Modeling of state parameter and hardening function for granular materials

A modified plastic strain energy as hardening state parameter for dense sand was proposed, based on the results from a series of drained plane strain tests on saturated dense Japanese Toyoura sand with precise stress and strain measurements along many stress paths. In addition, a unique hardening function between the plastic strain en--ergy and the instantaneous stress path was also presented, which was independent of stress history. The proposed state parameter and hardening function was directly verified by the simple numerical integration method. It is shown that the proposed hardening function is independent of stress history and stress path and is appropriate to be used as the hardening rule in constitutive modeling for dense sand, and it is also capable of simulating the effects on the de-formation characteristics of stress history and stress path for dense sand.     

Experimental investigation and numerical modeling for elasto-plastic notch-root stress/strain analysis under monotonic loadings

Experimental investigation and numerical modeling on elasto-plastic notch-root stress/strain distributions under monotonic loadings of both the Ni-based directionally solidified (DS) superalloy and Titanium alloy were carried out simultaneously. For measuring inhomogeneous deformation fields at notch roots, an optical-numerical full-field surface deformation measurement system was developed based on the digital image correlation (DIC) method. The obtained strain distributions were then verified with reasonable accuracy by finite element simulation, where an anisotropic elastic-viscoplastic constitutive model was developed for DS superalloy and a simple isotropic stress-strain relationship was adopted for Titanium alloy. Meanwhile, factors affecting elasto-plastic notch-root stress/strain distributions were systematically investigated numerically, where the emphasis was placed on temperature, loading stress rate, sample shape, anisotropy and notch features. The results show that stress/strain behavior at notch root is significantly affected by the mentioned factors, which are concretely embodied in the distribution of tensile stress/strain, equivalent stress and accumulative equivalent plastic strain.     

超固结土的蛋形弹塑性本构模型

为了描述超固结软土在不同应力条件下的强度变形特征,以蛋形函数为基本框架,建立并发展适用于超固结土体的弹塑性本构模型. 通过对一系列超固结土应力路径三轴压缩试验结果的分析,探讨土体在超固结状态下塑性应变的发展规律(剪胀/剪缩). 在先前提出的旋转塑性势面流动法则基础上对其进行发展与改进,引入峰值应力比,构建剪胀状态下归一化塑性势面旋转角与应力状态参数之间的近似线性关系,以满足超固结土的塑性变形特性. 结合基于等效硬化参量的广义塑性功硬化原理构建超固结软土的蛋形弹塑性本构模型. 将三轴压缩试验数据与数值预测结果进行对比以验证模型有效性,结果表明该模型可以有效反映超固结软土在不同加载条件下的应力应变特性,比如软化与剪胀.     

Numerical study on deformation and failure of reinforced sand

In order to investigate the deformation and failure of reinforced sand, and the reinforcing mechanism of flexible and rigid reinforcement, a set of plane strain compression tests of dense Toyoura reinforced sand with planar reinforcement of a wide range of stiffness were analysed by a nonlinear finite element method. The analysis was incorporated into an energy-based elasto-plastic constitutive model for sand to develop a stress path-independent workhardening parameter based on the modified plastic strain energy concept. Numerical results indicate that the global stress-strain relations of sand specimens are reinforced by using relatively flexible and rigid reinforcement, and an unreinforced sand specimen can be reasonably simulated by the current finite element method. It is also found that the reinforcing mechanism and progressive failure with a development of shear bands in reinforced sand can be reasonably examined by the finite element method.     

强震下弦支穹顶结构的动力失效探讨

为了揭示强震下弦支穹顶结构的动力失效机理,分别采用双线性本构模型和应变-损伤耦合本构模型,对一个8点支承的弦支穹顶结构进行了不同地震加速度下的全过程动力时程分析,考察了2种不同材料模型下的结构动力失效.同时对采用应变-损伤耦合本构模型的结构进行了深入研究,对该结构最大位移、塑性杆件数、杆件的应变能密度和动能密度、构件应力及应力变化率等多个物理量准则进行了考察分析.结果表明:采用应变-损伤耦合本构模型能更加准确地反映结构的动力失效,且这些物理量都能大致反映结构动力失效过程中的失效时刻;同时也反映了失效时结构最大位移、杆件塑性发展、索力松弛等失效特征.     

粘土数值建模方法与Duncan模型的对比研究

以塑性体应变与塑性剪应变之间的相互作用原理为指导,对粘土本构关系的数值建模方法进行了研究。采用包含应力路径函数的两个本构泛函作为模型基本框架,可以反映出应力路径相关性。应力应变增量关系的表达式包含两个偏导数的交叉项,用于反映塑性体应变与塑性剪应变的相互作用。利用三轴试验结果建立了粘土的弹塑性本构模型,该模型能够反映出土的三大基本力学特性:压硬性、剪胀性和应力路径相关性。通过可视化,分别给出在整个应力场中剪切和体积的三维变形曲面。此外,从模型的理论基础、基本框架和预测结果等方面与Duncan模型进行对比,显示出数值建模方法优于传统方法。     

修正的Giuffre-Menegotto-Pinto钢筋滞回本构模型

针对Giuffre-Menegotto-Pinto钢筋滞回本构模型（MP模型）发生小幅卸载再加载履历（小幅循环）时存在应变和刚度突变、高估材料强度缺陷的问题,通过定义钢筋材料的弹性域半径引入新的小幅循环判别方法,将小幅循环分为2种类型,提出对小幅反转点重新赋值的修正方法,消除不合理的履历;应用修正后的MP模型和Mander混凝土模型,开发基于空间纤维梁单元理论的RC结构弹塑性分析程序;分析含小幅循环的钢筋滞回曲线、模拟RC柱的拟静力试验结果,检验修正方法的有效性.结果表明：修正的MP模型发生小幅循环时履历合理,避免了原模型刚度和应力偏大的问题;修正模型改进了RC结构中钢筋在地震作用下的滞回履历,在弹塑性分析中有较好的计算效率.     

