Constitutive Model For Granular Materials Research Articles

An Elastoplastic Model for Granular Materials Exhibiting Particle Crushing

A practical elastoplastic constitutive model for granular materials is presented. And the model is suitable for description of the material behaviour for a wide range of stresses, including those sufficient to cause particle crushing. With a limited number of model parameters, the model can predict the confining-pressure dependent stress-strain relation and shear strength of granular materials in three-dimensional stresses, especially of variation of shear strength and dilatancy characteristics due to particle crushing under high confining pressure. The model parameters, which have clear physical meanings, can be determined from the results of isotropic compression test and conventional triaxial compression tests. The model performance is demonstrated for triaxial compression tests of a sand for a wide range of the confining-pressure from 0.2MPa to 8.0MPa.

Microstructure Characterization for Modeling HMA Behaviour using Imaging Technology

ABSTRACT The properties of hot mix asphalt (HMA) highly depend on the microstructure. The ability to experimentally characterize the microstructure is fundamental in describing the macroscopic behavior of HMA. It improves our understanding of the influence of the microstructure distribution on the macroscopic response of the material, which is at the heart of constitutive modeling of granular materials. This paper is an attempt to summarize the recent advances in imaging technology and its applications to the characterization of HMA microstructure including aggregate orientation distribution, aggregate contact, aggregate shape properties, air void distribution, permeability, crack distribution, three-dimensional (3-D) microstructure reconstruction, and microstructure evolution. The microstructure of HMA is linked to the macroscopic behavior of the material within the framework of continuum modeling via microstructure tensors that are incorporated in the continuum modeling formulations. It is envisioned that this link will fill in the gap that has always been present between interpreting laboratory results and the reality of the interior behavior of HMA.

Die compaction of copper powder designed for material parameter identification

This article presents uniaxial compaction experiments of a fine copper powder in a cylindrical die. The compaction process consists of monotonic loading and of loading paths with inserted unloading and reloading cycles. An experimental setup that has been developed for determining the axial and radial stresses during the compaction is described and the calibration of the new device using highly accurate p-finite element simulations of the dies response to internal pressure is shown. The experimental results were subsequently used for the identification of the material parameters of a constitutive model for granular materials recently proposed by Bier and Hartmann [A finite strain constitutive model for metal powder compaction using a unique and convex single surface yield function. accepted for publication by European Journal of Mechanics, Series A/Solids 2006.]. The identification of the elasticity parameters was treated with special attention.

Critical state plasticity. Part VI: Meso-scale finite element simulation of strain localization in discrete granular materials

Development of more accurate mathematical models of discrete granular material behavior requires a fundamental understanding of deformation and strain localization phenomena. This paper utilizes a meso-scale finite element modeling approach to obtain an accurate and thorough capture of deformation and strain localization processes in discrete granular materials such as sands. We employ critical state theory and implement an elastoplastic constitutive model for granular materials, a variant of a model called “Nor-Sand”, allowing for non-associative plastic flow and formulating it in the finite deformation regime. Unlike the previous versions of critical state plasticity models presented in a series of “Cam-Clay” papers, the present model contains an additional state parameter ψ that allows for a deviation or detachment of the yield surface from the critical state line. Depending on the sign of this state parameter, the model can reproduce plastic compaction as well as plastic dilation in either loose or dense granular materials. Through numerical examples we demonstrate how a structured spatial density variation affects the predicted strain localization patterns in dense sand specimens.

A multi-scale approach to granular materials

It is now well established that the micro-structure of granular materials plays a significant role in their overall constitutive behavior. In the past few years, a great deal of theoretical and experimental research has been devoted to this domain, giving rise to constructive micro-mechanical approaches. However, constitutive models for granular materials based on a micro-mechanical approach remain scarce; solving practical engineering problems most often requires using phenomenological models, which often introduce numerous parameters with no physical meaning. This paper derives a “parameter-free” constitutive behavior of granular materials on the macroscopic level from a microscopic-scale description, taking a statistical description of the fabrics into account. In this approach, the location of each particle is ignored, but the probability of contact in a given direction is investigated. Modelling the creation or the loss of contacts in given directions makes it possible to analyze how the probability density of having contacts in these directions evolves, and thus a directional constitutive model can be developed. Highlighting micro-structural processes responsible for the transmission of local contact forces, the existence of two phases in the granular assembly was accounted for, giving rise to a partition of the stress tensor. The capability of the model is assessed from the simulation of standard tests, leading to satisfying preliminary qualitative results.

A constitutive model for granular materials with grain crushing and its application to a pyroclastic soil

AbstractA constitutive model for granular materials is developed within the framework of strain–hardening elastoplasticity, aiming at describing some of the macroscopic effects of the degradation processes associated with grain crushing. The central assumption of the paper is that, upon loading, the frictional properties of the material are modified as a consequence of the changes in grain size distribution.The effects of these irreversible microscopic processes are described macroscopically as accumulated plastic strain. Plastic strain drives the evolution of internal variables which model phenomenologically the changes of mechanical properties induced by grain crushing by controlling the geometry of the yield locus and the direction of plastic flow.An application of the model to Pozzolana Nera is presented. The stress–dilatancy relationship observed for this material is used as a guidance for the formulation of hardening laws. One of the salient features of the proposed model is its capability of reproducing the stress–dilatancy behaviour observed in Pozzolana Nera, for which the minimum value of dilatancy always follows the maximum stress ratio experienced by the material. Copyright © 2002 John Wiley & Sons, Ltd.

