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1.
A self‐consistent approach for micro–macro modeling of elastic–plastic deformation in polycrystalline geomaterials 
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下载免费PDF全文 This paper is devoted to multi‐scale modeling of elastic–plastic deformation of a class of geomaterials with a polycrystalline microstructure. We have extended and improved the simplified polycrystalline model presented in [Zeng T. et al., 2014. Mech. Mater. 69 (1):132–145]. A rigorous and fully consistent self‐consistent (SC) scheme is proposed to describe the interaction among plastic mineral grains. We have also deeply discussed the numerical issues related to the numerical implementation of the proposed micromechanical model. The efficiency of the proposed model and the related numerical procedure is evaluated in several representative cases. We have compared the numerical results respectively obtained from the fully SC model and two simplified ones. It is found that the SC model produces a softer stress–strain response than that of the simplified models. The comparisons between the estimation of overall behavior of a granite in different loading conditions and experimental data are also conducted. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
2.
In this article we present closed‐form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr–Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non‐associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short‐term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed‐form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
3.
The paper presents a hypoplastic constitutive model for the three-dimensional non-linear stress–strain and dilatant volume change behaviour of sand. The model is developed without recourse to the concept in elastoplasticity theory such as yield surface, plastic potential and decomposition into elastic and plastic parts. Benefited from the non-linear tensorial functions available from the representation theorem the model possesses simple mathematical formulation and contains only four material parameters, which can be easily identified with triaxial compression tests. Comparison of the predictions with the experimental results shows that the model is capable of capturing the salient behaviour of sand under monotonic loading and is applicable to both drained and undrained conditions. 相似文献
4.
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
5.
A Lagrangian numerical approach for the simulation of rapid landslide runouts is presented and discussed. The simulation approach is based on the so‐called Particle Finite Element Method. The moving soil mass is assumed to obey a rigid‐viscoplastic, non‐dilatant Drucker–Prager constitutive law, which is cast in the form of a regularized, pressure‐sensitive Bingham model. Unlike in classical formulations of computational fluid mechanics, where no‐slip boundary conditions are assumed, basal slip boundary conditions are introduced to account for the specific nature of the landslide‐basal surface interface. The basal slip conditions are formulated in the form of modified Navier boundary conditions, with a pressure‐sensitive threshold. A special mixed Eulerian–Lagrangian formulation is used for the elements on the basal interface to accommodate the new slip conditions into the Particle Finite Element Method framework. To avoid inconsistencies in the presence of complex shapes of the basal surface, the no‐flux condition through the basal surface is relaxed using a penalty approach. The proposed model is validated by simulating both laboratory tests and a real large‐scale problem, and the critical role of the basal slip is elucidated. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
6.
The propagation of hydraulic fracture in elastic rocks has widely been investigated. In the paper, we shall focus on numerical modeling of hydraulic fracturing in a class of porous rocks exhibiting plastic deformation. The plastic strain of porous rocks is described by a non-associated plastic model based on Drucker–Prager criterion. The plastic deformation is coupled with fluid pressure evolution described by the lubrication theory. An extended finite element method is used for modeling the propagation of fracture. The fracture propagation criterion is based on the J-integral. The proposed numerical model is validated by comparisons with numerical and analytical results. The influence of plastic deformation on fracture propagation process is investigated.
相似文献7.
Simulation of large deformation and post‐failure of geomaterial in the framework of smoothed particle hydrodynamics (SPH) are presented in this study. The Drucker–Prager model with associated and non‐associated plastic flow rules is implemented into the SPH code to describe elastic–plastic soil behavior. In contrast to previous work on SPH for solids, where the hydrostatic pressure is often estimated from density by an equation of state, this study proposes to calculate the hydrostatic pressure of soil directly from constitutive models. Results obtained in this paper show that the original SPH method, which has been successfully applied to a vast range of problems, is unable to directly solve elastic–plastic flows of soil because of the so‐called SPH tensile instability. This numerical instability may result in unrealistic fracture and particles clustering in SPH simulation. For non‐cohesive soil, the instability is not serious and can be completely removed by using a tension cracking treatment from soil constitutive model and thereby give realistic soil behavior. However, the serious tensile instability that is found in SPH application for cohesive soil requires a special treatment to overcome this problem. In this paper, an artificial stress method is applied to remove the SPH numerical instability in cohesive soil. A number of numerical tests are carried out to check the capability of SPH in the current application. Numerical results are then compared with experimental and finite element method solutions. The good agreement obtained from these comparisons suggests that SPH can be extended to general geotechnical problems. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
8.
