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Leo Rothenburg - One of the best experts on this subject based on the ideXlab platform.
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a strain displacement fabric relationship for Granular Materials
International Journal of Solids and Structures, 2019Co-Authors: Nicolaas P Kruyt, Leo RothenburgAbstract:Abstract In this micromechanical study of the behaviour of Granular Materials, relationships are investigated between deformation at the continuum macro-scale and at the micro-scale of interparticle contacts. Special attention is paid to the role of the microstructure, or fabric, as it is well known to have a strong influence on the behaviour of Granular Materials. Two-dimensional Discrete Element Method simulations of isobaric tests have been used to formulate truncated Fourier series representations for suitably-averaged relative displacement increment vectors at interparticle contacts and of parameters that describe the fabric. Based on a micromechanical expression for the average strain tensor that is valid in the two-dimensional case considered here and on these Fourier series representations, a Strain–Displacement–Fabric relationship has been derived that links the macro-scale dilatancy rate to the micro-scale relative displacements and fabric. Results of the Discrete Element Method simulations, using samples with different densities, have been employed to verify the accuracy of the proposed relationship for the dilatancy rate.
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a micromechanical study of dilatancy of Granular Materials
Journal of The Mechanics and Physics of Solids, 2016Co-Authors: Nicolaas P Kruyt, Leo RothenburgAbstract:Abstract In micromechanics of Granular Materials, relationships are investigated between micro-scale characteristics of particles and contacts and macro-scale, continuum characteristics. Dilatancy is an important property of Granular Materials, defined as volume changes (dilative or compressive) induced by shear deformation. To obtain detailed information at the micro-scale, two-dimensional Discrete Element Method simulations of isobaric tests with disk-shaped particles have been performed. The required information includes the fabric tensor which characterizes statistical properties of the contact network. The dependence of the dilatancy rate on the shear strength and the fabric tensor has been investigated, based on the results of the simulations employing a dense and a loose initial system. The dilatancy rate depends in a complex, non-unique way on the shear strength, while the dependence on the fabric tensor is more amenable to analytical description. Two micromechanical mechanisms of dilatancy have been identified: (i) dilatancy due to deformation of loops that are determined by the interparticle contact network and (ii) dilatancy due to topological changes in the interparticle contact network that correspond to the creation or disruption of contacts. For the first mechanism the anisotropy in the contact network is the primary parameter, while for the second mechanism the average number of contacts per particle is the primary parameter. A fabric-based micromechanical relation for the dilatancy rate has been formulated that describes these identified mechanisms. Parameters present in this relation are determined by fitting this relation to the results of the Discrete Element Method simulations, using combined data for the dense and the loose initial system. Employing these fitted coefficients, good agreement is obtained between the results of the simulations and the predictions of the micromechanical dilatancy relation.
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micromechanical definition of an entropy for quasi static deformation of Granular Materials
Journal of The Mechanics and Physics of Solids, 2009Co-Authors: Leo Rothenburg, Nicolaas P KruytAbstract:A micromechanical theory is formulated for quasi-static deformation of Granular Materials, which is based on information theory. A reasoning is presented that leads to the definition of an information entropy that is appropriate for quasi-static deformation of Granular Materials. This definition is based on the hypothesis that relative displacements at contacts with similar orientations are independent realisations of a random variable. This hypothesis is made plausible based on the results of Discrete Element simulations. The developed theory is then used to predict the elastic behaviour of Granular Materials in terms of micromechanical quantities. The case considered is that of two-dimensional assemblies consisting of non-rotating particles with an elastic contact constitutive relation. Applications of this case are the initial elastic (small-strain) deformation of Granular Materials. Theoretical results for the elastic moduli, relative displacements, energy distribution and probability density functions are compared with results obtained from the Discrete Element simulations for isotropic assemblies with various average numbers of contacts per particle and various ratios of tangential to normal contact stiffness. This comparison shows that the developed information theory is valid for loose systems, while a theory based on the uniform-strain assumption is appropriate for dense systems.
