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1.
A granular material consists of an assemblage of particles with contacts newly formed or disappeared, changing the micromechanical structures during macroscopic deformation. These structures are idealized through a strain space multiple mechanism model as a twofold structure consisting of a multitude of virtual two‐dimensional mechanisms, each of which consists of a multitude of virtual simple shear mechanisms of one‐dimensional nature. In particular, a second‐order fabric tensor describes direct macroscopic stress–strain relationship, and a fourth‐order fabric tensor describes incremental relationship. In this framework of modeling, the mechanism of interlocking defined as the energy less component of macroscopic strain provides an appropriate bridge between micromechanical and macroscopic dilative component of dilatancy. Another bridge for contractive component of dilatancy is provided through an obvious hypothesis on micromechanical counterparts being associated with virtual simple shear strain. It is also postulated that the dilatancy along the stress path beyond a line slightly above the phase transformation line is only due to the mechanism of interlocking and increment in dilatancy due to this interlocking eventually vanishing for a large shear strain. These classic postulates form the basis for formulating the dilatancy in the strain space multiple mechanism model. The performance of the proposed model is demonstrated through simulation of undrained behavior of sand under monotonic and cyclic loading. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
2.
鉴于Jaumann率型本构关系难以得到应力应变全量之间的严格解析形式,采用有限元法研究了一维大变形过程中Kirchhoff应力和Green应变之间的变化规律。首先,基于虚功原理推导了完全拉格朗日描述的大变形有限元方程,然后提出了模拟大变形本构关系的双曲线模型和割线模量处理方法。算例分析结果表明,双曲线模型能够较好地拟合大变形本构关 系。大变形计算本构关系应当考虑初始孔隙比的影响。 相似文献
3.
A methodology has been developed to extend the incremental (Eulerian) Digital Image Correlation (DIC) technique to enable a Lagrangian‐based large‐strain analysis framework to examine the nature of strain and kinematic nonuniformity within shear bands in sands. Plane strain compression tests are performed on dense sands in an apparatus that promotes unconstrained persistent shear band formation. DIC is used to capture incremental, grain‐scale displacements in and around shear bands. The performance of the developed accumulation algorithm is validated by comparing accumulated displacements with two sources of reference measurements. A comparison between large and infinitesimal rotation is performed, demonstrating the nature of straining within shear bands in sands and the necessity of using a finite strain formulation to characterize ensuing behavior. Volumetric strain variation along the shear band is analyzed throughout macroscopic postpeak deformation. During softening, volumetric activity within the shear band is purely dilative. During the global critical state, the shear band material is seen on the average to deform at zero volumetric strain; however, locally, the sand is seen to exhibit significant nonzero volumetric strain, putting into question the current definition of critical state. At the softening‐critical state transition, a spatially periodic pattern of alternating contraction and dilation along the shear band is evidenced, and a preliminary evaluation indicates that the periodicity appears to be a physical phenomenon dictated only in part by median grain size. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
4.
This paper presents a numerical method that can be used to evaluate the post-failure deformation of slopes and embankments. The method is based on a large deformation finite element analysis employing the updated Lagrangian formulation. It can simulate the changing geometry of slopes during failure. An extended Mohr–Coulomb constitutive model represents the strain softening behaviour of slope material. The results of a series of analyses show that the post-failure deformation of slopes is a function of the rate of strength reduction and also the stiffness of the slope material. These two factors influence the initiation of progressive failure of slopes. The validity of the method is evaluated by simulation of a test embankment failure and comparison of the predicted results with the observed record of the failure. 相似文献
5.
Similar to plane strain, axisymmetric stress problem is also highly kinematics constrained. Standard displacement‐based finite element exhibits volumetric locking issue in simulating nearly/fully incompressible material or isochoric plasticity under axisymmetric loading conditions, which severely underestimates the deformation and overestimates the bearing capacity for structural/geotechnical engineering problems. The aim of this paper is to apply variational multiscale method to produce a stabilized mixed displacement–pressure formulation, which can effectively alleviate the volumetric locking issue for axisymmetric stress problem. Both nearly incompressible elasticity and isochoric J2 elastoplasticity are investigated. First‐order 3‐node triangular and 4‐node quadrilateral elements are tested for locking issues. Several representative simulations are provided to demonstrate the performance of the linear elements, which include the convergence study and comparison with closed‐form solutions. A comparative study with pressure Laplacian stabilized formulation is also presented. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
6.
