基于Cosserat连续体的颗粒破碎影响研究

颗粒破碎对颗粒材料宏观力学行为有重要影响。 结合Hardin的破碎经验公式,将表征破碎程度的破碎参量与Cosserat连续体的内部长度参数相关联,形成一个基于Cosserat连续体且能考虑颗粒破碎的弹塑性模型。数值算例主要考察了颗粒破碎对颗粒材料承载能力、塑性应变及局部化行为的影响,数值结果表明,颗粒破碎主要发生在剪切带内,颗粒破碎使得剪切带明显变窄且剪切带内外等效塑性应变梯度明显增大。     

地基渐进破坏及极限承载力的Cosserat连续体有限元分析

利用Cosserat连续体理论和所发展的有限元数值方法,模拟了地基由应变软化引起的以应变局部化为特征的渐进破坏过程,并从等价塑性应变的发展变化,阐述了渐进破坏过程对所能发挥的极限承载能力的影响。结果表明,Cosserat连续体模型能有效地模拟由应变软化引起以应变局部化为特征的渐进破坏现象,对地基等土工结构物有必要进行渐进破坏分析。同时指出,在求解软化型土体地基的极限承载力时,如果仍按传统的极限平衡或极限分析理论进行分析,可能得出偏于危险的结果。     

Modelling strain localization in granular materials using micropolar theory: mathematical formulations

It has been known that classical continuum mechanics laws fail to describe strain localization in granular materials due to the mathematical ill‐posedness and mesh dependency. Therefore, a non‐local theory with internal length scales is needed to overcome such problems. The micropolar and high‐order gradient theories can be considered as good examples to characterize the strain localization in granular materials. The fact that internal length scales are needed requires micromechanical models or laws; however, the classical constitutive models can be enhanced through the stress invariants to incorporate the Micropolar effects. In this paper, Lade's single hardening model is enhanced to account for the couple stress and Cosserat rotation and the internal length scales are incorporated accordingly. The enhanced Lade's model and its material properties are discussed in detail; then the finite element formulations in the Updated Lagrangian Frame (UL) are used. The finite element formulations were implemented into a user element subroutine for ABAQUS (UEL) and the solution method is discussed in the companion paper. The model was found to predict the strain localization in granular materials with low dependency on the finite element mesh size. The shear band was found to reflect on a certain angle when it hit a rigid boundary. Applications for the model on plane strain specimens tested in the laboratory are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Investigation of influence of particle characteristics on the non‐coaxiality of anisotropic granular materials using DEM

As a result of deposition process and particle characteristics, granular materials can be inherently anisotropic. Many researchers have strongly suggested that the inherent anisotropy is the main reason for the deformation non‐coaxiality of granular materials. However, their relationships are not unanimous because of the limited understanding of the non‐coaxial micro‐mechanism. In this study, we investigated the influence of inherent anisotropy on the non‐coaxial angle using the discrete element method. Firstly, we developed a new discrete element method approach using rough elliptic particles and proposed a novel method to produce anisotropic specimens. Secondly, the effects of initial specimen density and particle characteristics, such as particle aspect ratio A _m, rolling resistance coefficient β , and bedding plane orientation δ , were examined by a series of biaxial tests and rotational principal axes tests. Findings from the numerical simulations are summarized as follows: (1) the peak internal friction angle ? _p and the non‐coaxial angle i both increase with the initial density, A _m and β , and they both increase initially and then decrease with δ in the range of 0–90°; (2) among the particle characteristics, the influence of A _m is the most significant; and (3) for anisotropic specimens, the non‐coaxial angle can be calculated using the double slip and rotation rate model. Then, an empirical formula was proposed based on the simulation results to depict the relationship between the non‐coaxial angle and the particle characteristics. Finally, the particle‐scale mechanism of non‐coaxiality for granular materials was discussed from the perspective of energy dissipation. Copyright © 2016 John Wiley & Sons, Ltd.     

