Symmetrization Method for the Generalized Plasticity Model with Nonassociated Plastic Flow Rule
Publication: International Journal of Geomechanics
Volume 15, Issue 6
Abstract
When the generalized plasticity model with nonassociated flow rule is utilized to simulate the mechanical behaviors of sands, the asymmetric elastoplastic matrices or coefficient matrix has to be encountered in finite-element (FE) computations, posing a great challenge to the solution of large-scale asymmetric linear systems of equations. In this study, a simple symmetrization method for the asymmetric stiffness matrix attributable to the generalized plasticity model is presented and then verified by simulating a series of triaxial tests involving the asymmetric stiffness matrices. Furthermore, the symmetric and asymmetric preconditioned iterative methods are employed to solve the asymmetric and symmetrized FE linear systems of equations, respectively, arising from a three-dimensional earth dam example. Finite-element elastoplastic dynamic analyses of the dam show that compared with the solution method based on the asymmetric FE equation, the symmetrization method can produce accurate results, but with remarkably less computational time and random-access memory (RAM) requirement.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is supported by National Nature Science Foundation of China (51179092 and 51379103) and State Key Laboratory of Hydroscience and Engineering Project (2013-KY-4).
References
Barton, N., and Choubey, V. (1977). “The shear strength of rock joints in theory and practice.” Rock Mech., 10(1–2), 1–54.
Chen, X., Toh, K. C., and Phoon, K. K. (2006). “A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations.” Int. J. Numer. Methods Eng., 65(6), 785–807.
Deb, D., Das, K. C., and Raja Sekhar, G. P. (2013). “Generalized symmetric formulation of tangential stiffness for nonassociative plasticity.” J. Eng. Mech., 105–113.
Drucker, D. C., Gibson, R. E., and Henkel, D. J. (1957). “Soil mechanics and work-hardening theories of plasticity.” Trans. Am. Soc. Civ. Eng., 122(1), 338–346.
Famiyesin, O. O. R. (1999). “Robust symmetric formulations for nonassociated plasticity problems.” J. Eng. Mech., 1071–1080.
Freund, R. W., and Nachtigal, N. M. (1991). “QMR: A quasi-minimal residual method for non-Hermitian linear systems.” Numer. Math., 60(1), 315–339.
Freund, R. W., and Nachtigal, N. M. (1994). “A new Krylov-subspace method for symmetric indefinite linear systems.” Proc., 14th IMACS World Congress on Computational and Applied Mathematics, International Association for Mathematics and Computers in Simulation (IMACS), Brussels, Belgium, 1253–1256.
Khoei, A. R., Azami, A. R., and Haeri, S. M. (2004). “Implementation of plasticity based models in dynamic analysis of earth and rockfill dams: A comparison of Pastor–Zienkiewicz and cap models.” Comput. Geotech., 31(5), 384–409.
Lade, P. V., and Duncan, J. M. (1975). “Elastoplastic stress-strain theory for cohesionless soil.” J. Geotech. Engrg. Div., 101(10), 1037–1053.
Ling, H. I., and Liu, H. (2003). “Pressure-level dependency and densification behavior of sand through generalized plasticity model.” J. Eng. Mech., 851–860.
Ling, H. I., and Yang, S. (2006). “Unified sand model based on the critical state and generalized plasticity.” J. Eng. Mech., 1380–1391.
Luo, T., Qin, Z., Feng, X., Xia, F., Yao, Y., and Sheng, D. (2013). “A symmetrisation method for non-associated unified hardening model.” Comput. Geotech., 52(Jul), 38–45.
Manzanal, D., Fernández Merodo, J. A., and Pastor, M. (2011). “Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part 1: Saturated state.” Int. J. Numer. Anal. Methods Geomech., 35(12), 1347–1362.
Mroz, Z., and Zienkiewicz, O. C. (1984). “Uniform formulation of constitutive equations for clays and sands.” Chapter 22, Mechanics of engineering materials, C. S. Desai and R. H. Gallagher, eds., Wiley, Chichester, U.K., 415–449.
Pande, G. N., and Pietruszczak, S. (1986). “Symmetric tangential stiffness formulation for non-associated plasticity.” Comput. Geotech., 2(2), 89–99.
Pastor, M., Zienkiewicz, O. C., and Chan, A. H. C. (1990). “Generalized plasticity and the modelling of soil behavior.” Int. J. Numer. Anal. Methods Geomech., 14(3), 151–190.
Roscoe, K. H., Schofield, A. N., and Thurairajah, A. (1963). “Yielding of clays in states wetter than critical.” Géotechnique, 13(3), 211–240.
Toh, K.-C., and Phoon, K.-K. (2008). “Comparison between iterative solution of symmetric and non-symmetric forms of Biot’s FEM equations using the generalized Jacobi preconditioner.” Int. J. Numer. Anal. Methods Geomech., 32(9), 1131–1146.
Xiong, W. (1993). “Symmetric formulation of tangential stiffnesses for non-associated visco-plasticity with an implicit time integration scheme.” Appl. Math. Mech., 14(3), 251–257.
Xiong, W.-L. (1986). “Symmetric formulation of tangential stiffnesses for non-associated plasticity.” Appl. Math. Mech., 7(11), 1043–1052.
Xu, B., Zou, D., and Liu, H. (2012). “Three-dimensional simulation of the construction process of the Zipingpu concrete face rockfill dam based on a generalized plasticity model.” Comput. Geotech., 43, 143–154.
Zienkiewicz, O. C., Chan, A. H. C., Pastor, M., Schrefler, B. A., and Shiomi, T. (1999). Computational geomechanics with special reference to earthquake engineering, Wiley, Chichester, U.K.
Zienkiewicz, O. C., and Mroz, Z. (1984). “Generalized plasticity formulation and applications to geomechanics.” Chapter 33, Mechanics of engineering materials, C. S. Desai and R. H. Gallagher, eds., Wiley, Chichester, U.K., 655–679.
Zienkiewicz, O. C., Wood, W. L., Hine, N. W., and Taylor, R. L. (1984). “A unified set of single step algorithms. Part 1: General formulation and applications.” Int. J. Numer. Methods Eng., 20(8), 1529–1552.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 14, 2014
Accepted: Oct 2, 2014
Published online: Oct 28, 2014
Published in print: Dec 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.