Micromechanical modelling of monotonic drained and undrained shear behaviour of granular media using three‐dimensional DEM

AbstractIn this paper, numerical simulation results of isotropic compression and triaxial static shear tests under drained and undrained stress paths on polydisperse assembly of loose and dense spheres are presented. An examination of the micromechanical behaviour of loose and dense assemblies under drained and undrained conditions, considering the particulate nature of granular materials, has been carried out to explain micromechanically the granular material behaviour at the grain scale level. The numerical simulations have been carried out using a discrete element model (DEM) which considers a 1000 sphere particle polydisperse assembly with periodic space representing an infinite three‐dimensional space. In this paper, we present how DEM simulations can contribute to developments in constitutive modelling of granular materials through micromechanical approach using information on microstructure evolution. A series of numerical tests are performed using DEM on 3‐D assemblages of spheres to study the evolution of the internal variables such as average co‐ordination number and induced anisotropy during deformation along with the macroscopic behaviour of the assemblage in drained and undrained shear tests. In a qualitative sense, the macroscopic stress–strain results and stress path evolution in these simulations using 3‐D assemblies demonstrate that DEM simulations are capable of reproducing realistic compression and shear behaviour of granular materials. Copyright © 2002 John Wiley & Sons, Ltd.

Constitutive Modelling of Geomaterials

Constitutive Modelling of Geomaterials

Constitutive models for granular materials including quasi-static frictional behaviour: Toward a thermodynamic theory of plasticity

Note: Sols Reference LMS-ARTICLE-1999-005View record in Web of Science Record created on 2006-11-09, modified on 2016-08-08

BEYOND FAILURE IN GRANULAR MATERIALS

Recent investigations on the hypoplastic constitutive model for granular materials show that the failure surface can be surpassed by some stress paths. This is contradictory to the conventional definition of failure surface in plasticity, according to which the stress is allowed to move on the failure surface but never across it. In the present paper, the interrelations among the different constitutive models are discussed with special reference to failure and stability. For the hypoplastic constitutive equation, the accessible stress states and the stable stress states are found to be enclosed by a bound surface and a stability surface in the stress space, respectively. Theoretical findings about the bound surface and the stability surface are verified qualitatively by presenting results of triaxial tests on dry sand. © 1997 by John Wiley & Sons, Ltd.

Concept of effective strain in constitutive modeling of granular materials. Technical note : Iai, S Soils FoundV33, N2, June 1993, P171–180

Concept of effective strain in constitutive modeling of granular materials. Technical note : Iai, S Soils FoundV33, N2, June 1993, P171–180

Fabric related probabilistic model for granular materials : Jahedi, J Proc 6th ASCE Speciality Conference on Probabilistic Mechanics and Structural and Geotechnical Reliability, Denver, 8–10 July 1992P475–478. Publ New York: ASCE, 1992

A new anisotropic noncoaxial incremental constitutive model for granular materials (Jahedi et al., 1990) was developed, in which a Fabric reconstruction factor 'β + ', was incorporated. In this paper, the Fabric factor 'β + ' is further enhanced in order to offer more flexibility to the model, and to better fit the statistical data and related probability density functions.

Into The Hourglass: Reflections on the Forces Acting on a Granular Material

The storage and flow of granular materials is common to many industries. For example, coal is stored in large bunkers at electric generating plants, to be used later in fueling the plant furnaces. A very different kind of material storage occurs at cereal manufacturing facilities; here the corn flakes are baked, stored in large bins temporarily, and then packaged. A natural question to ask is How strong do the storage bins have to be? Engineers would like to be sure that the coal bunkers do not collapse under the weight of the coal (as sometimes happens, often with loss of life). At the same time, the cereal manufacturer wants to be sure that he doesn't crush the corn flakes into tiny bits before packaging. How does one model the forces acting in a granular medium? What kind of pressures build up inside a vessel storing granular materials? These are the questions we address in this article. It would be natural to examine each particle individually, resolve all the forces acting on each particle, and then solve Newton's law Force = Mass Acceleration for each particle. Needless to say, with perhaps 108 or more particles in a bin, such a procedure would be prohibitively difficult to carry out. We make a simplification here. In trying to determine forces inside the bin, we forget the particle nature of the material and treat it as a continuum. Once we make this simplification, we are faced with the issue of describing the forces in a continuum, in particular of describing the constitutive behavior of the material [that is, explaining the stressstrain relationship which models the continuum]. We examine a simple constitutive model later on. Before looking at the pressures inside a bin of granular material, it would be useful to recall the analogous question for fluids. How much pressure is there at the bottom of a tall water tower? A look at your basic physics textbook will tell you that the pressure at a point at the bottom of a water tower equals the weight of all the water above that point. The density of water is 1 gram/cm3; you should calculate the pressure at the base of a water tower comprised of a cylindrical tower, perhaps 20 meters in diameter and 30 meters high, with a spherical top of perhaps 20 meters radius. In order to estimate the pressure inside a bin of granular material, such as illustrated in FIGURE 2, we need to introduce the concept of stress; this is the subject of the next section. We then introduce a generalization of sliding friction laws as a constitutive model for granular material. Finally we look at the forces inside a cylindrical bin and a converging hopper. In the sections to follow, we restrict attention to two dimensions; an analysis can be carried out in three dimensions, but the 2-D case is a little easier to work out.