基于CLoE与Gudehus-Bauer亚塑性模型的颗粒材料应变局部化对比研究

基于CLoE与Gudehus-Bauer亚塑性模型数值模拟了平面应变条件下Hostun砂的应变局部化现象。从侧向压力和初始缺陷两个方面对比研究了两种模型所预测应变局部化的产生及演化模式。结果表明：（1）两种模型均能反映Hostun砂刚度随着侧向压力提高而增大的现象。（2）相比Gudehus-Bauer亚塑性模型,CLoE亚塑性模型所得出的应变局部化形态与试验结果更加一致。（3）CLoE亚塑性模型能够反映随着荷载增加,砂的体积先膨胀后缩小的特点。（4）相比Gudehus-Bauer亚塑性模型,CLoE亚塑性模型所得到的应变-应力曲线能够更明显地反映应变局部化带中单元的软化现象。（5）CLoE亚塑性模型能够更好地模拟由初始缺陷导致的不均匀应变。总的来说,所得的数值结果表明,CLoE亚塑性模型能够较好地模拟侧向压力和初始缺陷对应变局部化的影响,在模拟应变局部化现象方面较Gudehus-Bauer更有优势。然而,现有CLoE亚塑性模型无法考虑孔隙比,也未包含颗粒材料内尺度变量,有待进一步完善。     

Numerical investigations of shear localization in a micro‐polar hypoplastic material

In this paper a micro‐polar continuum approach is proposed to model the essential properties of cohesionless granular materials like sand. The model takes into account the influence of particle rotations, the mean grain size, the void ratio, the stresses and couple stresses. The constitutive equations for the stresses and couple stresses are incrementally non‐linear and based on the concept of hypoplasticity. For plane strain problems the implementation of the model in a finite element program is described. Numerical studies of the evolution of micro‐polar effects within a granular strip under plane shearing are presented. It is shown that the location and evolution of shear localization is strongly influenced by the initial state and the micro‐polar boundary conditions. For large shearing the state quantities tend towards a stationary state for which a certain coupling between the norm of the stress deviator and the norm of the couple stress tensor can be derived. Copyright © 2003 John Wiley & Sons, Ltd.     

Discrete element modelling of material non‐coaxiality in simple shear flows

We investigate the quasi‐static simple shear flow of a two‐dimensional assembly of cohesionless particles using discrete element method (DEM) simulations. We focus on the unsteady flow regime where the solid would experience significant evolution of stresses, mobilised shear strength and dilation. We construct the DEM model using a discretised‐wall confined granular cell where the apparent boundary is allowed to dilate or contract synchronously with the confined solid. A rather uniform simple shear field is achieved across the whole assembly, which benefits rheological studies in generalising constitutive laws for continuum methods. We examine two aspects of the simple shear behaviour: macroscopic stress and strain rate evolution, particularly the non‐coaxiality between the principal directions of the two; and micromechanics such as evolution of fabric. For an initially anisotropic specimen sheared under constant normal pressure, the direction of principal stress rotates towards that of the principal strain rate, gradually reducing the degree of non‐coaxiality from about 45° to fluctuating around 0°. The rate in approaching coaxiality is slower in samples with larger initial porosity, stress ratio and mean stress. Generally, a faster rate in approaching coaxiality in simple shear is observed in a more dilatant sample, which often shows a larger degree of mobilised fabric anisotropy, suggesting the possible important role of instantaneous internal friction angle. The evolution of principal fabric direction resembles that of the principal stress direction. © 2013 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons, Ltd.     

基于罚函数偶应力理论的土体应变局部化研究

与 Cosserat 理论相比,偶应力理论在一定程度上可以降低数值框架的复杂度,已逐渐应用于岩土体应变局部化分析中。然而,一般的偶应力有限元法需要满足 C¹连续性,即单元内部和单元交界面上的应变都需要具有连续性。为了避免开发较为复杂的C¹型偶应力单元,在 Cosserat 连续体理论框架下,通过借助罚函数方法对 C¹连续性进行松弛来获得偶应力理论的逼近解,建立了基于罚函数的偶应力有限元方法 PCS-FEM。通过平面应变条件下的弹性圆孔应力集中问题对 PCS-FEM 方法的有效性进行了验证,并应用于土体应变局部化分析中。通过对Ottawa砂的平面应变试验进行数值模拟,发现 PCS-FEM 方法获得的应力−应变曲线及剪切带破坏形态与试验结果基本一致,且能够克服经典连续体理论病态的网格敏感性问题,保证应变局部化问题的适定性;通过对承受偏心荷载作用下的土坡应变局部化经典算例进行分析,发现 PCS-FEM 方法同样可以克服土坡应变软化阶段的网格敏感性问题,展现土体的渐进破坏过程。     

