Abstract
An introduction into standard elasto-plasticity is presented. Return mapping algorithms are introduced, and the consistent linearization of the equations ensuing from standard elasto-plastic models is given. Then, generalized plasticity is introduced, and its implicit integration is shown. Further, the theory is applied to a generalized plasticity model for sand. Subsequently, the same is done for hypoplasticity. It follows that standard plasticity, generalized plasticity and hypoplasticity can be numerically treated in a unified algorithmic setting. Finally, numerical examples are given to illustrate the theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Auricchio, E, and Taylor, R. L. (1995). Two material models for cyclic plasticity: nonlinear kinematic hardening and generalized plasticity. International Journal of Plasticity 11 (1): 65–98.
Borja, R. (1991). Cam-Clay plasticity, Part II, Implicit integration of constitutive equations based on a nonlinear stress predictor. Computer Methods in Applied Mechanics and Engineering 88: 225–240.
Bushnell, D. (1977). A strategy for the solution of problems involving large deflections, plasticity and creep. International Journal for Numerical Methods in Engineering 11: 682–708.
de Borst, R. (1986). Non-linear analysis of frictional materials. Ph.D. Dissertation, Delft University of Technology.
Desrues, J. (1998). Localization patterns in ductile and brittle geomaterials. In de Borst, R., and van der Giessen, E., eds., Material Instabilities in Solids, 137–158.
Golub, G. H., and van Loan, C. F. (1996). Matrix Computations, third edition. The John Hopkins University Press, London.
Green, A. E. (1956). Hypoelasticity and plasticity. Proc. Roy. Soc. 234: 46–59.
Kolymbas, D. (2000). Introduction to Hypoplasticity. Balkema, Rotterdam.
Krieg, R. D., and Krieg, D. B. (1977). Accuracies of numerical solution methods for the elastic-perfectly plastic model. Journal of Pressure and Vessel Technology 99.
Larsson, R., and Runesson, K. (1996). Implicit integration and consistent linearization for yield criteria of the mohr-coulomb type. Mechanics of Cohesive-Frictional Materials 1: 367–383.
Lemaitre, J., and Chaboche, J.-L. (1990). Mechanics of Solid Materials. Cambridge University Press. Lubliner, J. (1974). A simple theory of plasticity. International Journal of Solids and Structures 10: 313–319.
Mrôz, Z., and Zienkiewicz, O. C. (1984). Uniform formulation of constitutive equations for clays and sand. In Desai, C. S., and Gallagher, R. H., eds., Mechanics of Engineering Materials, 415–450.
Nayak, G. C., and Zienkiewicz, O. C. (1972). Elastoplastic stress analysis. A generalization of various constitutive equations including stress softening. International Journal for Numerical Methods in Engineering 5: 113–135.
Ortiz, M., and Popov, E. P. (1985). Accuracy and stability of integration algorithms for elastoplastic constitutive equations. International Journal for Numerical Methods in Engineering 21: 1561–1576.
Ortiz, M., and Simo, J. C. (1986). An analysis of a new class of integration algorithms for elastoplastic constitutive relations. International Journal for Numerical Methods in Engineering 23: 353–366.
Owen, D. R. J., and Hinton, E. (1980). Finite Elements in Plasticity: Theory and Practice. Pineridge Press, Swansea.
Pastor, M., Zienkiewicz, O. C., and Chan, A. C. (1990). Theme/Feature paper. Generalized plasticity and the modeling of soil behavior. International Journal for Numerical and Analytical Methods in Geomechanics 14: 151–190.
Pérez-Foguet, A., Rodriguez-Ferran, A., and Huerta, A. (1998). Numerical differentiation for local and global tangent operators in computational plasticity. Technical Report 144, CIMNE Barcelona.
Potts, D., Doumas, G., and Vaughan, P. (1987). Finite element analysis of the direct shear box test. Geotechnique 37: 11–23.
Rice, J. R., and Tracey, D. M. (1971). Computational fracture mechanics. In S. J. Fence et al., ed., Proc.Symp.Num.Comp.Meth.Struct.Mech., 585–624. Academic Press, NewYork.
Schreyer, H. L., Kulak, R. L., and Kramer, J. M. (1979). Accurate numerical solutions for elastic-plastic models. Journal of Pressure and Vessel Technology 101: 226–334.
Simo, J. C., and Taylor, R. L. (1985). Consistent tangent operators for rate-independent elastoplasticity. Computer Methods in Applied Mechanics and Engineering 48: 101–118.
von Wolffersdorff, P. A. (1996). A hypoplastic relation for materials with a predefined limit state surface. Mechanics of Cohesive-Frictional Materials 1: 251–271.
Wu, W., and Bauer, E. (1992). A hypoplastic model for barotropy and pycnotropy of granular soils. In Kolymbas, D., ed., Modern Approaches to Plasticity, 225–246.
Wu, W., and Niemunis, A. (1996). Failure criterion, flow rule and dissipation function derived from hypoplasticity. Mechanics of Cohesive-Frictional Materials 1: 145–163.
Zienkiewicz, O. C., and Mroz, Z. (1984). Generalized plasticity formulation and applications to geome- chanics. In Desai, C. S., and Gallagher, R. H., eds., Mechanics of Engineering Materials, 655–680.
Zienkiewicz, O. C., and Taylor, R. L. (1989). The Finite Element Method, 4-th ed. McGraw-Hill, Berkshire, England.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Wien
About this chapter
Cite this chapter
de Borst, R., Heeres, O. (2001). Computational Plasticity. In: Schrefler, B.A. (eds) Environmental Geomechanics. International Centre for Mechanical Sciences, vol 417. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2592-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2592-2_4
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83680-4
Online ISBN: 978-3-7091-2592-2
eBook Packages: Springer Book Archive