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1.
由于经典的塑性力学无法根据Drucker塑性公设从理论上证明非相关联流动准则,因而从连续介质热力学基本原理出发研究土的弹塑性模型。根据率无关塑性力学理论,通过Gibbs自由能和多个独立耗散函数,建立土的多重屈服准则及其流动准则,证明了屈服准则重数和独立耗散函数个数相等,分析了耗散函数形式对屈服准则和塑性流动准则的影响。分析了一簇新的能够同时考虑相关联流动准则和非相关联流动准则的粘土的Gibbs自由能和耗散函数的表达式,殷宗泽双屈服面模型是其特例,但新模型具有更为明确的物理含义,能考虑非相关联流动准则的情况。根据粘土室内实验选取了模型参数,并与实测应力-应变曲线进行对比,说明新模型可以模拟粘土的多重屈服面本构关系。 相似文献
2.
A relatively simple yield model is developed for isotropic, porous rocks which yield in a ductile manner. The flow rule and yield function are derived using an adaptation of the work-balance approach of critical state soil mechanics. This adaptation allows for the dissipation of work by frictional and volume change mechanisms, including the dissipation of frictional work at sensibly constant plastic volumetric strain. The yield model uses two material parameters—a basic frictional parameter and a plastic volumetric strain adjustment parameter which is assumed to be constant for the yield locus corresponding to a particular specific volume. The model gives excellent fits to yield loci for two limestones, a chalk and gypsum plaster prepared at different initial void ratios. 相似文献
3.
基于广义热力学基本理论,通过考虑塑性剪切变形产生的能量一部分以塑性自由能的形式储存,并且该部分自由能与超固结度相关,结合修正剑桥模型的热力学函数形式建立了适用于超固结土的自由能函数和耗散函数。该耗散函数与当前应力状态无关,相关联流动法则仍然适用。由建立的耗散函数和自由能函数,推导了弹塑性本构关系的屈服函数、流动法则、硬化定律。通过4种不同超固结土的试验结果和计算结果进行比较,验证了模型的合理性。 相似文献
4.
在材料塑性本构理论中应用热动力学原理一般有两种方法,一是在引入的屈服（包括硬化）、破坏函数和塑性势概念的基础上,从数学上或者根据试验规律,假设（拟合）其函数形式,然后将热力学定律或准热力学公设作为附加约束引入本构模型;二是直接从热动力学出发,通过构造能量函数（热力学势）、耗散函数及较少的限制条件给出全部的塑性本构理论,而得到的本构理论自动满足热动力学原理。长期以来,针对各种不同材料提出的大量屈服破坏函数,许多都是按照第一种方法给出的,却并未见到进行过严格的热动力学限制的验证。研究从塑性本构理论中上述两种研究方式在热力学定律的满足上的一致性出发,将求屈服函数对应的耗散势的问题归结为关于耗散势的偏微分方程求解问题,从理论上演绎出塑性理论中一族率无关线性屈服破坏函数对应的耗散势函数,从而将屈服破坏函数的热动力学验证问题转化为其对应耗散势的正负判断问题,也沟通了塑性理论中屈服破坏函数同热动力学中耗散势在概念上的联系,对于理解屈服破坏函数的热动力学内涵有重要理论意义。特别地,文中给出的求耗散势的方法具有一般性,不仅适合于线性的屈服破坏函数,也适合于非线性的屈服破坏函数。最后,利用热力学第2定律给出了一族线性屈服破坏函数具体的热力学限制条件。 相似文献
5.
《Geomechanics and Geoengineering》2013,8(3):147-157
The performance of a new constitutive model called ‘kinematic hardening modified Cam clay’ (KHMCC) is presented. The model is described using the ‘continuous hyperplasticity’ framework. Essentially this involves an infinite number of yield surfaces, thus allowing a smooth transition between elasticity and plasticity. The framework allows soil models to be developed in a relatively succinct mathematical form, since the entire constitutive behaviour can be determined through the specification of two scalar potentials. An implementation of the continuous hyperplasticity model is also described. The model requires eight parameters plus a viscosity coefficient for rate-dependent analysis. The model is defined in terms of triaxial stress–strain variables for this study, and is used to model monotonic triaxial tests on Bangkok clay. Comparisons of the theoretical predictions with the results of cyclic undrained triaxial compression tests on Bangkok clay are also presented. 相似文献
6.
