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Plastic Dissipation of the Fractional Plasticity using Modified Cam-Clay Yielding Function

Published online by Cambridge University Press:  17 January 2020

P. Tai  and
Y. Sun Open the ORCID record for Y. Sun [Opens in a new window]
P. Tai
Affiliation:
Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Hong Kong
Y. Sun*
Affiliation:
Faculty of Civil and Environmental Engineering, Ruhr-Universität Bochum, Bochum, Germany
*
*Corresponding author (06047112@hhu.edu.cn; yifei.sun@rub.de)
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Abstract

Soils usually exhibit state-dependent frictional behaviour that undergoes plastic volumetric deformation. To correctly capture such response under the framework of classical plasticity, a non-associated flow rule using additional plastic potential is inevitably needed. Recently, a novel fractional plasticity (FP) without using plastic potential has been developed, and successfully applied in modelling the state-dependent nonassociated behaviour of soils. However, the energy dissipation characteristics of FP has not been probed in depth. This note examines the plastic dissipation behaviour of FP, when modelling the constitutive behaviour of soils. It is found that the plastic dissipation of FP increases continuously with the shear strain. However, the rate of plastic dissipation depends on the initial material state in relation to the critical state line.

Keywords

Fractional plasticityplastic dissipationstate dependence
Type
Technical Note
Information
Journal of Mechanics , Volume 36 , Issue 3 , June 2020 , pp. N1 - N7
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

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References

REFERENCES

Vermeer, P.A. “A double hardening model for sand”. Géotechnique, 28(4), 413–433 (1978)CrossRefGoogle Scholar
Gens, A. and Potts, D.M. “Critical state models in computational geomechanics”. Engineering Computations, 5(3), 178–197 (1988)CrossRefGoogle Scholar
Xiao, Y., Long, L., Matthew Evans, T., et al. “Effect of Particle Shape on Stress-Dilatancy Responses of Medium-Dense Sands”. Journal of Geotechnical and Geoenvironmental Engineering, 145(2), 04018105 (2019)CrossRefGoogle Scholar
Xiao, Y., Meng, M., Chen, Q., et al. “Friction and dilatancy angles of granular soils incorporating effects of shearing modes”. International Journal of Geomechanics, 18(11), 06018027 (2018)CrossRefGoogle Scholar
Lade, P.V., Nelson, R.B. and Ito, Y.M. “Nonassociated flow and stability of granular materials”. Journal of Engineering Mechanics, 113(9), 1302–1318 (1987)CrossRefGoogle Scholar
Pastor, M., Zienkiewicz, O.C. and Chan, A.H.C. “Generalized plasticity and the modelling of soil behaviour”. International Journal for Numerical and Analytical Methods in Geomechanics, 14(3), 151–190 (1990)CrossRefGoogle Scholar
Collins, I.F. and Houlsby, G.T. “Application of thermomechanical principles to the modelling of geotechnical materials”. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 453(1964), 1975–2001 (1997)CrossRefGoogle Scholar
Sumelka, W. and Nowak, M. “Non-normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study”. International Journal for Numerical and Analytical Methods in Geomechanics, 40(5), 651–675 (2016)CrossRefGoogle Scholar
Sun, Y., Gao, Y. and Zhu, Q. “Fractional order plasticity modelling of state-dependent behaviour of granular soils without using plastic potential”. International Journal of Plasticity, 102, 53–69 (2018)CrossRefGoogle Scholar
Sun, Y., Gao, Y., Song, S., et al. “Three-dimensional state-dependent fractional plasticity model for soils”. International Journal of Geomechanics, 10.1061/(ASCE) GM.1943-5622.0001353, (2019)Google Scholar
Dafalias, Y.F. “Bounding surface plasticity. I: Mathematical foundation and hypoplasticity”. Journal of Engineering Mechanics, 112(9), 966–987 (1986)CrossRefGoogle Scholar
Schofield, A. and Wroth, P. “Critical state soil mechanics”. In. New York, USA, McGraw-Hill London (1968)Google Scholar
Sun, Y. and Sumelka, W. “State-dependent fractional plasticity model for the true triaxial behaviour of granular soil”. Archives of Mechanics, 71(1), 23–47 (2019)Google Scholar
Hardin, B.O. and Richart, J.F.E. “Elastic wave velocities in granular soils”. Journal of the Soil Mechanics and Foundations Division, ASCE, 89(1), 33–66 (1963)Google Scholar
Xiao, Y., Liu, H., Chen, Y., et al. “Bounding surface model for rockfill materials dependent on density and pressure under triaxial stress conditions”. Journal of Engineering Mechanics, 140(4), 04014002 (2014)CrossRefGoogle Scholar
Collins, I.F. and Kelly, P.A. “A thermomechanical analysis of a family of soil models”. Géotechnique 52(7), 507–518 (2002)CrossRefGoogle Scholar