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maximum entropy methods in the mechanics of quasi static deformation of Granular Materials
Materials: Processing Characterization and Modeling of Novel Nano-Engineered and Surface Engineered Materials, 2002Co-Authors: Nicolaas P Kruyt, Leo RothenburgAbstract:In statistical physics of dilute gases maximum entropy methods are widely used for theoretical predictions of macroscopic quantities in terms of microscopic quantities. In this study an analogous approach to the mechanics of quasi-static deformation of Granular Materials is proposed. The reasoning is presented that leads to the definition of an entropy that is appropriate to quasi-static deformation of Granular Materials. This entropy is formulated in terms of contact quantities, since contacts constitute the relevant microscopic level for Granular Materials that consist of semirigid particles. The proposed maximum entropy approach is then applied to two cases. The first case deals with the probability density functions of contact forces in a two-dimensional assembly with frictional contacts under prescribed hydrostatic stress. The second case deals with the elastic behaviour of two-dimensional assemblies of non-rotating particles with bonded contacts. For both cases the probability density functions of contact forces are determined from the proposed maximum entropy method, under the constraints appropriate to the case. These constraints form the macroscopic information available about the system. With the probability density functions for contact forces thus determined, theoretical predictions of macroscopic quantities can be made. These theoretical predictions are then compared with results obtained from two-dimensional Discrete Element simulations and from experiments.Copyright © 2002 by ASME
Nicolaas P Kruyt - One of the best experts on this subject based on the ideXlab platform.
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a strain displacement fabric relationship for Granular Materials
International Journal of Solids and Structures, 2019Co-Authors: Nicolaas P Kruyt, Leo RothenburgAbstract:Abstract In this micromechanical study of the behaviour of Granular Materials, relationships are investigated between deformation at the continuum macro-scale and at the micro-scale of interparticle contacts. Special attention is paid to the role of the microstructure, or fabric, as it is well known to have a strong influence on the behaviour of Granular Materials. Two-dimensional Discrete Element Method simulations of isobaric tests have been used to formulate truncated Fourier series representations for suitably-averaged relative displacement increment vectors at interparticle contacts and of parameters that describe the fabric. Based on a micromechanical expression for the average strain tensor that is valid in the two-dimensional case considered here and on these Fourier series representations, a Strain–Displacement–Fabric relationship has been derived that links the macro-scale dilatancy rate to the micro-scale relative displacements and fabric. Results of the Discrete Element Method simulations, using samples with different densities, have been employed to verify the accuracy of the proposed relationship for the dilatancy rate.
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a micromechanical study of dilatancy of Granular Materials
Journal of The Mechanics and Physics of Solids, 2016Co-Authors: Nicolaas P Kruyt, Leo RothenburgAbstract:Abstract In micromechanics of Granular Materials, relationships are investigated between micro-scale characteristics of particles and contacts and macro-scale, continuum characteristics. Dilatancy is an important property of Granular Materials, defined as volume changes (dilative or compressive) induced by shear deformation. To obtain detailed information at the micro-scale, two-dimensional Discrete Element Method simulations of isobaric tests with disk-shaped particles have been performed. The required information includes the fabric tensor which characterizes statistical properties of the contact network. The dependence of the dilatancy rate on the shear strength and the fabric tensor has been investigated, based on the results of the simulations employing a dense and a loose initial system. The dilatancy rate depends in a complex, non-unique way on the shear strength, while the dependence on the fabric tensor is more amenable to analytical description. Two micromechanical mechanisms of dilatancy have been identified: (i) dilatancy due to deformation of loops that are determined by the interparticle contact network and (ii) dilatancy due to topological changes in the interparticle contact network that correspond to the creation or disruption of contacts. For the first mechanism the anisotropy in the contact network is the primary parameter, while for the second mechanism the average number of contacts per particle is the primary parameter. A fabric-based micromechanical relation for the dilatancy rate has been formulated that describes these identified mechanisms. Parameters present in this relation are determined by fitting this relation to the results of the Discrete Element Method simulations, using combined data for the dense and the loose initial system. Employing these fitted coefficients, good agreement is obtained between the results of the simulations and the predictions of the micromechanical dilatancy relation.
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micromechanical definition of an entropy for quasi static deformation of Granular Materials
Journal of The Mechanics and Physics of Solids, 2009Co-Authors: Leo Rothenburg, Nicolaas P KruytAbstract:A micromechanical theory is formulated for quasi-static deformation of Granular Materials, which is based on information theory. A reasoning is presented that leads to the definition of an information entropy that is appropriate for quasi-static deformation of Granular Materials. This definition is based on the hypothesis that relative displacements at contacts with similar orientations are independent realisations of a random variable. This hypothesis is made plausible based on the results of Discrete Element simulations. The developed theory is then used to predict the elastic behaviour of Granular Materials in terms of micromechanical quantities. The case considered is that of two-dimensional assemblies consisting of non-rotating particles with an elastic contact constitutive relation. Applications of this case are the initial elastic (small-strain) deformation of Granular Materials. Theoretical results for the elastic moduli, relative displacements, energy distribution and probability density functions are compared with results obtained from the Discrete Element simulations for isotropic assemblies with various average numbers of contacts per particle and various ratios of tangential to normal contact stiffness. This comparison shows that the developed information theory is valid for loose systems, while a theory based on the uniform-strain assumption is appropriate for dense systems.
