Abstract
The objective of this paper is to assess the predictive capability of different classes of extended plasticity theories (bounding surface plasticity, generalized plasticity and generalized tangential plasticity) in the modeling of incremental nonlinearity, which is one of the most striking features of the mechanical behavior of granular soils, occurring as a natural consequence of the particular nature of grain interactions at the microscale. To this end, the predictions of the various constitutive models considered are compared to the results of a series of Distinct Element simulations performedad hoc. In the comparison, extensive use is made of the concept of incremental strain-response envelope in order to assess the directional properties of the material response for a given initial state and stress history.
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References
V.V. Sokolowski,Statics of Granular Media. Oxford: Pergamon (1965) 270 pp.
W.F. Chen,Limit Analysis and Soil Plasticity. Amsterdam: Elsevier (1976) 637 pp.
K.H. Roscoe and J.B. Burland, On the generalised stress-strain behaviour of ‘wet’ clay. In: J. Heyman and F.A. Leckie (eds.),Engineering Plasticity. Cambridge: Cambridge Univ. Press (1968) pp. 535–609.
A.N. Schofield and C.P. Wroth,Critical State Soil Mechanics. London: McGraw-Hill (1968) 310 pp.
G. Gudehus, F. Darve and I. Vardoulakis (eds.), Constitutive Relations for Soils. Rotterdam: Balkema (1984) 497 pp.
A.S. Saada and G.F. Bianchini (eds.),Constitutive Equations for Granular Non-Cohesive Soils. Rotterdam: Balkema (1989) 733 pp.
D. Kolymbas (ed.),Modern Approaches to Plasticity. Amsterdam: Elsevier (1993) 780 pp.
D. Kolymbas (ed.),Constitutive Modelling of Granular Materials. Berlin: Springer (1999) 554 pp.
F. Calvetti, G. Viggiani and C. Tamagnini, A numerical investigation of the incremental behavior of granular soils.Rivista Italiana di Geotecnica, 37 (2003) 11–29.
C.A. Truesdell and W. Noll, The non-linear field theories of mechanics. In: S. Flügge (ed.),Encyclopedia of Physics, vol. III/3. Berlin: Springer (1965) pp. 1–602
D.R. Owen and W.O. Williams, On the time derivatives of equilibrated response functions.Arch. Rat’l. Mech. Anal. 33 (1969) 288–306.
C. Tamagnini and G. Viggiani, Constitutive modelling for rate-independent soils: a review.Revue FranÇaise de Génie Civil. 6 (2002) 933–974.
F. Darve, The expression of rheological laws in incremental form and the main classes of constitutive equations. In:F Darve (ed.),Geomaterials: Constitutive Equations and Modelling. Amsterdam: Elsevier (1990) pp. 123–148.
A. Anandarajah, K. Sobhan and N. Kuganenthira, Incremental stress-strain behavior of a granular soil.J. Geotech. Engng. ASCE 121 (1995) 57–68.
P. Royis and T. Doanh, Theoretical analysis of strain response envelopes using incrementally non-linear constitutive equations.Int. J. Num. Anal. Meth. Geomech. 22 (1998) 97–132.
J.-P. Bardet and J. Proubet, Application of micromechanics to incrementally nonlinear constitutive equations for granular media. In: J. Biarez and R. Gourves (eds.),Proc. Powders and Grains 1989. Rotterdam: Balkema (1989) pp. 265–273.
J.-P. Bardet, Numerical tests with discrete element method. In: D. Kolymbas (ed.),Proc. Modern Approaches to Plasticity. Amsterdam: Elsevier (1993) pp. 179–197.
J.-P. Bardet, Numerical simulations of the incremental responses of idealized granular materials.Int. J. Plasticity 10 (1994) 879–908.
F. Calvetti and C. di Prisco, Fabric evolution of granular materials: a numerical approach. In:Proc. First Forum Young European Researchers. Liege, Belgium (1993) pp. 115–120.
F. Calvetti, C. Tamagnini and G. Viggiani, On the incremental behaviour of granular soils. In G.N. Pande and S. Pietruszczak (eds.),Proc. NUMOG VIII. Rotterdam: Balkema (2002) pp. 3–10.
F. Calvetti, G. Viggiani and C. Tamagnini, Micromechanical inspection of constitutive modelling. In: C. Viggiani (ed.),Constitutive Modelling and Analysis of Boundary Value Problems in Geotechnical Engineering. Benevento: Hevelius (2003) pp. 187–216.
ITASCA.PFC-3D User Manual, Itasca Consulting Group, Minneapolis (1995) 110 pp.
P.A. Cundall, A computer model for simulating progressive large scale movements in blocky rock systems. In:Proc. Symp. ISRM, Nancy, France. Rotterdam: Balkema (1971) Paper no. 11–8.
P.A. Cundall and O.D.L. Strack, A discrete numerical model for granular assemblies.Géotechnique 29 (1979) 47–65.
P.A. Cundall and R.D. Hart, Numerical modeling of discontinua.Engg. Comp. 9 (1992) 101–113.
Y. Kishino and C. Thornton, Discrete element approaches. In: F. Oka and T. Tamura (eds.),Mechanics of Granular Materials. An Introduction. Rotterdam: Balkema (1999) pp. 147–223.
