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1.
A hierarchical thermo‐hydro‐plastic constitutive model for unsaturated soils and its numerical implementation 
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下载免费PDF全文 《国际地质力学数值与分析法杂志》2018,42(15):1785-1805
Unsaturated soils are highly heterogeneous 3‐phase porous media. Variations of temperature, the degree of saturation, and density have dramatic impacts on the hydro‐mechanical behavior of unsaturated soils. To model all these features, we present a thermo‐hydro‐plastic model in which the hydro‐mechanical hardening and thermal softening are incorporated in a hierarchical fashion for unsaturated soils. This novel constitutive model can capture heterogeneities in density, suction, the degree of saturation, and temperature. Specifically, this constitutive model has 2 ingredients: (1) it has a “mesoscale” mechanical state variable—porosity and 3 environmental state variables—suction, the degree of saturation, and temperature; (2) both temperature and mechanical effects on water retention properties are taken into account. The return mapping algorithm is applied to implement this model at Gauss point assuming an infinitesimal strain. At each time step, the return mapping is conducted only in principal elastic strain space, assuming no return mapping in suction and temperature. The numerical results obtained by this constitutive model are compared with the experimental results. It shows that the proposed model can simulate the thermo‐hydro‐mechanical behavior of unsaturated soils with satisfaction. We also conduct shear band analysis of an unsaturated soil specimen under plane strain condition to demonstrate the impact of temperature variation on shear banding triggered by initial material heterogeneities. 相似文献
2.
An extended version of the classical Generalized Backward Euler (GBE) algorithm is proposed for the numerical integration of a three‐invariant isotropic‐hardening elastoplastic model for cemented soils or weak rocks undergoing mechanical and non‐mechanical degradation processes. The restriction to isotropy allows to formulate the return mapping algorithm in the space of principal elastic strains. In this way, an efficient and robust integration scheme is developed which can be applied to relatively complex yield surface and plastic potential functions. Moreover, the proposed algorithm can be linearized in closed form, thus allowing for quadratic convergence in the global Newton iteration. A series of numerical experiments are performed to illustrate the accuracy and convergence properties of the algorithm. Selected results from a finite element analysis of a circular footing on a soft rock layer undergoing chemical weathering are then presented to illustrate the algorithm performance at the boundary value problem level. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
3.
In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non‐trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress‐point algorithm for the numerical integration of a single‐surface mixed isotropic–kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid‐shaped yield function, inside which a stress‐dependent reversible stiffness is accounted for by a non‐linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam‐Clay one to include plastic strain‐driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global‐level Newton–Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
4.
在实际隧道施工过程中,隧道开挖引起地下岩体应力重分布使得围岩的微裂纹扩展损伤,并伴随有塑性流动变形。在地下水环境中对于孔隙和微裂隙围岩介质受到应力作用时,在内部将产生高孔隙水压力影响岩石的力学性质,也改变了围岩的破坏模式。为了研究损伤引起的刚度退化和塑性导致的流动两种破坏机制的耦合作用,从弹塑性力学和损伤理论的角度出发,同时引入修正有效应力原理来考虑孔隙水压力的作用,建立基于Drucker-Prager屈服准则的弹塑性损伤本构模型;针对该本构模型推导了孔隙水压力作用下弹塑性损伤本构模型的数值积分算法-隐式返回映射算法,分别对预测应力返回到屈服面的光滑圆锥面或尖点奇异处两种可能的情况给出了详细的描述,隐式返回映射算法具有稳定性和准确性的特点;大多数弹塑性损伤模型中涉及参数多且不易确定的问题,采用反分析方法获得损伤参数,解决了损伤参数不易确定的难题;采用面向对象的编程方法,使用C++语言编制了弹塑性损伤本构求解程序,并对所建立的弹塑性损伤模型和所编程序进行了试验和数值两个方面的验证;最后将其在吉林抚松隧道工程中进行应用,模拟了塑性区和损伤区的发展变化。研究结果表明：所建立的弹塑性损伤本构模型能够较好地描述岩石的力学性能、塑性和损伤变化趋势,所编程序能够进行实际工程问题的模拟,对现场施工给予一定的指导。 相似文献
5.
基于Drucker-Prager准则的岩石弹塑性损伤本构模型研究 总被引：1，自引：0，他引：1
大多数岩石材料软化本构模型在硬化函数中引入塑性内变量来表示材料的硬化/软化性质,但并不能反映岩石微裂隙损伤对材料力学性能的影响及单轴拉伸和压缩所表现的初始屈服强度f0与屈服极限fu的差异。基于D-P准则同时考虑塑性软化及损伤软化,建立岩石类材料的弹塑性本构关系及其数值算法。塑性屈服函数采用Borja等的应力张量的硬化/软化函数,反映塑性内变量及应力状态对硬化函数的影响;由于岩石损伤软化是微裂隙扩展所导致的体积膨胀引起的,因此,提出用体积应变表征岩石损伤变量的演化,并用回映隐式积分算法编制了岩石的弹塑性损伤本构程序。对单轴压缩及拉伸荷载作用下的岩石材料试验进行数值模拟,结果表明,所提出的岩石弹塑性损伤本构模型可以较好地符合岩石材料的力学特性。 相似文献
6.
