Constitutive Equations and Instabilities of Granular Materials

Constitutive equations for geomaterials constitute a very intricate field. In the first part of this chapter, a synthetic view of constitutive formalism is presented. An intrinsic classification of all existing constitutive relations is deduced. Then examples of incrementally non-linear relations are given and some applications follow. A numerical study of the so-called “yield surfaces” is presented, and is followed by a discussion on the validity of the principle of superposition for incremental loading. Finally the question of bifurcations and instabilities in geomaterials is investigated. Essentially because of the non-associative character of geomaterial plastic strains, a large domain of failure with various modes of ruptures is exhibited.

[1]  Éléments finis déplacements. Nouvelle forme du problème algébrique et algorithmes adaptés , 1997 .

[2]  F. Darve.  Une loi rheologique incrementale non-lineaire pour les solides , 1980 .

[3]  Adel S. Saada,et al.  Constitutive equations for granular non-cohesive soils , 1989 .

[4]  Yannis F. Dafalias,et al.  BOUNDING SURFACE PLASTICITY, I: MATHEMATICAL FOUNDATION AND HYPOPLASTICITY , 1986 .

[5]  Zdenek P. Bažant,et al.  ENDOCHRONIC INELASTICITY AND INCREMENTAL PLASTICITY , 1978 .

[6]  Dimitrios Kolymbas,et al.  A rate-dependent constitutive equation for soils , 1977 .

[7]  R. J. Crawford,et al.  Mechanics of engineering materials , 1986 .

[8]  Poul V. Lade,et al.  Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces , 1977 .

[9]  M. Goldscheider,et al.  Formation of shear bands in sand bodies as a bifurcation problem , 1978 .

[10]  Félix Darve,et al.  INCREMENTAL CONSTITUTIVE LAW FOR SANDS AND CLAYS: SIMULATIONS OF MONOTONIC AND CYCLIC TESTS , 1982 .

[11]  R. Nova,et al.  Theoretical investigation of the undrained stability of shallow submerged slopes , 1995 .

[12]  P. A. Vermeer,et al.  A double hardening model for sand , 1978 .

[13]  R. Nova,et al.  A constitutive model for sand in triaxial compression , 1979 .

[14]  Félix Darve,et al.  Instabilities in granular materials and application to landslides , 2000 .

[15]  R. Hill.  A general theory of uniqueness and stability in elastic-plastic solids , 1958 .

[16]  G. Mullenger,et al.  A rate-type constitutive model for soil with a critical state , 1978 .

[17]  C. Truesdell,et al.  The Non-Linear Field Theories of Mechanics , 1965 .

[18]  M. De.  Handbuch der Physik , 1957 .

[19]  D. Muir Wood,et al.  Localisation and bifurcation theory for soils and rocks , 1998 .

[20]  Zenon Mróz,et al.  On the description of anisotropic workhardening , 1967 .

[21]  Roberto Nova,et al.  Stability problems related to static liquefaction of loose sand , 1994 .

[22]  Robert Charlier,et al.  CLoE, a new rate-type constitutive model for geomaterials theoretical basis and implementation , 1994 .

[23]  S. Imposimato,et al.  An investigation on the uniqueness of the incremental response of elastoplastic models for virgin sand , 1998 .

[24]  F. Darve.  Liquefaction phenomenon of granular materials and constitutive stability , 1996 .

[25]  Jean H. Prevost,et al.  PLASTICITY THEORY FOR SOIL STRESS-STRAIN BEHAVIOR , 1978 .

[26]  Mourad Meghachou.  Stabilité des sables lâches : essais et modélisations , 1993 .

[27]  David R. Owen,et al.  On the time derivatives of equilibrated response functions , 1969 .