An infinite dilatant elastic–plastic soil mass contains a single cylindrical or spherical cavity within which a slowly increasing pressure is applied. The removal of the cavity pressure takes place after a partly plastic state of the soil has been reached. Closed form solutions for the stress and displacement fields in the soil during any stage of the unloading process are derived. The non-associated Mohr–Coulomb yield criterion is used to account for dilation of the soil during shearing. Large strains are taken into account by adopting an appropriate strain definition within the plastically deforming region. 相似文献
9.
This paper presents a u‐p (displacement‐pressure) semi‐Lagrangian reproducing kernel (RK) formulation to effectively analyze landslide processes. The semi‐Lagrangian RK approximation is constructed based on Lagrangian discretization points with fixed kernel supports in the current configuration. As a result, it tracks state variables at discretization points while allowing extreme deformation and material separation that is beyond the capability of Lagrangian formulations. The u‐p formulation following Biot theory is incorporated into the formulation to describe poromechanics of saturated geomaterials. In addition, a stabilized nodal integration method to ensure stability of the domain integration and kernel contact algorithms to model contact between bodies are introduced in the u‐p semi‐Lagrangian RK formulation. The proposed method is verified with several numerical examples and validated with an experimental result and the field data of an actual landslide. 相似文献
10.
W. G. Pariseau 《国际地质力学数值与分析法杂志》1999,23(7):577-594
Consolidation of a poroelastic material that yields according to Drucker–Prager or Mohr–Coulomb criteria leads to a Stefan problem for time-dependent pore fluid pressure. The solution to the Stefan problem for a column of infinite depth is known and is adapted to poroelastic/plastic consolidation of a weightless material under a uniform surface load applied instantaneously and subsequently maintained constant. In this approach, the plastic potential and yield criterion need not be the same. If yielding occurs concurrently with application of load, then collapse is instantaneous. Otherwise, yielding may occur during the consolidation period. If so, then the elastic–plastic zone first appears at the surface and subsequently moves down the column. Depth to the elastic–plastic boundary is given by the simple expression Z = 2β√t where β is a constant determined from continuity conditions at the elastic–plastic boundary. Time-dependent surface displacement that occurs during consolidation is directly proportional to Z. There is little difference between elastic–plastic and purely elastic results in a numerical example because there is little difference in the respective consolidation coefficients. Elastic–plastic finite element results obtained from a column of finite depth are in close agreement with analytical results as long as the pore pressure at the bottom of the column does not change significantly from the value induced by application of the surface load. The analytical solution provides for: (1) efficient evaluation of material properties effects on consolidation, including strength and fluid compressibility, and (2) an accurate way of validating poroelastic/plastic computer codes that are based on Drucker–Prager and Mohr–Coulomb criteria. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
11.
《Geomechanics and Geoengineering》2013,8(1):61-74
A simple unified critical state constitutive model for bonded geomaterials is presented in this paper. The model, which is called CASM-n, is an enhancement of an existing unified critical state model for reconstituted geomaterials (CASM). Characteristic behaviours of a bonded geomaterial such as the pre-yield higher strength and stiffness and the cohesive–frictional shearing mode in the post-yield region are taken into account and included in the reference model. The salient feature of the proposed model is the incorporation of cohesive component into the stress–dilatancy relationship. Consideration of the contribution of cohesion to plastic flow allows the modelling of delayed dilatancy and softening–contraction behaviour, which are two interesting phenomena observed in bonded geomaterials. 相似文献
12.
The method of smoothed particle hydrodynamics (SPH) has recently been applied to computational geomechanics and has been shown to be a powerful alternative to the standard numerical method, that is, the finite element method, for handling large deformation and post‐failure of geomaterials. However, very few studies apply the SPH method to model saturated or submerged soil problems. Our recent studies of this matter revealed that significant errors may be made if the gradient of the pore‐water pressure is handled using the standard SPH formulation. To overcome this problem and to enhance the SPH applications to computational geomechanics, this article proposes a general SPH formulation, which can be applied straightforwardly to dry and saturated soils. For simplicity, the current work assumes hydrostatic pore‐water pressure. It is shown that the proposed formulation can remove the numerical error mentioned earlier. Moreover, this formulation automatically satisfies the dynamic boundary conditions at a submerged ground surface, thereby saving computational cost. Discussions on the applications of the standard and new SPH formulations are also given through some numerical tests. Furthermore, techniques to obtain the correct SPH solution are also proposed and discussed throughout. As an application of the proposed method, the effect of the dilatancy angle on the failure mechanism of a two‐sided embankment subjected to a high groundwater table is presented and compared with that of other solutions. Finally, the proposed formulation can be considered a basic formulation for further developments of SPH for saturated soils. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
13.
