Modeling of Bifurcation and Post-Bifurcation Response of Granular Materials: Insights From Discrete Element Modeling
Keywords:
hardening plasticity, smeared shear band, StrainLocalization, non-associated flow rule, Prager’s consistency condition, Noncoaxiality, Stress rotationsAbstract
A softening elastoplasticity model for sand has been constructed and its mathematical derivations are described in this paper. The proposed model is based on the concept of a non-associated elastoplastic material description. The model first was coupled with a strain hardening plasticity model, as developed by Gutierrez 2010 [1], for granular soil before the bifurcation point. The softening elastoplasticity model then develops a tangential stiffness matrix which plays a crucial role in describing the softening behavior. The smeared shear band model proposed by Pietruszczak and Mroz 1981 [2] is employed in this model to incorporate a characteristic length dimension (i.e. shear band thickness). The objectivity of the constitutive model has been established from the form-invariance principal. The plastic module in terms of stress and strain-increments is provided for simulating stress and strain-controlled biaxial tests. The results of a study of RF-Huston sand and of DEM simulation served as a basis for evaluating the capabilities of the model. The results indicate that, the softening elastoplasticity model accurately depicts the trends observed in the experimental data of RF-Hostun and the DEM sand simulation.
References
Gutierrez, M.2010. Effects of constitutive parameters on strain localization in sands. Int. j. Numer. Anal. Geomech. 35(2): 161-178.
Pietruszczak, S. and Mroz, Z. 1981. Finite Element Analysis of Deformation of Strain Softening Materials. Int. J. Num. Meth. Eng. 17: 327-334.
Nayak, G.C and Zienkiewicz, O.C.1972. Elasto-plastic stress analysis: a generalization for various constitutive relations including strain softening. Int. J. numer. Meth Engng. 5: 113–135.
Bazant. Z.P. 1988. Softening Instability: Part I — Localization into a Planar Band. Trans. ASME,
J. Appl. Mech. 55: 517.
Rice, J.R. 1976. The Localization of Plastic Deformation, in Theoretical and Applied Mechanics, Proceedings of the 14th International Congress on Theoretical and Applied Mechanics, Delft, 1: 207-220.
Rudnicki, J.W., and Rice, J.R. 1975. Conditions for the Localization of Deformation in Pressure- Sensitive Dilatant Materials, Journal of the Mechanics and Physics of Solids, 23: 371-394.
Vermeer, P.A. 1982. A simple shear-band analysis using compliances. In: IUTAM Conf. on Deformation and Failure on Granular Materials, 439–499.
Vardoulakis, I. and Sulem, J. 1995. Bifurcation Analysis in Geomechanics, Blackie Academic and Professional.
Conte,E.; Silvestri, F.; Troncone, A. 2010. Stability analysis of slopes in soils with strain- softening behaviour. Computers and Geotechnics, 37(5):710-722.
Wanatowski, D., Chu, J., Lo, R.C.2008. Strain-softening behavior of sand in strain path testing under plane-strain conditions · ActaGeotechnica 3: 99-114.
Broja and Regueiro R.A. 2001. Strain localization of frictional materials, Computer Methods in Applied Mechanics and Engineering, 190:2555-2580.
Prager W. 1956. A New Method of Analyzing Stresses and Strains in ... ASME Journal of Applied Mechanics.78: 493-496.
Prager, W. 1949. Recent developments in the mathematical theory of plasticity. J. appl. Phys.20: 235.
De Borst R., Sluys, L.J., Muhlhaus, H.B. and PAMIN, J. 1993. Fundamental issues in finite element analyses of localization of deformation. Engineering Computations, 10(2): 99-121.
Schaeffer, David G.1990. Instability and ill-posedness in the deformation of granular materials,Int. J. Numer. Anal. Methods Geomech. 14(4): 253-278.
De Borst R, Muhlhaus H. B.1992. Gradient-dependent plasticity: Formulation and algorithmic aspects. Int. J. Numer. Methods Eng. 35:521-539.
Desrues J, Hammad W. 1989. Experimental study of the localization of deformation on sand: influence of mean stress. Proceedings of the 12th International Conference on Soil Mechanics and Foundation Engineering, Rio de Janeiro 1: 31-32.
Mohamed, A., and Gutierrez, M. 2010. Comprehensive study of the effects of rolling resistance on the stress–strain and strain localization behavior of granular materials, Gran. Matter 12 (5): 527– 541.
Desrues J, Viggiani G.2004. Strain localization in sand: an overview of expertimental results obtained in Grenoble using stereo photogrammetry. International Journal for Numerical and Analytical Methods in Geomechanics28: 231–279.
Bazant, ZP, and Chang, TP. 1987. Nonlocal Finite Element Analysis of Strain- Softening Solids," J. Struct. Eng. (ASCE), 113(1):89-105.
Belytschko, T., and Mish, K. 2001. Computability in non-linear solid mechanics, International Journal for Numerical Methods in Engineering, 52 (1-2):3.