Fluctuations of temperature and degree of saturation have considerable influence on the mechanical, hydraulic and retention properties of unsaturated soils. Localized failure is a ubiquitous feature of geomaterials. Major research on localized failure of geomaterials has been focused on geomaterials under the isothermal condition. In this article, we study the localized failure of unsaturated soils under non-isothermal conditions. In particular, we derive the isothermal and adiabatic bifurcation conditions from a homogeneous deformation at the constitutive level under a locally drained condition. A recently proposed meso-scale constitutive model for thermal unsaturated soils is used to derive the isothermal and adiabatic acoustic tensors. We present the spectral form of the consistent tangential elasto-plastic operator from a local material integration algorithm. The numerical simulations at the material level are conducted to study the impact of temperature on localized failure of unsaturated soils under the plane strain condition. The numerical results show that the timing and the critical angle of bifurcation are dependent on temperature. 相似文献
7.
一种高温下混凝土化学塑性-损伤耦合本构模型 总被引：2，自引：0，他引：2
提出了一个用于模拟高温下混凝土化学塑性-损伤耦合本构行为的数值模型。发展了一个化学塑性-损伤耦合分析的一致性应力返回映射算法。为了保证对于全局守恒方程Newton迭代过程的2阶收敛率,推导并形成了一致性切线模量矩阵。数值算例显示了文中发展的化学塑性-损伤耦合本构模型在模拟高温下混凝土中复杂破坏过程的能力和有效性。 相似文献
8.
R. G. Wan 《Computers and Geotechnics》1992,14(3):149-177
A realistic strength criterion often used to describe the yielding behaviour of a jointed rock mass at a continuum level is the well-known Hoek and Brown criterion. This paper is concerned with a 3-D stress generalization of the Hoek-Brown failure criterion by means of an elliptical functional which leads to a smooth deviatoric trace in the stress space. For its incorporation into a finite element analysis involving plasticity calculations, the formulation of an implicit stress integration algorithm is presented. The key computational methodology alludes to the notion of consistent tangent modulus and implicit return mapping schemes (radial and closest point return) for stress integration in a finite element analysis. Within the context of non-linear elastoplastic analysis, it is found that formulation of such consistent modulus and success into achieving numerical efficiency are closely intertwined. Indeed, the procedure results into accurate and rapid convergence of the displacement finite element scheme during the search for equilibrium. This means that considerable savings in computational time can be achieved for large scale problems. Numerical examples which focus on the Hoek-Brown plasticity model are presented in order to fully appreciate the robustness of the algorithm, and hence the viability of such method to practical problems. 相似文献
9.
For a potential geological barrier of high-level radioactive waste repositories in France, the long-term mechanical behavior of the Callovo-Oxfordian (COx) argillite is the most concern for engineers. In this paper, a micromechanical-based elasto-viscoplastic model is proposed, and its numerical realization is our main object. The COx argillite is considered as a three-phase composite consists of porous clay, quartz, and calcite. By assigning appropriate constitutive laws to those constituents, the macroscopic elasto-viscoplastic behavior of the COx argillite is determined with an extended Hill's incremental approach. The numerical aspects includes (a) a new formulation is proposed for the plastic multiplier when adopting the overstress (Perzyna) model to define the viscoplastic strain. Meanwhile, a new formulation is also proposed to solve it within the framework of an implicit returning mapping scheme. (b) The corresponding consistent tangent moduli are strictly derived by extending the method proposed for solving plastic problems; (c) the efficiency of the proposed integration algorithms for the local constitutive equations and the homogenization procedure are validated, receptively, by a built-in porous plasticity model of a commercial finite element (FE) program ABAQUS and by FE computations of a two-phase unit cell; and (d) the proposed micromechanical model is finally applied to simulate experiment data in short-term triaxial compression tests and long-term triaxial creep tests. And the numerical results show that it is able to reflect the variation of the mechanical behavior with respect to the varied mineralogical compositions. 相似文献
10.
In finite element calculations the constitutive model plays a key role. The evaluation of the stress response of the constitutive relation for a given strain increment, which is a time integration in the case of models of the rate type, is a typical sub task in such calculations. Adaptive behaviour of the time integration is essential to assure numerical stability and to control the accuracy of the solution. An adaptive second order semi-implicit method is developed in this paper. Its numerical behaviour is compared with an adaptive second order explicit scheme. The two proposed methods control the local error and guarantee numerical stability of the time integration. We include several numerical geotechnical element tests using hypoplasticity with intergranular strain. The element tests simulate the behaviour of a finite element method based on the displacement formulation. 相似文献
11.
