Implementation algorithm for a single hardening constitutive model for frictional materials

An advanced elasto‐plastic constitutive model for frictional materials, whose incremental version is presented in a companion paper (Int. J. Numer. Anal. Meth. Geomech., 2002; 26 :647), is implemented in a user‐defined material module. The general calculation strategy inside this module is presented and discussed, including the initial intersection of the yield surface and the techniques for updating of stresses and hardening modulus. Several integration schemes are implemented in the module and their capabilities in relation to the advanced, three‐dimensional constitutive model are evaluated. The forward Euler, modified Euler, and Runge–Kutta–Dormand–Prince integration schemes are explained in detail, compared, and evaluated in view of error tolerances and computational efficiency. Copyright © 2002 John Wiley & Sons, Ltd.     

A bounding surface elasto‐viscoplastic constitutive model for non‐isothermal cyclic analysis of asphaltic materials

An elasto‐viscoplastic constitutive model for asphaltic materials is presented within the context of bounding surface plasticity theory, taking into account the effects of the stress state, void binder degree of saturation, temperature and strain rate on the material behaviour. A stress state dependent non‐linear elasticity model is introduced to represent time‐independent recoverable portion of the deformation. The consistent visco‐plasticity framework is utilised to capture the rate‐dependent, non‐recoverable strain components. The material parameters introduced in the model are identified, and their determination from conventional laboratory tests is discussed. The capability of the model to reproduce experimentally observed response of asphaltic materials is demonstrated through numerical simulations of several laboratory test data from the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

堆石料状态相关弹塑性本构模型

堆石料的强度变形特性与初始孔隙及应力状态等因素相关。建立了能够预测不同初始孔隙与初始围压影响的堆石料弹塑性本构模型。在剑桥类本构模型框架内,模型能够反映随着孔隙与围压的增大,变形特性由剪胀趋于剪缩的规律。模型采用了基于颗粒体材料细观结构变化的屈服函数和非关联流动准则,提出了能够反映堆石料正常固结线不唯一的硬化参数。为了反映状态相关性,假定堆石料存在唯一的临界状态面,探讨了考虑状态相关性需要满足的数学条件,从而对剪胀方程与硬化参数进行了修正。提出了基于粒子群优化算法的模型参数快速确定方法,将某筑坝堆石料不同初始孔隙比与围压条件下模型预测结果与三轴试验结果对比,验证了模型的合理性。     

Approximate model for blunt objects indenting cohesive‐frictional materials

An approximate two‐dimensional model for indentation of blunt objects into various types of rigid‐perfectly plastic cohesive‐frictional material is derived. Particular emphasis is placed on considering indentation as a process involving evolution of the boundary of material displaced by the indenter. Force–penetration relationships are obtained by an incremental approach utilizing key kinematic and static information from indentation of a flat punch. Albeit approximate, the proposed model applies to arbitrary indenter geometry and weightless or ponderable cohesive‐frictional materials exhibiting associated or non‐associated plastic flow. Two specific indenter geometries, the cylinder and blunt wedge, are explored in detail. Favorable agreement is found between the analytic results and those obtained using the finite element method (FEM). For both the wedge and cylinder, it is further shown that accurate analytic expressions relating indentation force explicitly to penetration can be derived. In the case of the wedge and weightless material, predictions of indentation force obtained from the derived expressions are very close to those computed from implicit equations available in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

A yield criterion for isotropic and cross‐anisotropic cohesive‐frictional materials

This paper proposes a yield and failure criterion for cohesive and frictional materials. The function is given by the combination of a Lode dependence for the behaviour in the deviatoric plane and a meridian function for the pressure‐dependent behaviour. A variety of shapes can be achieved with the proposed criterion including Lode dependences which are able to reproduce the behaviour of isotropic and cross‐anisotropic materials in the deviatoric plane. The criterion is validated through the comparison with experimental data based on multiaxial experimental tests on clays, sands, rocks and concrete. Finally, the convexity of the criterion is analysed and discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Single hardening constitutive model for frictional materials I. Plastic potential Function

Based on review and evaluation of a large number of test data, a general three-dimensional plastic potential function expressed in terms of stress invariants is proposed. Three parameter values are required in this function, but one is redundant with one of the failure surface parameters. The plastic potential surface resembles an asymmetric cigar in the principal stress space. It includes tensile behavior of materials with effective cohesion. Its capabilities are examined by comparisons with experimental data from two- and three-dimensional tests on different frictional materials.     

