D. Kolymbas

An outline of hypoplasticity

SummaryThe 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.ÜbersichtDie sogenannten hypoelastischen Stoffgleichungen, die durch die Gleichungℸ=h(T, D) definiert sind, werden durch die Forderung, daßh linear inD sein soll, eingeschränkt. Der Ersatz dieser Forderung rung durch die schw]:achere Forderung, daßh positiv homogen 1. Ordnung inD sein soll, führt zu einer breiteren Gruppe von Stoffgleichungen, die alshypoplastisch bezeichnet werden können. Sie sind gut geeignet, das anelastische Verhalten von Granulaten zu beschreiben. Einige ihrer Eigenschaften werden in dieser Arbeit diskutiert einschließlich der Fließ-und Grenzflächen, welchen eine total andere Bedeutung als in der klassischen Plastizitätstheorie zukommt. Möglichkeiten zur Erweiterung der vorgeschlagenen Theorie in Richtung von geschwindigkeitsabhängigen Stoffen und Stoffen mit einem komplexen Gedächtnis werden aufgezeigt.

Hypoplastic constitutive model with critical state for granular materials

Abstract This paper presents a hypoplastic constitutive model for the three-dimensional nonlinear stress-strain and dilatant volume change behavior of granular materials. The model is based on nonlinear tensorial functions and is developed without recourse to the concepts of elasto-plasticity theory such as yield surface, plastic potential, flow and hardening rules and decomposition of deformation into elastic and plastic parts. The material constants in the model can be identified with triaxial compression tests. The effect of void ratio and stress level on the behavior of granular materials is accounted for by integrating the critical state into the constitutive equation. It is shown that the model is applicable to both initial and fully developed plastic deformation of granular materials, and many well established concepts in soil mechanics, which are otherwise entirely independent, can be unified with the constitutive model. Simulations of various elementary tests, including oedometer, triaxial and simple shear tests, show that the model is capable of capturing the salient behavior of granular materials under monotonic as well as cyclic loading.

A rate-dependent constitutive equation for soils

A const i tu t ive equation of the rate type is presented here which removes the d i f f i c u l t i e s impeding the application of the usual p las t i c i t y theory. These d i f f i c u l t i e s arise because of rate-dependence and because of the so-called incremental nonl inear i ty of i r revers ib le deformation of solids. The results presented here are obtained from the consideration of soil behaviour (sand and clay) but i t is asserted that they remain valid at least in pr inc ip le for the deformation of any sol id.

Constitutive modelling of granular materials

The misery of constitutive modelling Does engineering need science The role of models in civil engineering Hypoplasticity then and now A review of two different approaches to hypoplasticity Uniqueness, second order work and bifurcation in hypoplasticity Stationary states in hypoplasticity Microscopic approach contributions to constitutive modelling Discrete and continuum modelling of granular materials 2nd Gradient constitutive models Micro-mechanically based higher-order continuum models for granular materials Relevant local variables for the change of scale in granular materials On the physical background of soil strength The influence of time derivative terms on the mechanical behaviour of loose sands An approach to plasticity based on generalised thermodynamics Comparison of hypoplasticity and elastoplastic modelling of undrained triaxial tests on loose sand Hypoplastic and elastoplastic modelling - a comparison with test data Strain response envelope: a complementary tool for evaluating hypoplastic constitutive equations Modelling wathering effects on the mechanical behaviour of granite A plasticity-based constitutive model for natural soils: a hierarchical approach Experimental bases for a new incremental non-linear constitutive relation with 5 parameters Implicit integration of hypoplastic models Soil-water coupling analysis of progressive failure in cuts with a strain softening model Advances in modelling soil anisotropy Exemples of finite element calculations with the hypoplastic law Hypoplastic simulation of complex loading paths.

Numerical testing of the stability criterion for hypoplastic constitutive equations

Abstract An outline of so-called hypoplastic constitutive equations is presented. The stability criterion proposed by Hill is applied to a hypoplastic constitutive equation for granular materials. The response envelope as proposed by Gudehus is used to check the stability criterion numerically.