Soil models based on kinematic hardening together with elements of bounding surface plasticity, provide a means of introducing some memory of recent history and stiffness variation in the predicted response of soils. Such models provide an improvement on simple elasto‐plastic models in describing soil behaviour under non‐monotonic loading. Routine use of such models requires robust numerical integration schemes. Explicit integration of highly non‐linear models requires extremely small steps in order to guarantee convergence. Here, a fully implicit scheme is presented for a simple kinematic hardening extension of the Cam clay soil model. The algorithm is based on the operator split methodology and the implicit Euler backward integration scheme is proposed to integrate the rate form of the constitutive relations. This algorithm maintains a quadratic rate of asymptotic convergence when used with a Newton–Raphson iterative procedure. Various strain‐driven axisymmetric triaxial paths are simulated in order to demonstrate the efficiency and good performance of the proposed algorithm. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
12.
对于密实砂土峰值后应变软化特性引起的材料强非线性问题,利用常规有限元所采用的隐式算法很难求解,而动态松弛法在求解这类非线性问题方面却具有独特的优势。针对砂土应变软化强非线性问题,将动态松弛法与有限单元法相结合,提出了一种新的动态松弛有限元法。该方法根据动态松弛法的显式特性,由中心差分法导出了动态松弛有限元法的基本控制方程,并实现了对应力-应变空间中整个平衡路径的追踪。将动态松弛法嵌入到非线性有限元程序中,即可对砂土材料应变软化引起的强非线性问题进行有限元数值计算。该有限元程序中,应力更新采用回归映射算法。最后通过对砂土平面应变压缩试验进行有限元模拟,验证了动态松弛有限元法在求解材料强非线性问题方面的优越性。 相似文献
13.
The restrictions imposed by the form-invariance principle on the structure of the elasto-plastic constitutive law for small strains are examined. It is shown that the yield and plastic potential functions may depend on the joint invariants of the stress and plastic strain tensors in addition to their dependence on the direct invariants of these tensors and additional scalar hardening parameters such as the plastic work; inclusion of the joint invariants as parameters in the constitutive functions allows for induced anisotropy during plastic deformation. It is demonstrated that the physical meaning of the joint invariants is related to the deviation of the principal directions of the stress tensor from those of the plastic strain tensor. It is also shown that only three cases of anisotropy (orthorhombic, transverse and isotropy) are possible in the types of material models discussed herein. The model proposed in this paper does not imply coaxiality between the principal directions of the stress and, plastic strain increment tensors; however, implications of the assumption of coaxiality on the structure of the constitutive equations is investigated. It is shown that coaxiality does not necessarily imply isotropy, but no deviations from coaxiality can be expected in isotropic materials. 相似文献
14.
在弹塑性模型数值实现的过程中,需要进行应力更新的回映算法。针对三维应力空间回映算法在奇异点收敛性方面的不足,提出主应力空间的回映算法,讨论了算法实现过程的应力空间转化问题,分析了应力更新过程中确定回映区域的方法,建立了相应的一致性刚度矩阵。基于大型有限元软件ABAQUS提供的用户材料子程序UMAT接口,利用 Fortran 编程语言,实现了Hoek-Brown准则主应力空间的隐式积分算法,利用开发的模型,进行了岩石常规三轴压缩试验的数值模拟,通过与ABAQUS内部的Mohr-Coulomb准则计算结果的对比,验证了模型和程序的可行性和准确性 相似文献
15.
不同应力路径下剪切带的数值模拟 总被引：4，自引：1，他引：3
采用回映应力更新算法,编写了基于伏斯列夫面的超固结黏土本构关系模型子程序,嵌入非线性有限元软件ABAQUS。通过对单元试验进行三轴压缩、三轴伸长及平面应变等问题的模型预测,再现了超固结黏土在不同初始超固结比和应力路径时的变形和强度特性,从而验证了子程序的正确性。借助该本构模型,对三轴压缩、三轴伸长及平面应变应力路径下超固结黏土体变形局部化问题,进行了三维数值模拟。分析结果表明：超固结黏土在三轴压缩及伸长状态时,土体变形局部化在应力-应变关系软化时出现,而平面应变状态时,在应力-应变关系硬化阶段出现,其超固结黏土的剪胀特性在剪切带的形成过程中起重要作用。 相似文献
16.