Effects of periodic fluctuations of micro‐polar boundary conditions on shear localizations in granular soil–structure interaction

In this work, the interface behavior between an infinite extended narrow granular layer and a rough surface of rigid body is investigated numerically, using finite element method in the updated Lagrangian (UL) frame. In this regard, the elasto‐plastic micro‐polar (Cosserat) continuum approach is employed to remove the limitations caused by strain‐softening of materials in the classical continuum. The mechanical properties of cohesionless granular soil are described with Lade's model enhanced by polar terms, including Cosserat rotations, curvatures, and couple stresses. Furthermore, the mean grain diameter as the internal length is incorporated into the constitutive relations accordingly. Here, the evolution and location of shear band, within the granular layer in contact with the rigid body, are mainly focused. In this regard, particular attention is paid to the effects of homogeneous distribution and periodic fluctuation of micro‐polar boundary conditions, prescribed along the interface. Correspondingly, the effects of pressure level, mean grain diameter, and stratified soil are also considered. The finite element results demonstrate that the location and evolution of shear band in the granular soil layer are strongly affected by the non‐uniform micro‐polar boundary conditions, prescribed along the interface. It is found that the shear band is located closer to the boundary with less restriction of grain rotations. Furthermore, the predicted thickness of shear band is larger for higher rotation resistance of soil grains along the interface, larger mean grain diameter, and higher vertical pressure. Regarding the stratified soil, comprising a thin layer with slightly different initial void ratio, the shear band moves towards the layer with initially higher void ratio. Copyright © 2011 John Wiley & Sons, Ltd.     

Non‐coaxiality and stress–dilatancy rule in granular materials: FE investigation within micro‐polar hypoplasticity

This paper deals with FE investigations of shear localization in dilatant granular bodies. The calculations were carried out with a hypoplastic constitutive law enhanced by micro‐polar terms to properly model the shear zone evolution. The behaviour of an initially medium dense sand specimen with very smooth and very rough horizontal boundaries was analyzed during a plane strain compression test. A stochastic distribution of the initial void ratio was assumed to be spatially correlated. Attention was focused on the non‐coaxiality of the directions of the principal strain increments and principal stresses in the shear zone and on the stress–dilatancy rule. Copyright © 2008 John Wiley & Sons, Ltd.     

Wave propagation and strain localization in a fully saturated softening porous medium under the non‐isothermal conditions

The (THM) coupling effects on the dynamic wave propagation and strain localization in a fully saturated softening porous medium are analyzed. The characteristic polynomial corresponding to the governing equations of the THM system is derived, and the stability analysis is conducted to determine the necessary conditions for stability in both non‐isothermal and adiabatic cases. The result from the dispersion analysis based on the Abel–Ruffini theorem reveals that the roots of the characteristic polynomial for the THM problem cannot be expressed algebraically. Meanwhile, the dispersion analysis on the adiabatic case leads to a new analytical expression of the internal length scale. Our limit analysis on the phase velocity for the non‐isothermal case indicates that the internal length scale for the non‐isothermal THM system may vanish at the short wavelength limit. This result leads to the conclusion that the rate‐dependence introduced by multiphysical coupling may not regularize the THM governing equations when softening occurs. Numerical experiments are used to verify the results from the stability and dispersion analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

Non‐coaxial elasto‐plasticity model and bifurcation prediction of shear banding in sands

Numerous constitutive models built on coaxial theory and validated under axi‐symmetric condition often describe the stress–stain relationships and predict the inceptions of shear banding in sands inaccurately under true triaxial condition. By adopting an elaborated Mohr–Coulomb yield function and using non‐coaxial non‐associated flow rule, a 3D non‐coaxial elasto‐plasticity model is proposed and validated by a series of true triaxial tests on loose sands. The bifurcation analysis of true triaxial tests on dense sands predicts the influence of the intermediate principal stress ratio on the onset of shear band accurately. The failure of soils is shown to be related to the formation of shear band under most intermediate principal stress ratio conditions except for those which are close to the axi‐symmetric compression condition. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical simulation of the effect of interface friction of a bounding structure on shear deformation in a granular soil