Equivalent continuum strain calculations based on 3D particle kinematic measurements of sand 
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下载免费PDF全文 Siavash Amirrahmat Khalid A. Alshibli Maha F. Jarrar Boning Zhang Richard A. Regueiro 《国际地质力学数值与分析法杂志》2018,42(8):999-1015
Constitutive modeling of granular materials has been a subject of extensive research for many years. While the calculation of the Cauchy stress tensor using the discrete element method has been well established in the literature, the formulation and interpretation of the strain tensor are not as well documented. According to Bagi, 1 researchers mostly adopt well‐known continuum or discrete microstructural approaches to calculate strains within granular materials. However, neither of the 2 approaches can fully capture the behavior of granular materials. They are considered complementary to each other where each has its own strengths and limitations in solving granular‐mechanics problems. Zhang and Regueiro 2 proposed an equivalent continuum approach to calculating finite strain measures at the local level in granular materials subjected to large deformations. They used three‐dimensional discrete element method results to compare the proposed strains measures. This paper presents an experimental application of the Zhang and Regueiro 2 approach using three‐dimensional synchrotron microcomputed tomography images of a sheared Ottawa sand specimen. Invariant Eulerian finite strain measures were calculated for representative element volumes within the specimen. The spatial maps of Eulerian octahedral shear and volumetric strain were used to identify zones of intense shearing within the specimen and compared well with maps of incremental particle translation and rotation for the same specimen. The local Eulerian volumetric strain was compared to the global volumetric strains, which also can be considered as an averaging of all local Eulerian volumetric strains. 相似文献
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Analysis of large deformation of geomaterials subjected to time‐varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator‐split arbitrary Lagrangian–Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid–fluid coupling and strong material non‐linearity. Each time step of the operator‐split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one‐dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
9.
为了可以合理地描述岩石的体积变形行为,从分数阶微积分出发,基于分数阶常黏性和变黏性系数Abel黏壶元件,提出了环向-轴向应变分数阶黏壶,构建了岩石在单三轴压缩,松弛及蠕变条件下的分数阶体积应变-轴向应变关系,得到了模型的解析解,新模型可为求解岩石的体积应变提供一种新方法。在完整砂岩、泥岩试样及单裂隙砂岩试样的单三轴压缩、松弛及裂隙花岗岩蠕变试验数据的基础上,通过拟合分析确定了分数阶导数体积-轴向应变关系模型的参数,并进行了参数敏感性分析,揭示了围压、单裂隙倾角、微分阶数及模型参数对体积应变的影响规律。结果表明,利用该黏壶构建的体积-轴向应变关系模型,不仅可以更好地描述岩石体积变形的剪缩、剪胀特性,还能够反映岩石的松弛及蠕变变形特性。 相似文献
10.
An alternative approach for quasi‐static large deformation analysis of saturated porous media using meshfree method 下载免费PDF全文
下载免费PDF全文 An alternative coupled large deformation formulation combined with a meshfree approach is proposed for flow–deformation analysis of saturated porous media. The formulation proposed is based on the Updated Lagrangian (UL) approach, except that the spatial derivatives are defined with respect to the configuration of the medium at the last time step rather than the configuration at the last iteration. In this way, the Cauchy stresses are calculated directly, rendering the second Piola–Kirchhoff stress tensor not necessary for the numerical solution of the equilibrium equations. Moreover, in contrast with the UL approach, the nodal shape function derivatives are calculated once in each time step and stored for use in subsequent iterations, which reduces the computational cost of the algorithm. Stress objectivity is satisfied using the Jaumann stress rate, and the spatial discretisation of the governing equations is achieved using the standard Galerkin method. The equations of equilibrium are satisfied directly, and the nonlinear parts of the system matrix are derived independent of the stresses of the medium resulting in a stable numerical algorithm. Temporal discretisation is effected based on a three‐point approximation technique that avoids spurious ripple effects and has second‐order accuracy. The radial point interpolation method is used to construct the shape functions. The application of the formulation and the significance of large deformation effects on the numerical results are demonstrated through several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
11.