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maximum entropy methods in the mechanics of quasi static deformation of Granular Materials
Materials: Processing Characterization and Modeling of Novel Nano-Engineered and Surface Engineered Materials, 2002Co-Authors: Nicolaas P Kruyt, Leo RothenburgAbstract:In statistical physics of dilute gases maximum entropy methods are widely used for theoretical predictions of macroscopic quantities in terms of microscopic quantities. In this study an analogous approach to the mechanics of quasi-static deformation of Granular Materials is proposed. The reasoning is presented that leads to the definition of an entropy that is appropriate to quasi-static deformation of Granular Materials. This entropy is formulated in terms of contact quantities, since contacts constitute the relevant microscopic level for Granular Materials that consist of semirigid particles. The proposed maximum entropy approach is then applied to two cases. The first case deals with the probability density functions of contact forces in a two-dimensional assembly with frictional contacts under prescribed hydrostatic stress. The second case deals with the elastic behaviour of two-dimensional assemblies of non-rotating particles with bonded contacts. For both cases the probability density functions of contact forces are determined from the proposed maximum entropy method, under the constraints appropriate to the case. These constraints form the macroscopic information available about the system. With the probability density functions for contact forces thus determined, theoretical predictions of macroscopic quantities can be made. These theoretical predictions are then compared with results obtained from two-dimensional Discrete Element simulations and from experiments.Copyright © 2002 by ASME
Farhang Radjai - One of the best experts on this subject based on the ideXlab platform.
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Evolution of Granular Materials under isochoric cyclic simple shearing
Physical Review E, 2021Co-Authors: Ming Yang, Mahdi Taiebat, Patrick Mutabaruka, Farhang RadjaiAbstract:By means of 3D particle dynamics simulations, we analyze the microstructure of Granular Materials subjected to isochoric (constant volume) cyclic shearing, which drives the system towards a liquefaction state characterized by loops of jamming-unjamming transition with periodic loss of strength and irreversible accumulation of shear strain. We first show that the macroscopic response obtained by these simulations agrees well with the most salient features of the well-known cyclic behavior of Granular Materials both before and after liquefaction. Then we investigate the evolution of particle connectivity, force transmission, and anisotropies of contact and force networks. The onset of liquefaction is marked by partial collapse of the force-bearing network with rapid drop of the coordination number and nonrattler fraction of particles, and significant broadening of the contact force probability density function, which begins in the preliquefaction period. We find that the jamming transition in each cycle occurs for a critical value of the coordination number that can be interpreted as the percolation threshold of the contact network and appears to be independent of the initial mean stress, void ratio, and cyclic shear amplitude. We show that upon unjamming in each cycle an isotropic loss of contacts occurs and is followed by the development of high contact anisotropy and a large proportion of particles with only two or three contacts. The higher mobility of the particles also involves a lower degree of frustration of particle rotations and thus lower friction mobilization and tangential force anisotropy. These findings are relevant to both undrained cyclic deformations of saturated soils and rheology of dense non-Brownian suspensions where volume change is coupled with pore liquid drainage conditions.
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discrete element modeling of Granular Materials
2011Co-Authors: Farhang Radjai, Frederic DuboisAbstract:This book brings together in a single volume various methods and skills for particle-scale or discrete-element numerical simulation of Granular media. It covers a broad range of topics from basic concepts and methods towards more advanced aspects and technical details applicable to the current research on Granular Materials. Discrete-element simulations of Granular Materials are based on four basic models (molecular dynamics, contact dynamics, quasi-static and event driven) dealing with frictional contact interactions and integration schemes for the equations of dynamics. These models are presented in the first chapters of the book, followed by various methods for sample preparation and monitoring of boundary conditions, as well as dimensionless control parameters. Granular Materials encountered in real life involve a variety of compositions (particle shapes and size distributions) and interactions (cohesive, hydrodynamic, thermal) that have been extensively covered by several chapters. The book ends with two applications in the field of geo-Materials.
Marte Gutierrez - One of the best experts on this subject based on the ideXlab platform.
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comprehensive study of the effects of rolling resistance on the stress strain and strain localization behavior of Granular Materials
Granular Matter, 2010Co-Authors: Abdalsalam Mohamed, Marte GutierrezAbstract:This paper presents the results of a comprehensive study of the effects of rolling resistance on the stress–strain and strain localization behavior of Granular Materials using the discrete element method. The study used the Particle Flow Code (PFC) to simulate biaxial compression tests in Granular Materials. To study the effects of rolling resistance, a user-defined rolling resistance model was implemented in PFC. A series of parametric studies was performed to investigate the effects of different levels of rolling resistance on the stress–strain response and the emergence and development of shear bands in Granular Materials. The PFC models were also tested under a range of macro-mechanical parameters and boundary conditions. It is shown that rolling resistance affects the elastic, shear strength and dilation response of Granular Materials, and new relationships between rolling resistance and macroscopic elasticity, shear strength and dilation parameters are presented. It is also concluded that the rolling resistance has significant effects on the orientation, thickness and the timing of the occurrence of shear bands. The results reinforce prior conclusions by Oda et al. (Mech Mater 1:269–283, 1982) on the importance of rolling resistance in promoting shear band formation in Granular Materials. It is shown that increased rolling resistance results in the development of columns of particles in Granular Materials during strain hardening process. The buckling of these columns of particles in narrow zones then leads to the development of shear bands. High gradients of particle rotation and large voids are produced within the shear band as a result of the buckling of the columns.