A note on formulas for localized failure of frictional materials in compression and biaxial loading modes

The paper investigates aspects of the localization analysis of frictional materials. We derive closed formulas and diagrams for the inclination angle of critical discontinuity surfaces which develop in homogeneous compression and biaxial loading tests. The localization analysis is based on a Drucker–Prager‐type elastoplastic hardening model for non‐associated plastic flow at small strains, which we represent in spectral form. For this type of constitutive model, general analytical formulas for the so‐called critical hardening modulus and the inclination angle of critical discontinuity surfaces are derived for the plane strain case. The subsequent treatment then specializes these formulas for the analysis of compression and biaxial loading modes. The key contribution here is a detailed analysis of plane strain deformation modes where the localized failure occurs after subsequent plastic flow. The derived formulas and diagrams can be applied to the checking of an accompanying localization analysis of frictional materials in finite‐element computations. Copyright © 2001 John Wiley & Sons, Ltd.     

统一弹塑性本构模型在FLAC3D中的计算格式

统一强度理论是一个有着坚实理论基础、可表达各种岩土材料强度特性且被广泛应用的新的强度理论。FLAC3D是一个具有强大的计算分析功能且专门针对岩土工程问题开发并被广泛应用的数值分析软件。若能将二者结合起来,无疑会大大促进岩土工程领域相关问题的解决。针对这一问题,研究了统一弹塑性本构模型在有限差分方法中应用的基本理论格式。根据FLAC3D软件中UDM接口计算格式的要求,将统一强度理论引入其中,详细推导了统一弹塑性本构模型在FLAC3D软件中应用的计算公式。由于统一屈服面在应力空间内由12个面组成,在应力角为[0,π/3]的范围内,统一屈服面由两个相交面组成,为计算塑性因子及处理计算中应力超出屈服面的应力调整问题,利用应力角分析了应力空间的分区,推导了区域分界面的公式。最后,编制了相应的UDM接口程序对一圆形隧洞进行了弹塑性分析,对比了计算结果与解析解,结果很好地验证了此计算格式及相应接口程序的正确性。统一强度理论和FLAC3D软件的结合,将使二者的优点得以充分发挥,以解决更多的岩土工程问题。     

A multi‐mechanism constitutive model for plastic adaption under cyclic loading

As is well known, granular soils under cyclic loading dissipate a large amount of energy and accumulate large irreversible strains. Usually, with time, this second effect reduces and the accumulation rate decreases with the number of cycles until obtaining a sort of ideal stationary cyclic state at which ratcheting disappears. In this paper, only this ideal state is taken into consideration and simulated by means of a multi‐mechanism constitutive model for plastic adaptation. For this purpose, the concept of cycle is discussed, many different categories of cyclic stress/strain paths are considered and some theoretical issues concerning both the flow and the strain‐hardening rules are tackled. Even though the paper focuses on soil behaviour, the conclusions can be extended to all materials exhibiting ratcheting due to volumetric behaviour.Copyright © 2013 John Wiley & Sons, Ltd.     

循环荷载作用下考虑颗粒破碎的堆石体本构模型

中国西部兴建的很多200～300 m高的堆石坝处于高烈度地震区。应力水平高时堆石体的颗粒破碎对其在循环荷载作用下的应力、应变特性有重要的影响。基于广义塑性理论,通过引入状态参数,建立了循环荷载作用下考虑颗粒破碎的堆石体的本构模型,并给出了模型参数的确定方法。与堆石体在400、800、1 500、2 200 kPa围压作用时的试验结果对比,表明所提出的本构模型可以较好地模拟循环荷载作用下颗粒破碎时堆石体的动应力和动应变响应。     

A hierarchical single yield surface for frictional materials

This paper extends the formulation of a recent yield and failure criterion [Mortara G. A new yield and failure criterion for geomaterials. Géotechnique 2008;58(2):125–32] by modifying its shape in the deviatoric representation. Such a modification improves the performance of the surface introducing a constitutive parameter associated to the variation of the Lode angle. The criterion is validated through the comparison with experimental data obtained from multiaxial tests on soils, rocks and concrete. A special form of the criterion will be also derived for numerical applications in order to remove singularities of the previous criterion.     