The mathematical structure and numerical analysis of classical small deformation elasto–plasticity is generally well established. However, development of large deformation elastic–plastic numerical formulation for dilatant, pressure sensitive material models is still a research area. In this paper we present development of the finite element formulation and implementation for large deformation, elastic–plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process. The algorithm is tested in conjunction with the novel hyperelasto–plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto–plastic problems in geomechanics. We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS‐89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
12.
This paper studies the effects of initial fabric anisotropy of dry sand in simple shear deformation. The effects of anisotropy are taken into consideration through the modification of the mobilized friction in the Mohr–Coulomb‐type yield surface as a function of a fabric parameter. In addition, the constitutive model uses a gradient term that directly incorporates the effects of material length scale. The constitutive formulation is implemented into ABAQUS finite element code and used to simulate shearing of the dry sand under various conditions of simple shear. The numerical simulations show that while the shear stress response is affected by fabric anisotropy, its effects on strain localization in simple shear are minimal. This is in contrast to other devices such as the biaxial shear. The strain localization in simple shear is controlled more by the imposed boundary conditions. The use of material length scale is shown to remove the effects of strain localization in the shearing response. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
13.
A dynamic, large deformation problem of fluid–solid–geomembrane interaction is analysed by the use of material point method, a variant of the finite element method stated in a Lagrangian–Eulerian format. A low-order element is used for space discretisation and the fluid is treated as a compressible liquid with a high value of bulk modulus. Therefore, two algorithms known from literature are applied to mitigate the effects related to the volumetric locking phenomenon. Moreover, a procedure of detecting the free surface is proposed. The method is applied to problems of determining the shape of geo-tubes, collapsing water column, and finally, to the problem of installation of a geo-container on the bed of a water reservoir. The obtained numerical outcomes are compared with the experimental results and the analytic ones when available. 相似文献
14.
A computational method, based on an advanced elasto-plastic large strain formulation, well suited for the analysis of the cone penetration problem, is presented. A new approach of finite strain elasto-plastic analysis is employed.13 The basic (non-rate) constitutive relations are developed in a spatial reference space to preserve their physical significance. They are subsequently transformed in Lagrangian co-ordinates, and through simple time differentiation, their rate equations are introduced. The method is computationally implemented with the finite element method and special provisions are taken to allow for the moving boundary conditions of the problem. 相似文献
15.
Implementation and applications for a constitutive numerical model on F‐75 silica sand, course silica sand and two sizes of glass beads compressed under plane strain conditions are presented in this work. The numerical model is used to predict the stress versus axial strain and volumetric strain versus axial strain relationships of those materials; moreover, comparisons between measured and predicted shear band thickness and inclination angles are discussed and the numerical results compare well with the experimental measurements. The numerical model is found to respond to the changes in confining pressure and the initial relative density of a given granular material. The mean particle size is used as an internal length scale. Increasing the confining pressure and the initial density is found to decrease the shear band thickness and increase the inclination angle. The micropolar or Cosserat theory is found to be effective in capturing strain localization in granular materials. The finite element formulations and the solution method for the boundary value problem in the updated Lagrangian frame (UP) are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
16.
边坡大变形弹塑性有限元分析[Ⅱ] 总被引：1，自引：0，他引：1
本文应用Ｕｐｄａｔｅｄ Ｌａｇｒａｎｇｉａｎ有限元分析理论,分析了石龙庙滑坡的稳定性,其中包括滑坡的大变形,初始应力和超孔隙水压力。根据土的工程地质性质,滑坡体分为四层,土层被视为是弹塑性的,土的塑性屈服采用Ｄｒｕｃｋｅｒ－Ｐｒａｇｅｒ理想塑性屈服准则,挡土墙建成前后的滑坡应力和变形被分别分析和讨论,最后根据这些分析结果,提出了滑坡的整治方案。 相似文献
17.