Microphysical constitutive model for granular materials: II. Incorporating damage into the effective elastic moduli : Margolin, L G; Trent, B C Proc 33rd US Symposium on Rock Mechanics, Santa Fe, 3–5 June 1992P671–679. Publ Rotterdam: A A Balkema, 1992

Microphysical constitutive model for granular materials: II. Incorporating damage into the effective elastic moduli : Margolin, L G; Trent, B C Proc 33rd US Symposium on Rock Mechanics, Santa Fe, 3–5 June 1992P671–679. Publ Rotterdam: A A Balkema, 1992

Concept of Effective Strain in Constitutive Modeling of Granular Materials

ABSTRACT The concept of effective strain is proposed as a reciprocal concept of the effective stress. The effective strain is defined as strain minus volumetric strain due to dilatancy. Though the overall volume of granular material remains the same during shearing involving no volumetric strain increment, the volume of void can change due to the rearrangement of the particles. On this reflection, it is postulated that the relative displacements of the centers of the particles which are in contact in granular materials are, in the average, consistent with the effective strain. This leads to the concept of the effective strain energy which is defined with respect to the effective strain. Though a plasticity model with micromechanical background (Iai, 1993b) is not exactly expressed in the associated form, its flow rule becomes associated if it is defined in the effective strain space. Drucker’s stability postulates defined with respect to the effective strain energy are also seen to be satisfied by the present model. Thus, introduction of the concept of the effective strain may be one of the efficient approaches to solve the controversy over the non-associated flow rule and Drucker’s postulates in the constitutive modeling of granular materials.

Micromechanics Modeling for Stress‐Strain Behavior of Granular Soils. II: Evaluation

A micromechanics-based constitutive model for granular material is evaluated. The predicted stress-strain behavior for idealized material is compared with that observed from experiments for sands. Under small strain conditions, the model capability is evaluated for predicting initial moduli, secant moduli, and damping ratio when the material is subjected to low-amplitude loading. Under large strain conditions, the model capability is evaluated for predicting the stress-strain strength behavior when the material is subjected to various stress paths. In the predictions, three material parameters are used to represent the stiffness and friction of the interparticle contact. Although the predictions are made for idealized spherical particles, the predicted behaviors are found to be remarkably similar to that observed for sands in experiments. The potential capability of the proposed constitutive theory is illustrated, and the model performance is discussed on various aspects of granular material behavior, such as stress-induced anisotropy, path dependence, plastic flow, dilatancy, and noncoaxial behavior under rotation of principal stress.

Verification of a constitutive model for granular materials : Saxena, S K; Reddy, R K; Sengupta, A Proc International Workshop on Constitutive Equations for Granular Non-Cohesive Soils, Cleveland, 22–24 July 1987P629–645. Publ Rotterdam: A A Balkema, 1989

Verification of a constitutive model for granular materials : Saxena, S K; Reddy, R K; Sengupta, A Proc International Workshop on Constitutive Equations for Granular Non-Cohesive Soils, Cleveland, 22–24 July 1987P629–645. Publ Rotterdam: A A Balkema, 1989

A Fabric-Related Constitutive Model for Granular Materials

A new anisotropic constitutive model for granular materials is developed. This model exhibits the noncoaxiality of the principal axes of stress and strain rate as a natural consequence of a kinematic hypothesis. A fabric reconstruction parameter ℬ plays an important role in this model. The pressure sensitivity parameter, μ, and two different hardening parameters often employed in modeling granular materials, come out to be expressible in terms of this fabric reconstruction factor. The stress criterion in this model is not friction based, and therefore the rolling of granules can be taken into account through the fabric paramater. Numerical results are presented on the basis of a phenomenological trial function for ℬ.

Constitutive model for granular materials based on two plasticity mechanisms : Cambou, B; Jafari, K Proc International Workshop on Constitutive Equations for Granular Non-Cohesive Soils, Cleveland, 22–24 July 1987P149–167. Publ Rotterdam: A A Balkema, 1989

Constitutive model for granular materials based on two plasticity mechanisms : Cambou, B; Jafari, K Proc International Workshop on Constitutive Equations for Granular Non-Cohesive Soils, Cleveland, 22–24 July 1987P149–167. Publ Rotterdam: A A Balkema, 1989

Soil models as a basis for modelling the behaviour of geophysical materials

The aim of this paper is to show that the conceptual structure of constitutive models for granular materials, such as soils, may be taken as a starting point to model the mechanical behaviour of materials of geophysical interest. Clearly some modifications are necessary to cope with the range of pressures, time and temperature which are relevant in geophysics.