应变软化岩体分析原理及其应用 总被引：2，自引：0，他引：2
应变软化是指应力-应变曲线中轴向应力随应变的增加而减小的现象,许多种类的岩土介质在工程扰动的作用下呈现应变软化的行为。在分析应变软化问题时,其应力-应变关系式中的切线刚度矩阵是非正定的,由此导致计算求解的困难。将岩体应变软化过程简化为一系列脆塑性过程,于是应变软化问题的求解归结为一系列脆塑性过程的分析。基于经典弹塑性力学理论,提出了应变软化过程模拟方法及其相应的有限元求解过程,编制了计算程序,研究了应变软化本构模型中不同强度弱化速率对圆形洞室围岩塑形区分布的影响,进一步分析了应变软化模型对应的隧道径向变形沿洞轴方向的分布特征,并与已有监测数据得到的分布规律进行了对比。初步的研究结果表明,应变软化模型得到的计算结果是比较合理的 相似文献
14.
Effects of recoverable deformation induced anisotropy in the elastic stiffness of isotropic materials are described. In isotropic materials, thermodynamics predicts coupling of hydrostatic and deviatoric responses. It is shown that the coupling of the two responses is more significant than previously recognized in the literature. Properly accounting for the coupling of hydrostatic and deviatoric responses requires re‐evaluating elastic materials characterization data, allowing for the coupled response. The result is an apparent decrease in the pressure sensitivity of the elastic shear modulus. The decrease in the pressure sensitivity of the shear modulus leads to stress paths that are more tangential to the yield surface in stress space, resulting in an increase in predicted elastic strain at each step of an elastic–plastic stress update. Consequently, predicted plastic strains and, in particular, volumetric plastic strains, are smaller than if recoverable deformation induced anisotropy had been neglected. The result is an associated plasticity model, which appears to be non‐associated. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
15.
A discrete plastic–damage model is developed for cohesive‐frictional geomaterials subjected to compression‐dominated stresses. Macroscopic plastic strains of material are physically generated by frictional sliding along weakness planes. The evolution of damage is related to the evolution of weakness planes physically in connection with the propagation of microcracks. A discrete approach is used to account for anisotropic plastic flow and damage evolution, by introducing two stress invariants and one plastic hardening variable for each family of sliding weakness planes. Plastic flow in each family is coupled with damage evolution. The proposed model is applied to typical geomaterials and comparisons between numerical predictions and experimental data are presented. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
16.
Wei Wu 《国际地质力学数值与分析法杂志》1998,22(11):921-940
The paper presents a constitutive model for the three-dimensional deformation–strength behaviour of inherently anisotropic sand. Based on non-linear tensorial functions, the model is developed without recourse to the concepts in plasticity theory such as yield surface and plastic potential. Benefited from the fact that no decomposition of strain into elastic and plastic parts is assumed, a unified treatment of anisotropic behaviour of deformation and strength is achieved. Anisotropy is characterized by a vector normal to the bedding plane. The extension of the constitutive model is furnished by incorporating the vector under consideration of the principle of objectivity and the condition of material symmetry. Distinct features of the model are its elegant formulation and its simple structure involving few material parameters. Model performance and comparison with experiments show that the model is capable of capturing the salient behaviour of anisotropic sand. © 1998 John Wiley & Sons, Ltd. 相似文献
17.
In this paper, we propose an anisotropic plastic damage model for semi-brittle geomaterials based on a discrete thermodynamic approach. The macroscopic plastic deformation is generated by frictional sliding of weakness planes. The evolution of damage is related to growth of such weakness planes. The local frictional sliding in each family of weakness planes is described by a non-associated plastic model taking into account material softening and volumetric dilatancy. The damage evolution is coupled with plastic deformation and modelled by an isotropic damage criterion. The proposed model is applied to modelling mechanical responses of typical sandstone under different loading paths. There is good agreement between numerical predictions and experimental data. Further, the anisotropic distributions of plastic deformation and induced damage are analysed and discussed. 相似文献
18.
Porosity strongly affects the overall ductile behavior of cohesive geomaterials undergoing plastic deformation. In the present paper, we proposed an original micromechanical approach that suitably couples Drucker–Prager‐type plasticity, evolving porosity under general triaxial loadings. The resulting model has the advantage to be based on a single macroscopic yield function, which also plays the role of plastic potential. It is shown that this yield function is particularly appropriate to account for the pore collapse and plastic shearing mechanisms that govern the mechanical behavior of the studied Lixhe chalk. Finally, the new model is implemented and validated by comparison to triaxial tests data, covering a wide range of confining pressures. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
19.
This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
20.
A new phenomenological macroscopic constitutive model for the numerical simulation of quasi‐brittle fracture and ductile concrete behavior, under general triaxial stress conditions, is presented. The model is particularly addressed to simulate a wide range of confinement stress states, as also, to capture the strong influence of the mean stress value in the concrete failure mechanisms. The model is based on a two‐surface damage‐plastic formulation. The mechanical behavior in different domains of the stress space is separately described by means of a quasi‐brittle or ductile material response: