On virtual work and stress in granular media

Chang, Ching S.; Kuhn, Matthew R.

doi:10.1016/j.ijsolstr.2004.11.011

Cited by 51 publications

(47 citation statements)

References 11 publications

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“…The static relation between a discrete particle assembly and its effective Cosserat continuum model has been discussed by some authors [10,13,14,[35][36][37]. The definition of effective stress tensor has arrived at a uniform expression identical with Eq.…”

Section: The Macroscopic Stress and Couple Stressmentioning

confidence: 99%

“…This is consistent with the basic assumptions of the average-field theory. The representative work of this type includes the contribution by Kruyt [37] and Chang and Kuhn [14]. Kruyt gives definition and derivation based on the scale separation assumption and moments of equilibrium equations of the discrete particle assembly.…”

Section: The Macroscopic Stress and Couple Stressmentioning

confidence: 99%

“…According to the derivation in paper [37], l ij can be further expressed in terms of the contact quantities over the RVE domain as below À Á h i , is one of the essential results from paper [14], which insures that a shifting of the coordinate system will not affect the expression of the effective couple stress tensor. It should be again stressed that the derivation of Eq.…”

Section: The Macroscopic Stress and Couple Stressmentioning

confidence: 99%

“…The nature of granular medium is that each discrete particle possesses rotational degrees of freedom in addition to translational degrees of freedom in the kinematics and is capable of bearing and transmitting couples in addition to forces from one particle to the other in contact in the kinetics [10,11]. Thus, the RVE, considered as a discrete particle assembly characterizing the local microstructure, should be modeled as an equivalent Cosserat continuum [12][13][14][15] assumed at both microscopic and macroscopic scales in the homogenization procedures. Cosserat continuum model has been successfully applied to the simulation of phenomena with size effect, which is essentially a multi-scale phenomenon and stems from the influence of the microscopic structures on the macroscopic behavior [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…On the one hand, the expression of the macroscopic average couple stress tensor in terms of microscopic stresses and/or couple stresses is not unique in the average-field theory of Cosserat continuum [10,14,[21][22][23]. There are mainly two kinds of expression used in the literature, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Micro–macro homogenization of granular materials based on the average-field theory of Cosserat continuum

Liu

et al. 2014

Advanced Powder Technology

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Effective couple stress tensor Micromechanically based constitutive models a b s t r a c t This paper performs further study on the micro-macro homogenization approach of granular materials (Li et al., 2010) based on the advancement of Hill's lemma for Cosserat continuum (Liu, 2013). Firstly, the average couple stress tensor, expressed as the volume integration of quantities over the representative volume element (RVE) in the average-field theory of Cosserat continuum, is further deduced and expressed in terms of discrete quantities on the discrete particle assembly RVE of granular materials. The expression is also discussed and compared with other typical definitions of the effective couple stress tensor for granular materials in the literature. Then, rate forms of micromechanically based constitutive models consistent with different types of RVE boundary conditions are derived and discussed. Since the presented micro-macro homogenization approach is used, not only the micro-macro energy equivalence is satisfied, but also the microstructure and its evolution can be taken into account in the constitutive formulation with no need of specifying macroscopic phenomenological constitutive model.

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Section: The Macroscopic Stress and Couple Stressmentioning

confidence: 99%

Section: The Macroscopic Stress and Couple Stressmentioning

confidence: 99%

Section: The Macroscopic Stress and Couple Stressmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Micro–macro homogenization of granular materials based on the average-field theory of Cosserat continuum

Liu

et al. 2014

Advanced Powder Technology

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Micropolar effect on the cataclastic flow and brittle‐ductile transition in high‐porosity rocks

2016

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A micromechanical distinct element method (DEM) model is adopted to analyze the grain‐scale mechanism that leads to the brittle‐ductile transition in cohesive‐frictional materials. The cohesive‐frictional materials are idealized as particulate assemblies of circular disks. While the frictional sliding of disks is sensitive to the normal compressive stress exerted on contacts, normal force can be both caused by interpenetration and long‐range cohesive bonding between two particles. Our numerical simulations indicate that the proposed DEM model is able to replicate the gradual shift of porosity change from dilation to compaction and failure pattern from localized failures to cataclastic flow upon rising confining pressure in 2‐D biaxial tests. More importantly, the micropolar effect is examined by tracking couple stress and microcrack initiation to interpret the transition mechanism. Numerical results indicate that the first invariant of the couple stress remains small for specimen sheared under low confining pressure but increases rapidly when subjected to higher confining pressure. The micropolar responses inferred from DEM simulations reveal that microcracking may occur in a more diffuse and stable manner when the first invariant of the macroscopic couple stress are of higher magnitudes.

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A micromorphic elastoplastic model and finite element simulation on failure behaviors of granular materials

Xiu

Chu

2019

Num Anal Meth Geomechanics

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One of the purposes in this study is to develop a modified micromorphic continuum model for granular materials on the basis of a micromechanics approach. A symmetric curvature tensor is proposed in this model, and a symmetric couple stress tensor is derived conjugating the symmetric curvature tensor. In addition, a correct derivation is presented to obtain the symmetric stress tensor conjugated with the symmetric strain tensor. The modified model provides a complete deformation mode for granular materials by considering the decomposition for motions (displacement and rotation) of particles. Consequently, the macroscopic constitutive relationships and constitutive moduli are derived in expressions of the microstructural information. Furthermore, the balance equations and boundary conditions are obtained for the modified micromorphic model. By considering the extended Drucker-Prager yield criterion, the micromorphic elastoplastic model is developed. Another purpose of this study is to derive the finite element formulation for the developed micromorphic elastoplastic model. Based on the ABAQUS user element (UEL) interface, numerical simulations investigated the load-displacement relationship and the strain localization behavior of granular materials and investigated the influence of microscopic parameters in the micromorphic model on these macroscopic mechanical responses. Numerical results illustrate the presented model's capability of simulating the strain-softening and strain localization behaviors, and the capability of considering the influence of microstructural information on the macroscopic mechanical behaviors of granular materials. K E Y W O R D Selasto-plasticity, failure behaviors, granular materials, micromechanics, modified micromorphic model 1 | INTRODUCTION Granular materials are composed of solid particles and voids between particles with a high degree of heterogeneity and complex mechanical behaviors such as multi-scale behaviors, crushability, anisotropy. 1-4 These macroscopic behaviors of granular materials are closely related to the microstructure and the interaction between particles. Chang and Ma 5 believed that a microstructural continuum approach can consider the effect of the microstructure and the interaction. Therefore, the microstructural continuum approach can be used to describe the macroscopic measures reflecting

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On virtual work and stress in granular media

Cited by 51 publications

References 11 publications

Micro–macro homogenization of granular materials based on the average-field theory of Cosserat continuum

Micro–macro homogenization of granular materials based on the average-field theory of Cosserat continuum

Micropolar effect on the cataclastic flow and brittle‐ductile transition in high‐porosity rocks

A micromorphic elastoplastic model and finite element simulation on failure behaviors of granular materials

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