C. Tamagnini, G. Viggiani, R. Chambon and J. Desrues, Evaluation of different strategies for the integration of hypoplastic constitutive equations: Application to the cloe model.Mech. Cohesive-Frictional Mater 5 (2000) 263–289.
G. Gudehus, A comparison of some constitutive laws for soils under radially symmetric loading and unloading. In: Wittke (ed.),3rd Int. Conf. Num. Meth. Geomech. Rotterdam: Balkema (1979) pp. 1309–1324.
R. Nova, Sinfonietta classica: an exercise on classical soil modelling. In: Saada and Bianchini (eds.),Constitutive Equations for Granular Non-Cohesive Soils. Rotterdam: Balkema (1988) pp. 501–519.
C. di Prisco,Sand Anisotropy: Experimental Analysis and Mathematical Modelling. PhD thesis, Politecnico di Milano (1993) 222 pp. (in Italian).
di Prisco, R. Nova and J. Lanier, A mixed isotropic-kinematic hardening constitutive law for sand. In: D. Kolymbas (ed.),Modern Approaches to Plasticity. Amsterdam: Elsevier (1993) pp. 83–124.
R. Nova and D.M. Wood, A constitutive model for sand in triaxial compression.Int. J. Num. Anal. Meth. Geomech. 3 (1979) 255–278.
C. Tamagnini, R. Castellanza and R. Nova, A generalized backward euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials.Int. J. Num. Anal. Meth. Geomech. 26 (2002) 963–1004.
J.C. Simo and T.J.R. Hughes,Computational Inelasticity. Berlin: Springer (1997) 392 pp.
G. Maier, On associative incremental elastic-plastic constitutive models.Rend. 1st. Lombardo di Scienze e Lettere 100 (1966) 809–838. (in Italian).
R.I. Borja and C. Tamagnini, Cam-clay plasticity, part III: Extension of the infinitesimal model to include finite strains.Comp. Meth. Appl. Mech. Engng. 155 (1998) 73–95.
R. Lagioia, A.M. Puzrin and D.M. Potts, A new versatile expression for yield and plastic potential surfaces.Comput. Geotech. 19 (1996) 171–191.
H.A.M. van Eekelen, Isotropic yield surfaces in three dimensions for use in soil mechanics.Int. J. Numer. Anal. Meth. Geomech. 4 (1980) 89–101.
A. Anandarajah and Y.F. Dafalias, Bounding surface plasticity. III: Application to anisotropic cohesive soils.J. Engng. Mech. ASCE 112 (1986) 1292–1318.
D.M. Wood,Soil Behaviour and Critical State Soil Mechanics. Cambridge: Cambridge Univ. Press (1990) 462 pp.
R. Nova, On the hardening of soils.Arch. Mech. Stosowanej 29 (1977) 445–458.
J.H. Atkinson, D. Richardson and S.E. Stallebrass, Effect of recent stress history on the stiffness of overconsolidated clay.Géotechnique 40 (1986) 531–540.
S.E. Stallebrass,Modelling the Effect of Recent Stress History on the Behaviour of Overconsolidated Soils. PhD thesis. The City University, London (1990) 164 pp.
D.M. Wood, Laboratory investigations of the behaviour of soils under cyclic loading: a review. In: G.N. Pande and O.C. Zienkiewicz (eds.),Soil Mechanics — Cyclic and Transient Loads. Chichester: Wiley (1982) pp. 513–582.
Y.F. Dafalias and L.R. Herrmann, Bounding surface formulation of soil plasticity. In: G.N. Pande and O.C. Zienkiewicz (eds.),Soil Mechanics — Cyclic and Transient Loads. Chichester: Wiley (1982) pp. 253–283.
Y.F. Dafalias, Bounding surface plasticity. I: Mathematical foundation and hypoplasticity.J. Engng. Mech., ASCE 112 (1986) 966–987.
Y.F. Dafalias and L. R. Herrmann, Bounding surface plasticity. II: Application to isotropic cohesive soils.J. Engng. Mech., ASCE 112 (1986) 1263–1291.
M. Pastor, O.C. Zienkiewicz and A.H.C. Chan, Generalized plasticity and the modelling of soil behaviour.Int. J. Numer. Anal. Meth. Geomech. 14 (1990) 151–190.
O.C. Zienkiewicz and Z. Mroz, Generalized plasticity formulation and applications to geomechanics. In: C.S. Desai and R.H. Gallagher (eds.),Mechanics of Engineering Materials. Chichester: Wiley (1984) pp. 655–679.
E. Papamichos and I. Vardoulakis, Shear band formation in sand according to non-coaxial plasticity model.Géotechnique 4 (1995) 649–661.
D. Kolymbas, An outline of hypoplasticity.Arch. Appl. Mech. 61 (1991) 143–151.
C. Tamagnini, G. Viggiani and R. Chambon, A review of two different approaches to hypoplasticity. In: D. Kolymbas (ed.),Constitutive Modelling of Granular Materials. Berlin: Springer (2000) pp. 107–145.
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Tamagnin, C., Calvetti, F. & Viggiani, G. An assessment of plasticity theories for modeling the incrementally nonlinear behavior of granular soils. J Eng Math 52, 265–291 (2005). https://doi.org/10.1007/BF02694041
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DOI: https://doi.org/10.1007/BF02694041