A Micromechanical Description of Granular Material Behavior

Christoffersen, J.; Mehrabadi, Morteza M.; Nemat‐Nasser, Sia

doi:10.1115/1.3157619

Cited by 768 publications

(297 citation statements)

References 14 publications

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“…Conversely, (F e ) ' defines the stress-free, unloaded configuration of the material point X. The product decomposition (3.9) then represents the overall kinematics of deformation of the macroscopic material point X and may be interpreted as the volume average of the responses derived from the aforementioned micromechanical processes [26][27][28].…”

Section: Reduced Dissipation Inequalitymentioning

confidence: 99%

A mathematical framework for finite strain elastoplastic consolidation Part 1: Balance laws, variational formulation, and linearization

Borja

Alarcón

1995

Computer Methods in Applied Mechanics and Engineering

111

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A mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented. Strong and weak forms of the boundary-value problem are derived using both the material and spatial descriptions. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. Balance laws are written for the soil-water mixture following the motion of the soil matrix alone. It is shown that the motion of the fluid phase only affects the Jacobian of the solid phase motion, and therefore can be characterized completely by the motion of the soil matrix. Furthermore, it is shown from energy balance consideration that the effective, or intergranular, stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil-water mixture. Finally, it is shown that the mathematical model is amenable to consistent linearization, and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method.

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Section: Reduced Dissipation Inequalitymentioning

confidence: 99%

A mathematical framework for finite strain elastoplastic consolidation Part 1: Balance laws, variational formulation, and linearization

Borja

Alarcón

1995

Computer Methods in Applied Mechanics and Engineering

111

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“…Finally, the finite element equation for balance of linear momentum and angular momentum in domain B is written in a compact form as: (24) where T = [t 1t2m3 ] T and F = [ρg 1 ρg 2 ρ(J · c) 3 ] T are generalized traction and body force vectors, respectively. The non-linear system of equations is solved by a modified implicitexplicit scheme which is originally proposed in Hughes et al [27] and Prevost [28] to solve single-scale hydro-mechanical transient problems.…”

Section: Methodsmentioning

confidence: 99%

“…where f c is the contact force at the grain contact x c and l c is the branch vector that connects the centroids of two grains forming the contact (x a and x b ) [24,25]. V RVE is the volume of the RVE and N c is the total number of particles in the RVE.…”

Section: Micropolar Homogenization Procedures On Dem Unit Cellsmentioning

confidence: 99%

A Semi-Implicit Microplar Discrete-to-Continuum Method for Granular Materials

Wang¹,

Sun²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. A micropolar discrete-continuum coupling model is proposed to link the collectively particulate mechanical simulations at high-order representative elementary volume to field-scale boundary value problems. By incorporating high-order kinematics to the homogenization procedure, contact moment and force exerted on grain contacts are homogenized into a non-symmetric Cauchy stress and higher-order couple stress. These stress measures in return become the constitutive updates for the macroscopic finite element model for micropolar continua. Unlike the non-lcoal weighted averaging models in which the intrinsic length scale must be a prior knowledge to compute the nonlocal damage or strain measures, the proposed model introduces the physical length scale directly through the higher-order kinematics. As a result, there is no need to tune or adjust the intrinsic length scale. Furthermore, since constitutive updates are provided directly from micro-structures, there is also no need to calibrate any high-order material parameters that are difficult to infer from experiments. These salient features are demonstrated by numerical examples. The classical result from Mindlin is used as a benchmark to verify the proposed model.

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“…in which σ i j stands for the average stress over volume V [4,7,12,26,28,39,43]. To be consistent with the sign convention in soil mechanics, a contact vector is defined here as the vector pointing from the contact point to the particle centre.…”

Section: The Derivation Of the Sff Relationshipmentioning

confidence: 99%

Fabric, force and strength anisotropies in granular materials: a micromechanical insight

2014

Acta Mech

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In micromechanics, the stress-force-fabric (SFF) relationship is referred to as an analytical expression linking the stress state of a granular material with microparameters on contact forces and material fabric. This paper employs the SFF relationship and discrete element modelling to investigate the micromechanics of fabric, force and strength anisotropies in two-dimensional granular materials. The development of the SFF relationship is briefly summarized while more attention is placed on the strength anisotropy and deformation non-coaxiality. Due to the presence of initial anisotropy, a granular material demonstrates a different behaviour when the loading direction relative to the direction of the material fabric varies. Specimens may go through various paths to reach the same critical state at which the fabric and force anisotropies are coaxial with the loading direction. The critical state of anisotropic granular material has been found to be independent of the initial fabric. The fabric anisotropy and the force anisotropy approach their critical magnitudes at the critical state. The particle-scale data obtained from discrete element simulations of anisotropic materials show that in monotonic loading, the principal force direction quickly becomes coaxial with the loading direction (i.e. the strain increment direction as applied). However, material fabric directions differ from the loading direction and they only tend to be coaxial at a very large shear strain. The degree of force anisotropy is in general larger than that of fabric anisotropy. In comparison with the limited variation in the degree of force anisotropy with varying loading directions, the fabric anisotropy adapts in a much slower pace and demonstrates wider disparity in the evolution in the magnitude of fabric anisotropy. The difference in the fabric anisotropy evolution has a more significant contribution to strength anisotropy than that of force anisotropy. There are two key parameters that control the degree of deformation non-coaxiality in granular materials subjected to monotonic shearing: the ratio between the degrees of fabric anisotropy and that of force anisotropy and the angle between the principal fabric direction and the applied loading direction.

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A Micromechanical Description of Granular Material Behavior

Cited by 768 publications

References 14 publications

A mathematical framework for finite strain elastoplastic consolidation Part 1: Balance laws, variational formulation, and linearization

A mathematical framework for finite strain elastoplastic consolidation Part 1: Balance laws, variational formulation, and linearization

A Semi-Implicit Microplar Discrete-to-Continuum Method for Granular Materials

Fabric, force and strength anisotropies in granular materials: a micromechanical insight

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