Strain space formulation of the elasto-plastic theory and its finite element implementation 总被引：1，自引：0，他引：1
Zheng Yingren 《Computers and Geotechnics》1986,2(6):373-388
this paper systematically presents the research work of the authors in strain space formulation of elasto-plastic theory and its numerical implementation in the context of geotechnical problems. The following aspects are mainly discussed: the advantages of the theory, the relations between stress space and strain space, the generalized yield, constitutive relations in strain space, the strain path and strain path method. The theory has been implemented in a finite element program. Two numerical examples are given which prove that the proposed theory and method are not only simple and convenient but also practical. It opens up a new approach for the application of strain space theory in the geotechnical engineering. 相似文献
17.
The stability of integration is essential to numerical simulations especially when solving nonlinear problems. In this work, a continuum damage mechanics model proposed by the first author is implemented with an integration method named cutting plane algorithm (CPA) to improve the robustness of the simulation. This integration method is one type of return mapping algorithm that bypasses the need for computing the gradients. We compare the current integration method with the previous direct method, and the result shows that the cutting plane algorithm exhibits excellent performance under large loading rate conditions. To enhance accuracy of the new method, a control procedure is utilized in the implementation of the algorithm based on error analysis. Thereafter, the theory of poromechanics is utilized with the damage model to account for the effects of fluid diffusion. Laboratory tests simulated with finite element method illustrate distinct behaviors of shale with different loading rates and indicate the development of microcrack propagation under triaxial compression. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
18.
Two integration algorithms, namely the implicit return mapping and explicit sub-stepping schemes, are adopted in the anisotropic bounding surface plasticity model for cyclic behaviours of saturated clay and are implemented into finite element code. The model is a representative of a series of bounding surface models that have typical characteristics, including isotropic and kinematic hardening rules and a rotational bounding surface to capture complex but important cyclic behaviours of soils, such as cyclic shakedown and degradation. However, there is no explicit current yield surface in the model to which the conventional implicit algorithm returns the stress state back or the sub-stepping integration corrects the drift of the stress state. Hence, necessary modifications have been made for both of the integration schemes. First, the image stress point is mapped or corrected to the bounding surface instead of mapping back or correcting the stress state to the yield surface. Second, the unloading–loading criterion is checked to determine the image stress point rather than checking the yield criterion after giving the trial stress state in a conventional way. Comparative studies on the accuracy, stability and efficiency of the two integration schemes are conducted not only at the element level but also in solving boundary value problems of monotonic and cyclic bearing behaviours of rigid footings on saturated clay. For smaller strain increments, there is no significant difference in the accuracy between the two integration schemes, but the explicit integration shows a higher efficiency and accuracy. For relatively larger increments, the implicit return mapping algorithm presents good accuracy and more robustness, while the sub-stepping algorithm shows deteriorating accuracy and suffers the convergence problem. With the tolerance used in the present model, the bearing capacity of the rigid footing predicted by the return mapping algorithm is closer to the available analytical and numerical solutions, while the bearing capacity predicted by the sub-stepping algorithm shows a marginal increase. 相似文献
19.
This paper presents a reformulation of the original Matsuoka–Nakai criterion for overcoming the limitations which make its use in a stress point algorithm problematic. In fact, its graphical representation in the principal stress space is not convex as it comprises more branches, plotting also in negative octants, and it does not increase monotonically as the distance of the stress point from the failure surface rises. The proposed mathematical reformulation plots as a single, convex surface, which entirely lies in the positive octant of the stress space and evaluates to a quantity which monotonically increases as the stress point moves away from the failure surface. It is an exact reproduction, and not an approximated one, of the only significant branch of the original criterion. It is also suitable for shaping in the deviatoric plane the yield and plastic potential surfaces of complex constitutive models. A very efficient numerical algorithm for the implicit integration of the proposed formulation is presented, which enables the evaluation of the stress at the end of each increment by solving a single scalar equation, both for associated and non‐associated plasticity. The algorithm can be easily adapted for other smooth surfaces with linear meridian section. Finally, a close expression of the consistent Jacobian matrix is given for achieving quadratic convergence in the external structural newton loop. It is shown that all this results in extremely fast solutions of boundary value problems. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
20.
A new procedure to integrate critical state models including Cam–Clay and modified Cam–Clay is proposed here. The proposed procedure makes use of the linearity of the virgin isotropic compression curve and the parallel anisotropic consolidation lines in e–ln p space which are basic features of the formulation of critical state models. Using this algorithm, a unique final stress state may be found as a function of a single unknown for elastoplastic loading. The key equations are given in this article for the Cam–Clay and modified Cam–Clay models. The use of the Newton–Raphson iterative method to minimize residuals and obtain a converged solution is described here. This new algorithm may be applied using the assumptions of linear elasticity or non‐linear elasticity within a given loading step. The new algorithm proposed here is internally consistent and has computational advantages over the current numerical integration procedures. Numerical examples are presented to show the performance of the algorithm as compared to other integration algorithms. Published in 2005 by John Wiley & Sons, Ltd. 相似文献