense gravelly soils subjected to cyclic loading. Int. J. Numer. Anal. Methods Geomech. 38, 1503–1518 (2014)CrossRefGoogle Scholar
  3. 3.
    Kan, M.E., Taiebat, H.A.: A bounding surface plasticity model for highly crushable granular materials. Soils Found. 54, 1188–1201 (2014)CrossRefGoogle Scholar
  4. 4.
    Xiao, Y., Liu, H.: Elastoplastic constitutive model for rockfill materials considering particle breakage. Int. J. Geomech. 17, 04016041 (2016)CrossRefGoogle Scholar
  5. 5.
    Sun, Y., Indraratna, B., Carter, J.P., et al.: Application of fractional calculus in modelling ballast deformation under cyclic loading. Comput. Geotech. 82, 16–30 (2017)CrossRefGoogle Scholar
  6. 6.
    Liao, M., Lai, Y., Liu, E., et al.: A fractional order creep constitutive model of warm frozen silt. Acta Geotech. 12, 377–389 (2016)CrossRefGoogle Scholar
  7. 7.
    Xu, Z., Chen, W.: A fractional-order model on new experiments of linear viscoelastic creep of Hami Melon. Comput. Math. Appl. 66, 677–681 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Zhu, S., Cai, C., Spanos, P.D.: A nonlinear and fractional derivative viscoelastic model for rail pads in the dynamic analysis of coupled vehicle-slab track systems. J. Sound Vib. 335, 304–320 (2015)CrossRefGoogle Scholar
  9. 9.
    Yang, X., Chen, W., Sun, H.: Fractional time-dependent apparent viscosity model for semisolid foodstuffs. Mech. Time-Depend. Mater. (2017).  https://doi.org/10.1007/s11043-017-9366-8
  10. 10.
    Sun, Y., Xiao, Y., Zheng, C., et al.: Modelling long-term deformation of granular soils incorporating the concept of fractional calculus. Acta. Mech. Sin. 32, 112–124 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Zhou, H.W., Wang, C.P., Mishnaevsky, L., et al.: A fractional derivative approach to full creep regions in salt rock. Mech. Time-Depend. Mater. 17, 413–425 (2013)CrossRefGoogle Scholar
  12. 12.
    Zhou, H.W., Wang, C.P., Han, B.B., et al.: A creep constitutive model for salt rock based on fractional derivatives. Int. J. Rock Mech. Min. Sci. 48, 116–121 (2011)CrossRefGoogle Scholar
  13. 13.
    Sumelka, W.: Fractional viscoplasticity. Mech. Res. Commun. 56, 31–36 (2014)CrossRefGoogle Scholar
  14. 14.
    Sun, Y., Shen, Y.: Constitutive model of granular soils using fractional order plastic flow rule. Int. J. Geomech. 17, 04017025 (2017)CrossRefGoogle Scholar
  15. 15.
    Sun, Y., Xiao, Y.: Fractional order plasticity model for granular soils subjected to monotonic triaxial compression. Int. J. Solids Struct. 118–119, 224–234 (2017)CrossRefGoogle Scholar
  16. 16.
    Roscoe, K.H., Burland, J.B.: On the generalised stress–strain behaviour of ’wet’ clay. In: Heyman, J., Leckie, F.A. (eds.) Engineering Plasticity. Cambridge University Press, Cambridge (1968)Google Scholar
  17. 17.
    Been, K., Jefferies, M.G.: A state parameter for sands. Géotechnique 22, 99–112 (1985)CrossRefGoogle Scholar
  18. 18.
    Li, X., Wang, Y.: Linear representation of steady-state line for sand. J. Geotech. Geoenviron. Eng. 124, 1215–1217 (1998)CrossRefGoogle Scholar
  19. 19.
    Ishihara, K., Tatsuoka, F., Yasuda, S.: Undrained deformation and liquefaction of sand under cyclic stresses. Soils Found. 15, 29–44 (1975)CrossRefGoogle Scholar
  20. 20.
    Aursudkij, B., McDowell, G.R., Collop, A.C.: Cyclic loading of railway ballast under triaxial conditions and in a railway test facility. Granul. Matter 11, 391–401 (2009)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Ministry of Education for Geomechanics and Embankment EngineeringHohai UniversityNanjingChina

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