A hypoplastic theory for granular materials developed by Gudehus and Bauer is discussed. The description of asymptotic states is of particular interest. Three forms of asymptotic states are defined. Useful criteria to describe the tensorial part of the constitutive relation is developed for one of them, namely for the critical states. The terms proposed by Wu are correlated to the well-known formulations of elastic plastic theory: the Drucker/Prager model and the yield condition by Matsuoka/Nakai. The suitability of the Matsuoka/Nakai criterion for critical states is discussed.

Specification of tensorial functions follows in two steps. First the hypoplastic Drucker/Prager model is developed, and then the limit condition by Matsuoka/Nakai is implemented. The resulting tensorial functions require the critical friction angle as the only material constant. The limit condition in critical states obtained from the hypoplastic law coincide with the one by Matsuoka/Nakai. A more comprehensive hypoplastic constitutive relation based on these new tensorial functions is discussed and applied to simulations of element tests. These numerical results are compared with experimental results for sand.

A hypoplastic relation for granular materials with a predefined limit state surface

SUMMARY In order to eliminate ratcheting a so-called intergranular strain has been added to a hypoplastic constitutive model. This additional state variable represents the deformation of the interface layer between the grains. The new concept is outlined and comparisons with and without intergranular strain are presented. Some comments on numerical implementation and determination of material constants are made. A discussion on the uniqueness of the solution and objectivity of the rate of intergranular strain is added. # 1997 John Wiley & Sons, Ltd. Mech. of Cohes.-Frict. Mater., 2, 279‐299 (1997)

Hypoplastic model for cohesionless soils with elastic strain range

A constitutive equation is proposed for describing changes of states of granular materials which are sufficiently characterized by the void ratio and the stress tensor. It may be considered as an extension of the Critical State concept. It is based on recently published hypoplastic equations and covers a wide range of densities, pressures and deformations. A factorial decomposition allows a rather easy separation and determination of material parameters. Two factors depend on a relative void ratio so that it remains within lower and upper bounds. The bounding void ratios decrease monotonously from maximal values to zero with increasing pressure. The same reduction of the void ratio is proposed for an isotropic compression starting from a suspension. Thus a granulate hardness is defined, and a stiffness factor can be determined. Four material parameters can be estimated from classification tests and determined from the asymptotic behaviour in element tests. Four further parameters are determined by calibration; they are rather constant for wide groups of materials. Strength and stiffness values can be derived and used for the analysis of deformations, stability, and flow. The viscous behaviour is modelled by a rate dependent factor with one further parameter. Limitations and possible extensions of this comprehensive approach are also outlined.

A Comprehensive constitutive equation for granular materials

https://www.jstage.jst.go.jp/article/sandf1995/36/1/36_1_1/_pdf

A comprehensive constitutive equation for granular materials

Experimental results are presented from the extensive program of drained plane strain compression tests on sand carried out in Grenoble over the last two decades. Systematic analysis of photographs of the deforming specimen allowed for measuring deformations and determining strain fields throughout the test, that is: prior to, at, and after the onset of strain localization. The principles, details and accuracy of the procedure are described, as well as its suitability to properly depict the patterns of deformation. Findings concerning the occurrence and progression of strain localization are discussed. The issues of shear band orientation and thickness are addressed, as well as temporary and persistent complex localization patterns, and the volumetric behaviour inside a band after its formation. The influence of such variables as initial state of the sand (effective stress and relative density), specimen size and slenderness, as well as grain size, is discussed. Copyright © 2004 John Wiley & Sons, Ltd

Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry

The so-called hypoelastic constitutive equations, defined by the equationℸ=h(T, D), are limited by the requirement thath is linear inD. Dropping this requirement and retaining positive homogeneity of the first degreen inD leads to a broader class of equations which can be calledhypoplastic. Such equations are appropriate to describe the anelastic behaviour of granular materials. Some properties of hypoplastic equations are discussed in this paper including the new notions of yield and bound surfaces which are given a completely different meaning than in classical elastoplasticity. Possiblities to enlarge hypoplasticity towards rate-dependence and more complex intrinsic memory of the material are pointed to.

An outline of hypoplasticity

Hypoplastic constitutive model with critical state for granular materials

Groundwater ingress to tunnels - The exact analytical solution

Keywords: Loi constitutive ; Plasticite ; Tunnels Reference Record created on 2004-09-07, modified on 2016-08-08

Dimitrios Kolymbas

Papers

An outline of hypoplasticity

Hypoplastic constitutive model with critical state for granular materials

Groundwater ingress to tunnels - The exact analytical solution

Introduction to Hypoplasticity

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