模拟土体本构特性的热力学方法 总被引：4，自引：1，他引：3
简要介绍了建立岩土材料弹塑性本构模型的热力学方法。它不仅具有紧凑的数学结构,而且自动满足热力学定律,仅从两个热力学势函数,即自由能函数与耗散增量函数出发,就足以导出弹塑性理论必须的屈服条件,流动法则,硬化定律和弹性定律。通过理论证明指出,只要耗散增量函数依赖于当前应力,流动法则必然是非关联的,岩土材料的摩擦特性与非关联流动法则密不可分。介绍该方法在三维模型,岩土材料的微细观力学特性,应力应变的均匀化以及剪胀和各向异性方面应用的主要研究进展,并对一些重要的概念,诸如“储存的塑性功”,“Reynolds-Taylor状态”等,进行分析与解释。最后给出近期需进一步深入研究的几点建议。 相似文献
7.
H. W. Chandler 《国际地质力学数值与分析法杂志》1988,12(4):371-378
A major problem in the mathematical modelling of the deformation of granular materials has been the lack of an easily usable variational principle. This is because the frictional dissipation of energy in these materials does not allow the use of the classical extremum principles. In this paper, a variational principle is constructed which is valid even when frictional dissipation occurs. Its derivation uses results from the mathematical theory of envelopes. Both the stresses and the strains can be varied, and for the case of non-frictional plasticity it reduces to the maximum work principle of Hill. An example is presented to show how this new principle can be used to obtain approximate solutions to boundary-value problems with granular materials. The only requirements in advance are a displacement field that obeys the kinematic boundary conditions, and a stress field that obeys equilibrium and the static boundary conditions. The principle is therefore quite straightforward to apply. 相似文献
8.
从热力学定律出发,利用自由能函数和耗散函数,通过严格的理论推导得到屈服函数、流动法则和硬化规律。在临界状态模型的框架内,将基于热力学基础的各向异性模型和特定的旋转硬化规律结合起来,提出了一种新的处理方法用来模拟密砂在三轴试验中的变形曲线。给定多组模型参数,计算排水和不排水三轴试验,并简单讨论了模型参数对曲线规律的影响,结果表明这种方法是有效的。通过屈服面在变形不同阶段采用不同的旋转方向,能够考虑密砂的复杂试验曲线特征,又由模型的热力学基础保证了屈服面和剪胀函数的协调。这种方法确定的模型结构严密,适应性强,可以描述大范围土体的特性,且简单易于使用。 相似文献
9.
Soil–shallow foundation interaction has been theoretically analysed within the framework of thermomechanics. The design of a global interaction model has been achieved with an original treatment of the Clausius–Duhem inequality. The role of the gravity volume forces is emphasized. The paper is focused on a strip footing based on dense sand and subjected to time‐independent plastic processes. The theoretical approach has confirmed that an associated global flow rule cannot be expected to hold true. The analysis of the sources of dissipation has led to the development of a soil–footing interface model and a complete interaction model accounting for the interface constraints and the intrinsic frictional properties of the soil. Finally, the abilities of the complete model are checked by comparisons with experimental results found in the literature. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
10.
11.
极限分析是岩土工程稳定性评价的重要方法之一。传统的有限元极限分析方法,采用低阶三角形单元时需要引入速度间断面并采用特殊网格布局,或者采用高阶三角形单元等措施来克服体积锁定问题和提高数值精度。在光滑有限元法（smoothed finite element method,简称SFEM）的基础上,提出了一种基于新型混合常应力−光滑应变单元的极限分析方法（mixed constant stress-smoothed strain element limit analysis,简称MCSE-LA方法）。在服从关联流动法则和Mohr-Coulomb屈服准则的基础上,MCSE-LA方法最终将数值极限分析转化为以应力和极限荷载乘子为基本未知量的二阶锥规划（second order cone programming,简称SOCP）问题。MCSE-LA方法具有形式简单、优化变量相对较少和无需显式的写出塑性内能耗散函数的优点,并且根据凸锥优化的对偶理论,可以从对偶问题中获得速度场和塑性乘子等信息。此外,还采用基于最大塑性剪应变率的网格自适应加密算法,该算法在塑性区细化网格,显著提高了新数值极限分析方法的计算效率和精度。最后通过边坡稳定分析的结果对比,验证了MCSE-LA方法的计算精度和效率均高于传统的有限元极限分析方法。 相似文献
12.