Recently, the shear behavior of a cohesionless granular strip that is in contact with a very rough surface of a moving bounding structure has been numerically investigated by several authors by using a micropolar hypoplastic continuum model. It was shown that the micropolar boundary conditions assumed along the interface have a strong influence on the deformations within the granular layer. In previous investigations, only interface friction angles for very rough bounding structures were assumed. In contrast, the focus of the present paper is on the influence of the interface roughness on the deformation behavior of the granular strip when the interface friction angle is lower than the peak friction angle of the granular material. In addition to the interface friction angle, particular attention is also paid to the influence of the mean grain diameter, the solid hardness, the initial void ratio, and the vertical stress on the maximum horizontal shear displacement within the granular layer before sliding is started. Copyright © 2011 John Wiley & Sons, Ltd.     

On incremental non‐linearity in granular media: phenomenological and multi‐scale views (Part I)

On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto‐viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro‐mechanical models based on multi‐scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro‐mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non‐linear character of their behaviour. It is shown that both phenomenological and micro‐mechanical models exhibit an incremental non‐linearity. In addition, the multi‐scale approach reveals that the macroscopic incremental non‐linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright © 2005 John Wiley & Sons, Ltd.     

A non‐coaxial and unbalanced plastic flow rule for geomaterials and its application to the shear band orientation prediction

In this paper, the non‐coaxial relation between the principal plastic strain increments and the principal stresses, which results from the internal friction in geomaterials, is analyzed, and the phenomenon of the unbalanced development of plastic flow in two conjugate directions is discussed. A non‐coaxial, unbalanced plastic flow model for Coulomb frictional materials is developed and used to determine the orientation of shear band in geomaterials. It is shown that the unbalanced index r of plastic flow has important effect on the orientation of the shear band, and the orientation determined by the conventional plastic flow theory is only a special case of the proposed model when r=0. This result soundly explains the reason that the geomaterials with the same internal friction angle and dilatancy angle can have very different shear band orientations. In addition, the difference between the intrinsic and apparent dilatancy angles is analyzed, and it is emphasized that the dilatancy angle commonly used in practice is indeed the apparent dilatancy angle. Copyright © 2010 John Wiley & Sons, Ltd.     

Strain localization in soft rock—a typical rate‐dependent solid: experimental and numerical studies

Strain localization developing inside soft rock specimens is examined through experimental observation and numerical simulation. In the experimental study, soft rock specimens are sheared at different strain rates under plane strain conditions and deformation and strain localization characteristics are analysed. Transition of localization mode from highly localized mode for higher strain rate to distributed and diffused mode of strain localization for lower strain rates was observed. In the numerical study, simulations of plane strain compression tests are carried out at different strain rates by using an overstressed‐type elasto‐viscoplastic model in finite element computations. The role of strain rates on setting gradients of strain fields across shear band is clarified. The probable mechanism for transition of localization mode is discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

Dynamic analysis of strain localization in water‐saturated clay using a cyclic elasto‐viscoplastic model

A computational framework is presented for dynamic strain localization and deformation analyses of water‐saturated clay by using a cyclic elasto‐viscoplastic constitutive model. In the model, the nonlinear kinematic hardening rule and softening due to the structural degradation of soil particles are considered. In order to appropriately simulate the large deformation phenomenon in strain localization analysis, the dynamic finite element formulation for a two‐phase mixture is derived in the updated Lagrangian framework. The shear band development is shown through the distributions of viscoplastic shear strain, the axial strain, the mean effective stress, and the pore water pressure in a normally consolidated clay specimen. From the local stress–strain relations, more brittleness is found inside the shear bands than outside of them. The effects of partially drained conditions and mesh‐size dependency on the shear banding are also investigated. The effect of a partially drained boundary is found to be insignificant on the dynamic shear band propagation because of the rapid rate of applied loading and low permeability of the clay. Using the finer mesh results in slightly narrower shear bands; nonetheless, the results manifest convergency through the mesh refinement in terms of the overall shape of shear banding and stress–strain relations. Copyright © 2013 John Wiley & Sons, Ltd.