We derive the governing equations for the dynamic response of unsaturated poroelastic solids at finite strain. We obtain simplified governing equations from the complete coupled formulation by neglecting the material time derivative of the relative velocities and the advection terms of the pore fluids relative to the solid skeleton, leading to a so‐called us ? pw ? pa formulation. We impose the weak forms of the momentum and mass balance equations at the current configuration and implement the framework numerically using a mixed finite element formulation. We verify the proposed method through comparison with analytical solutions and experiments of quasi‐static processes. We use a neo‐Hookean hyperelastic constitutive model for the solid matrix and demonstrate, through numerical examples, the impact of large deformation on the dynamic response of unsaturated poroelastic solids under a variety of loading conditions. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
18.
提出了利用Lagrangian乘子网格来模拟顺层边坡层间结构面接触行为的方法,并推导了考虑接触约束的Lagrangian控制方程的弱形式及其有限元离散方程。Lagrangian乘子网格容许界面出现较大的切向滑移,较好地解决了接触问题中的高度非线性和响应不平滑性。应用以上方法对沪－蓉－西高速公路某顺层岩质高边坡进行了数值模拟分析,得到了临滑状态下的位移场、应力应变场、结构面上的接触状态、层间滑移距离以及接触摩擦力的分布规律。数值模拟结果表明,顺层岩质边坡的破坏是一个渐进的过程,由最初的层间错动,发展为顺层蠕滑,最后在坡底剪出而破坏;其破坏型式由最初的顺层滑动逐步向溃曲破坏转化。 相似文献
19.
首先讨论了Lagrangian和Eulerian无网格近似的联系和区别,然后基于稳定节点积分和增量本构理论,建立了分析边坡静动力破坏的高效大变形无网格法,并给出了详细的计算流程。该方法采用弹塑性损伤耦合本构关系来模拟岩土类材料的破坏演化过程,其中屈服函数采用Drucker-Prager准则,损伤准则为基于应变的各项同性损伤函数。由于无网格近似和稳定节点积分具有非局部近似的特性,在保证空间离散稳定性和提高计算效率的同时,也可准确有效地模拟应变集中所形成的剪切带的发生与扩展,通过数值算例验证了方法的有效性。 相似文献
20.
Zhechao Wang Shucai Li Liping Qiao Jiangang Zhao 《Rock Mechanics and Rock Engineering》2013,46(6):1603-1615
A series of laboratory tests were performed to examine the fatigue behavior of granite subjected to cyclic loading under triaxial compression condition. In these tests, the influences of volumetric change and residual strain on the deformation modulus of granite under triaxial cyclic compression were investigated. It is shown that the fatigue behavior of granite varies with the tendency for volumetric change in triaxial cyclic compression tests. In the stress–strain space, there are three domains for fatigue behavior of rock subjected to cyclic loading, namely the volumetric compaction, volumetric dilation with strain-hardening behavior, and volumetric dilation with strain-softening behavior domains. In the different domains, the microscopic mechanisms for rock deformation are different. It was also found that the stress level corresponding to the transition from volumetric compaction to volumetric dilation could be considered as the threshold for fatigue failure. The potential of fatigue deformation was compared with that of plastic deformation. The comparison shows that rocks exhibit higher resistances to volumetric deformation under cyclic loading than under plastic loading. The influence of residual strain on the fatigue behavior of rock was also investigated. It was found that the axial residual strain could be a better option to describe the fatigue behavior of rock than the loading cycle number. A constitutive model for the fatigue behavior of rock subjected to cyclic loading is proposed according to the test results and discussion. In the model, the axial residual strain is considered as an internal state variable. The influences of confining pressure and peak deviatoric stress on the deformation modulus are considered in a term named the equivalent stress. Comparison of test results with model predictions shows that the proposed model is capable of describing the prepeak fatigue behavior of rock subjected to cyclic loading. 相似文献