This paper presents a procedure for developing yield functions with consistent flow rules for granular materials from a family of two parameter dissipation functions in combination with appropriate kinematic constraints. Through a mathematical procedure described in the paper, a general formulation is developed that can, by adjusting the values of the two parameters, reproduce a wide range of yield surfaces, including the Drucker–Prager, Matsuoka–Nakai, and Lade–Duncan. Specifically, an analytical expression for the yield function is obtained in terms of a parameter that is a selected solution to a high order polynomial. The roots of this polynomial can always be found using the eigenvalues of the companion matrix and instructions on how to select the appropriate root are given in the paper. Two ways of incorporating anisotropy into the procedure are explored and the role within it of the recent history of deformation is examined. 相似文献
13.
A unified constitutive model for unsaturated soils is presented in a critical state framework using the concepts of effective stress and bounding surface plasticity theory. Consideration is given to the effects of unsaturation and particle crushing in the definition of the critical state. A simple isotropic elastic rule is adopted. A loading surface and a bounding surface of the same shape are defined using simple and versatile functions. The bounding surface and elastic rules lead to the existence of a limiting isotropic compression line, towards which the stress trajectories of all isotropic compression load paths approach. A non‐associated flow rule of the same general form is assumed for all soil types. Isotropic hardening/softening occurs due to changes in plastic volumetric strains as well as suction for some unsaturated soils, enabling the phenomenon of volumetric collapse upon wetting to be accounted for. The model is used to simulate the stress–strain behaviour observed in unsaturated speswhite kaolin subjected to three triaxial test load paths. The fit between simulation and experiment is improved compared to that of other constitutive models developed using conventional Cam‐Clay‐based plasticity theory and calibrated using the same set of data. Also, the model is used to simulate to a high degree of accuracy the stress–strain behaviour observed in unsaturated Kurnell sand subjected to two triaxial test load paths and the oedometric compression load path. For oedometric compression theoretical simulations indicate that the suction was not sufficiently large to cause samples to separate from the confining ring. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
14.
C. S. Desai 《国际地质力学数值与分析法杂志》1980,4(4):361-375
A new concept based on the use of a function expressed as a (complete) polynomial expansion in terms of the three invariants of the stress tensor is proposed for deriving yield, failure and plastic potential functions for use in plasticity based constitutive laws. A mathematical interpretation and physical meaning of the proposed concept are provided by using the idea of the singular nature of constiutive matrices in incremental hypoelastic laws. It is suggested that the proposed function and (polynomial) forms of material moduli can be synonymous. A number of specialized forms of the general function are adopted and their values at failure from advanced three-dimensional tests for a number of (geological) media are evaluated. The results indicate the possibility that there exist invariant numbers associated with the functions(s) that may apply to a wide range of materials. Some ideas on implementation of the proposed concept are also presented. 相似文献
15.
In this paper, a nonlinear numerical technique is developed to calculate the limit load and failure mode of structures obeying an ellipsoid yield criterion by means of the kinematic limit theorem, nonlinear programming theory and displacement-based finite element method. Using an associated flow rule, a general yield criterion expressed by an ellipsoid equation can be directly introduced into the kinematic theorem of limit analysis. The yield surface is not linearized and instead a nonlinear purely kinematic formulation is obtained. The nonlinear formulation has a smaller number of constraints and requires less computational effort than a linear formulation. By applying the finite element method, the kinematic limit analysis with an ellipsoid yield criterion is formulated as a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the dissipation power which is to be minimized and an upper bound to the plastic limit load of a structure can then be calculated by solving the minimum optimization problem. An effective, direct iterative algorithm has been developed to solve the resulting nonlinear programming formulation. The calculation is based purely on kinematically admissible velocities. The stress field does not need to be calculated and the failure mode of structures can be obtained. The proposed method can be used to calculate the bearing capacity of clay soils in a direct way. Some examples are given to illustrate the validity and effectiveness of the proposed method. 相似文献
16.