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non coaxiality and energy dissipation in Granular Materials
Soils and Foundations, 2000Co-Authors: Marte Gutierrez, Kenji IshiharaAbstract:ABSTRACT The paper presents a theoretical and experimental study of the effects of non-coaxiality or non-coincidence of the principal stress and the principal plastic strain increment directions on the behaviour of Granular Materials. Experimental results from hollow cylindrical tests on sand involving principal stress rotation which support previously published results on non-coaxiality are presented. These results imply that constitutive relations cannot be sufficiently formulated in the principal stress space unless the deviations between the principal stress and plastic strain increment directions are taken into consideration. It is shown that plasticity formulations with plastic potentials that are scalar functions of the stress invariants alone implicitly assume coaxiality and cannot be used for loading involving principal stress rotation. The paper presents a comprehensive analysis of the effects of non-coaxiality on the energy dissipation of sand. The paper shows that energy dissipation calculated from the principal stresses and the principal plastic strain increments or from the stress and plastic strain increment invariants, would be erroneous and would over-estimate the amount of dissipated energy during loading in the case of non-coaxial flow. A non-coaxiality factor is introduced in order to account for the effects of non-coaxiality on the energy dissipation equation and in a stress-dilatancy relation for Granular Materials. Explicit expressions of the non-coaxiality factor for two-and three-dimensional loading conditions are given at the end of the paper. Experimental results are presented to show the validity of the proposed energy dissipation and stress-dilatancy equations.
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non coaxiality and energy dissipation in Granular Materials
Soils and Foundations, 2000Co-Authors: Marte Gutierrez, Kenji IshiharaAbstract:ABSTRACT The paper presents a theoretical and experimental study of the effects of non-coaxiality or non-coincidence of the principal stress and the principal plastic strain increment directions on the behaviour of Granular Materials. Experimental results from hollow cylindrical tests on sand involving principal stress rotation which support previously published results on non-coaxiality are presented. These results imply that constitutive relations cannot be sufficiently formulated in the principal stress space unless the deviations between the principal stress and plastic strain increment directions are taken into consideration. It is shown that plasticity formulations with plastic potentials that are scalar functions of the stress invariants alone implicitly assume coaxiality and cannot be used for loading involving principal stress rotation. The paper presents a comprehensive analysis of the effects of non-coaxiality on the energy dissipation of sand. The paper shows that energy dissipation calculated from the principal stresses and the principal plastic strain increments or from the stress and plastic strain increment invariants, would be erroneous and would over-estimate the amount of dissipated energy during loading in the case of non-coaxial flow. A non-coaxiality factor is introduced in order to account for the effects of non-coaxiality on the energy dissipation equation and in a stress-dilatancy relation for Granular Materials. Explicit expressions of the non-coaxiality factor for two-and three-dimensional loading conditions are given at the end of the paper. Experimental results are presented to show the validity of the proposed energy dissipation and stress-dilatancy equations.
Jose E Andrade - One of the best experts on this subject based on the ideXlab platform.
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extracting inter particle forces in opaque Granular Materials beyond photoelasticity
Journal of The Mechanics and Physics of Solids, 2014Co-Authors: Ryan C Hurley, Eloise Marteau, Guruswami Ravichandran, Jose E AndradeAbstract:This paper presents the first example of inter-particle force inference in real Granular Materials using an improved version of the methodology known as the Granular Element Method (GEM). GEM combines experimental imaging techniques with equations governing particle behavior to allow force inference in cohesionless Materials with grains of arbitrary shape, texture, and opacity. This novel capability serves as a useful tool for experimentally characterizing Granular Materials, and provides a new means for investigating force networks. In addition to an experimental example, this paper presents a precise mathematical formulation of the inverse problem involving the governing equations and illustrates solution strategies.
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critical state plasticity part vi meso scale finite element simulation of strain localization in discrete Granular Materials
Computer Methods in Applied Mechanics and Engineering, 2006Co-Authors: Ronaldo I Borja, Jose E AndradeAbstract: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.