堆石料的临界状态与考虑颗粒破碎的本构模型

高应力水平时堆石料的颗粒破碎对其强度和变形机制有重要影响。临界状态土力学理论对重塑土的应力-应变关系的描述较为成功,但目前颗粒破碎对堆石料的临界状态的影响及其数学描述鲜有研究。对堆石料进行了固结应力从0.4 MPa到4 MPa的18组固结排水和固结不排水常规三轴压缩试验,以及6组等向压缩试验。试验结果表明：在排水条件和不排水条件下,不同的固结应力试样都趋于临界状态;堆石料的临界状态在q-p′平面和e-lgp′平面均为非线性变化。基于此试验结果,通过引入状态参数,在广义塑性力学的理论框架下,建立了考虑颗粒破碎的堆石料本构模型,并给出了模型参数的确定方法。与长河坝料的试验进行了对比,结果表明所建议的本构模型可以较好地模拟堆石料从低围压0.4 MPa到高围压 3.5 MPa下的应力-应变特性     

基于统计损伤本构模型的改进桩-土接触面模型研究

建立准确合理的接触面本构模型是研究桩基承载力、沉降及变形等问题的前提。考虑桩-土界面初始剪切刚度的深度效应,提出基于统计损伤本构模型的无厚度接触面本构模型,根据剪切试验的数据对改进的接触面本构模型参数进行拟合,得到了不同法向应力下的模拟曲线。利用FLAC3D软件内嵌的FISH语言,对桩-土界面进行改进本构模型的二次开发,提出的无厚度接触面模型合理地模拟出桩-土界面刚度的非线性,成功实现了桩-土剪切试验过程的数值模拟。计算结果表明：提出的无厚度接触面本构模型能够合理地模拟桩-土界面的力学行为,可以描述接触面刚度的非线性变化,也适于程序化计算,拓展了接触面统计损伤本构模型的应用领域,为深入探讨桩基承载变形性状奠定了基础。     

堆石料的剪胀特性与广义塑性本构模型

以三轴试验成果为基础,考虑颗粒破碎引起堆石料剪胀比与应力比之间的非线性关系,提出了能够反映堆石料低围压剪胀、高围压剪缩特性的剪胀方程。在广义塑性理论框架内构造堆石料的塑性流动方向向量和加载方向向量,引入依赖于密实度与平均应力的压缩参数,构造随平均应力、剪应力比和密实度变化的塑性模量,建立了一个考虑颗粒破碎的堆石料弹塑性本构模型。阐述了该模型10个参数的确定方法,并通过模拟不同围压和不同应力路径下堆石料的三轴压缩试验资料验证了模型与参数的合理性。     

以塑性功为硬化参数的Q2原状黄土弹塑性模拟

为了研究非饱和Q2原状黄土的力学特性,通过三轴压缩试验、各向等压试验和三轴试验卸载、再加载试验获得Q2原状黄土的力学参数,并结合弹塑性力学理论,推导出Q2原状黄土的屈服函数和以塑性功为硬化参数的硬化规律,采用相关联流动规则,建立非饱和Q2原状黄土弹塑性本构模型。通过模型计算与试验实测值比较,表明该模型基本上能反映Q2原状黄土的力学特性。     

岩体结构面新型本构模型研究

对于涉及需要单独考虑岩体结构面的工程岩体结构分析,采用能反映岩体结构面主要力学特性的合理的本构模型是取得合理解答的关键问题之一。针对在经典连续介质力学理论框架内建立岩体结构面本构模型的缺点,基于岩体结构面的实际受力变形特性,采用直接法建立了一种新型岩体结构面本构模型。所建立的模型依据岩体结构面切向应力变形曲线及剪胀曲线的实际特征,将其分为峰前线性段、峰前非线性段以及峰后软化段,并分别给出了用于描述岩体结构面变形和强度等主要力学特性的数学模型,进而推导建立了结构面各变形阶段的增量型本构模型。最后,编写相关计算程序,采用所建立的新型本构模型以及被广泛采用的Plesha模型对经典的岩体结构面直剪试验成果进行拟合分析。结果表明,所建立的新型本构模型能更为合理的描述岩体结构面的主要力学特性,且模拟能力优于Plesha模型     

基于广义热力学的超固结土本构模型

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。     

A kinematic hardening constitutive model for sands: the multiaxial formulation

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.     

Integration and calibration of a plasticity model for granular materials

A new macroscopic constitutive model for non‐cohesive granular materials, with the focus on coarse‐sized materials (railway ballast), is presented. The model is based on the concepts of rate‐independent isotropic plasticity. The Backward Euler rule is used for integrating the pertinent evolution equations. The resulting incremental relations are solved in the strain space that is extended with the internal (hardening) variables. The model is calibrated using data from Conventional Triaxial Compression (CTC) tests, carried out at the University of Colorado at Boulder. A function evaluation method is used for the optimization, whereby a ‘multi‐vector’ strategy for choosing the appropriate start vector is proposed. Copyright © 2002 John Wiley & Sons, Ltd.