Giuseppe Buscarnera 《Acta Geotechnica》2014,9(2):313-327
The paper investigates the mathematical structure of plasticity models for unsaturated soils and provides a strategy to capture the loss of uniqueness of the incremental solution upon loading and/or wetting paths. To derive bifurcation conditions in simple analytical form, the analysis is restricted to isotropic stress states. This choice has allowed the inspection of the most common classes of constitutive models through a unified notation, as well as the study of different forms of coupling between plasticity and state of saturation. It is shown that, similar to saturated soil plasticity, the loss of admissibility of the plastic solution is governed by critical values of the hardening modulus. At variance with the classical case, however, these moduli can be positive even if the plastic flow rule is associated (bifurcation in the hardening regime). The paper shows that such non-trivial features derive from hydro-mechanical coupling, i.e. they depend on the approach used to reproduce suction effects and evolving retention properties. In other words, although the problem of loss of uniqueness affects all classes of plasticity models for unsaturated soils, different constitutive assumptions may not have the same outcome in terms of bifurcation potential. As a result, new concepts are introduced to compare the mathematical robustness of the different constitutive approaches, as well as to interpret their predictions in the light of precise bifurcation criteria. 相似文献
17.
This paper presents a procedure for developing elasto‐plastic material models from a dissipation function and kinematic constraint that obviates the need to establish an expression for the yield function. This method could be applied to a wide range of different materials, but it is particularly suitable for testing new models of granular materials. This is because there is often a difficulty associated with finding an algebraic expression for the yield function for appropriate dissipation functions combined with realistic dilatancy rules. The procedure presented in this paper allows the approach to fulfill its potential for the easy incorporation of physical insight into the dissipation function and kinematic constraint without being hindered by algebraic complexity. The method is applied to the familiar von Mises model and also to a model for granular materials that incorporates a realistic dilatancy rule and extends into three dimensions a model presented in earlier work. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
18.
Hyperplasticity theory was developed by Collins and Houlsby (Proc. Roy. Soc. Lon. A 1997; 453 :1975–2001) and Houlsby and Puzrin (Int. J. Plasticity 2000; 16 (9):1017–1047). Further research has extended the method to continuous hyperplasticity, in which smooth transitions between elastic and plastic behaviour can be modelled. This paper illustrates a development of a new constitutive model for soils using hyperplasticity theory. The research begins with a simple one‐dimensional elasticity model. This is extended in stages to an elasto‐plastic model with a continuous internal function. The research aims to develop a soil model, which addresses some of the shortcomings of the modified cam‐clay model, specifically the fact that it cannot model small strain stiffness, or the effects of immediate stress history. All expressions used are consistent with critical state soil mechanics terminology. Finally, a numerical implementation of the model using a rate‐dependent algorithm is described. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
19.
Yannis F. Dafalias Majid T. Manzari Achilleas G. Papadimitriou 《国际地质力学数值与分析法杂志》2006,30(12):1231-1257
SANICLAY is a new simple anisotropic clay plasticity model that builds on a modification of an earlier model with an associated flow rule, in order to include simulations of softening response under undrained compression following Ko consolidation. Non‐associativity is introduced by adopting a yield surface different than the plastic potential surface. Besides, the isotropic hardening of the yield surface both surfaces evolve according to a combined distortional and rotational hardening rule, simulating the evolving anisotropy. Although built on the general premises of critical state soil mechanics, the model induces a critical state line in the void ratio–mean effective stress space, which is a function of anisotropy. To ease interpretation, the model formulation is presented firstly in the triaxial stress space and subsequently, its multiaxial generalization is developed systematically, in a form appropriate for implementation in numerical codes. The SANICLAY is shown to provide successful simulation of both undrained and drained rate‐independent behaviour of normally consolidated sensitive clays, and to a satisfactory degree of accuracy of overconsolidated clays. The new model requires merely three constants more than those of the modified Cam clay model, all of which are easily calibrated from well‐established laboratory tests following a meticulously presented procedure. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
20.
The implications of assuming isotropic elasto–plasticity to model the behaviour of soil under simple shear conditions are considered. For small strains, use of such a model implies the following three consequences: (1) strains and strain increments at any stage of shearing may be expressed as the sum of elastic and plastic components; (2) principal directions of stress and of plastic strain increment are collinear; (3) principal directions of stress increment and of elastic strain increment are collinear. These consequences are used in order to establish relationships between the stresses, stress increments and strains which develop in a simple shear test. No additional assumptions with regards the form of the yield function, the flow rule or the hardening function are required for this development. By defining the ratio of the plastic to the total shear strain increment on the horizontal plane (the plane of zero extension) as λ, it is possible to define the horizontal normal stress σx in terms of λ and other stresses and strains which are normally known during simple shear loading. As a result, all components of the stress tensor in the simple shear plane may be defined. Results of some direct simple shear tests on soft clay have been interpreted using the model and found to be generally consistent with some of the observations reported in the literature from tests in which boundary stresses were measured. 相似文献