Recent results of triaxial tests with granular materials

Abstract In this paper are presented some recent triaxial test results obtained with dry sand, sugar, rape, wheat and synthetic granulates. The device used was a triaxial apparatus specially designed to test dry silo materials. The results are reported with a view to facilitating development and checking of appropriate constitutive equations. This is only possible if special precautions have been taken to suppress error sources and guarantee a homogeneous deformation. The results presented here reveal some characteristics of the sample behaviour, namely (i) even during the initial isotropic consolidation the samples behave anisotropically, (ii) the inhomogeneous sample deformation sets in from the beginning of the triaxial compression and, therefore, the test results cannot be evaluated without a deconvolution technique, and (iii) with loose sands and granulates constituted from soft grains, as well as at high stress levels, a peak state is not obtained and, therefore, any reference to a friction angle is questionable. A simple deconvolution technique is also presented.

Hypoplasticity then and now

This paper is conceived primarily as an account of some interrelated ideas that we have contributed over a long period to the constitutive theory for soils known as hypoplasticity. Our previous publications on this issue have been purely seriatim and mainly for specialists. It now seems timely to attempt a unified, general presentation, which moreover is directed also to nonspe- cialists. In doing so, some emphasis is placed on the ideas and methodology underlying the model by skipping manipulative details, since the formulation may otherwise relapse into mathematical complexity, so obscuring the physical meaning. Despite the article’s review character some unpublished materials and background information are incorporated, which are otherwise omitted due to space limitation. Hopefully, the presentation will have a certain freshness, even for specialists.

Bifurcation analysis for sand samples with a non-linear constitutive equation

SummaryA thoroughly non-linear constitutive equation connecting stress-rates and strain-rates is shown to yield realistic predictions for the conditions at which bifurcation may appear in the course of axisymmetric and plane homogeneous deformations of sand samples. The features of the non-homogeneous deformation after the bifurcation are also realistically predicted, a fact which is of importance in understanding and describing rupture phenomena (formation of shear bands) in geomechanics.ÜbersichtIn dieser Arbeit wird gezeigt, daß eine nichtlineare Beziehung zwischen der Spannungsrate und der Deformationsgeschwindigkeit realistische Voraussagen für Verzweigungen liefert, die sich im Verlauf von achsensymmetrischer und ebener Verformung von Sandproben einstellen können. Die Geometrie der inhomogenen Verformung, die sich nach der Verzweigung einstellt, kann ebenfalls realistisch vorausgesagt werden. Diese Tatsache ist von Bedeutung für das Verständnis und die Beschreibung von Brucherscheinungen (Bildung von Scherfugen u. ä.) in der Geomechanik.

On Some Issues in Triaxial Extension Tests

Results of triaxial extension tests on dry sand are presented. Special attention is paid to the factors influencing the results in triaxial extension tests. It is found that factors such as accuracy of the axial force measurement, axial force carried by the rubber membrane surrounding the specimen, gravity, and inhomogeneous deformation have a much larger influence on the results in triaxial extension tests than in triaxial compression tests. Accurate measurement of the axial force is achieved by placing the load cell inside the pressure chamber. The influence of the confining pressure on the axial force measurement is avoided through a proper construction. The force carried by the rubber membrane is corrected with reference to the result of a tension test on a strip of rubber membrane. The effect of gravity is accounted for by adding the axial stress due to gravity to the applied axial stress. The inhomogeneous deformation is traced by three lateral strain collars placed along the specimen height. Results of triaxial extension tests cannot be appreciated if these influential factors are not taken into account. The failure mode of the specimen is found to be influenced largely by the initial density. Inhomogeneous deformation in the form of necking develops in the upper part of dense specimens and in the middle of loose specimens. For dense specimens, the necked region becomes wider with advanced deformation and develops into one single or two intersecting shear bands. For loose specimens, however, no shear bands can be observed.

Soft oedometer - a new testing device and its application for the calibration of hypoplastic constitutive laws

The problem addressed is how to obtain the material parameters of soils and other granular materials by means of a simple and fast laboratory test which fulfills the requirement of homogeneous specimen deformation. A new laboratory testing device called “soft oedometer,” characterized by an extensible lateral supporting ring, makes it possible to measure not only the vertical but also the lateral stress and strain of the specimen. The construction principles are presented as well as test results. The suggested evaluation of the latter makes it possible to determine the friction angle and all parameters entering hypoplastic constitutive equations without the need to achieve the limit state. In the present paper, the new apparatus is shown to make possible a particular test (oedometric test) which serves to fit a mathematical model called “hypoplastic constitutive law.” Using this model, other test types can be simulated realistically.