应变空间中一般加载规律的弹塑性本构关系

为了建立多维应力、应变空间的弹塑性本构关系,将一般加载规律一维全量理论的简单弹塑性模型推广到一般加载规律的多维增量理论,并且给出应力空间的加载函数和应变空间的加载函数以及它们之间的正确的变换关系.在此基础上,在应变空间中建立了推导一般加载规律的多维增量理论的本构关系的一种途径.应用这种途径,从应变空间的加载函数出发,推导了等向强化材料的一般加载规律的弹塑性本构关系.理论和实例表明,这种途径对等向强化材料、随动强化材料、理想弹塑性材料和热弹塑性问题都适用.     

基于增量本构关系弹塑性分析的无网格伽辽金法

在无网格伽辽金法的基础上，采用增量形式的无网格伽辽金法的插值方法，并利用应力应变增量形式表征材料的弹塑性本构关系，在小变形假设的前提下，提出了基于增量本构关系的弹塑性分析的无网格伽辽金法；采用罚参数修正了能量变分方程式，方便地实现了无网格伽辽金法的本质边界条件．对二维平面问题及轴对称问题的计算结果表明：运用增量形式的无网格伽辽金法进行弹塑性问题的数值分析，具有较高的计算精度，且适应性强，从而为材料的弹塑性分析计算提供了一种实用方法。     

循环荷载三面本构模型及与实验结果比较

为探求形式简洁,参数较少,便于工程应用的循环本构模型,本文基于边界面模型和多面模型理论,建立了一个可描述金属材料三轴循环加载力学行为的三面本构模型.把塑性应变分解成塑性应变1和塑性应变2,塑性应变1对应于一套屈服面-边界面模型,塑性应变2对应于一套单屈服面模型.提出了当前应力点与边界面上对偶点之间距离的演变公式,基于一致性条件得出边界面模型中塑性模量的计算与运动硬化准则的联系.采用塑性应变作为硬化参数,应用关联流动法则计算塑性应变.相比于经典的边界面模型,本文模型形式简明;相比于前人修正随动硬化准则模型,本文模型需要的材料参数较少.结合金属稳定材料U71Mn的单轴循环实验结果,对其4种力学行为进行模拟,分析了非对称应力循环下平均应力和应力幅值对稳定材料棘轮效应的影响,以及对称应变循环下材料的最大应变幅值记忆效应.研究结果表明,本文模型的模拟结果与前人文献的实验结果一致性较好,可为研究材料的本构行为提供一条新的途径.     

考虑应变强化的高压缩性黏土修正双曲线模型

研究了武汉地区高压缩性黏土弹塑性本构模型。基于Duncan E～v双曲线模型,对等压固结条件下CTC应力路径三轴实验数据进行了数据拟合,得到了该条件下的非线性应力应变关系,并将卸载-再加载试验曲线的平均斜率作为卸载模量,引入了加卸载函数作为判定加卸载的准则。将该模型嵌入有限元程序对三轴压缩试验进行数值模拟,并与Duncan模型数值解及试验曲线作对比。结果表明,该模型较Duncan模型能更好的体现正常固结黏土在CTC路径下的应力应变关系,特别是加载后期的应变强化效应,与试验曲线的最大相对误差不超过5％。     

应变非线性软化的预应力衬砌隧洞弹塑性应力解

基于岩体单轴应变非线性软化本构模型,采用全量理论将其推广,获得考虑中间主应力影响的复杂应力状态下的岩体等效应力和等效应变关系,由此对灌浆式预应力衬砌隧洞进行弹塑性分析.指出预应力作用下围岩可能处于弹性或弹塑性两种状态,给出了两种情况下围岩压力、塑性区半径及衬砌应力的解析计算式,得到了围岩产生塑性变形的临界灌浆压力,并结合某工程进行了具体分析.     

Elasto-plastic analysis of masonry with anisotropic plastic material model

This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fracture energies along each orthotropic axes.Considering the unique material properties of masonry,a new yield criterion for masonry is proposed combining the Hill’s yield criterion and the Rankine’s yield criterion.The new yield criterion not only introduces compression friction coefficient of shear but also considers yield functions for independent stress state along two material axes of tension.To solve the involved nonlinear equations in numerical analysis,several nonlinear methods are implemented,including Newton-Raphson method for nonlinear equations and Implicit Euler backward mapping algorithm to update stresses.To verify the proposed material model of masonry,a series of tests are operated.The simulation results show that the new developed material model implements successfully.Compared with isotropic material model,the proposed model performs better in elasto-plastic analysis of masonry in plane stress state.The proposed anisotropic model is capable of simulating elasto-plastic behavior of masonry and can be used in related applications.     

Development and verification of large deformation model considering stiffness deterioration and shear dilation effect in FLAC~(3D)

The existing constitutive models of rock with strain softening cannot successfully reflect the damageinduced anisotropy and nonlinearity of the post-peak failure behavior under progressive loading. In order to better reflect the nonlinear stress-strain behavior of rock, especially for the post-peak failure behavior,with expected stiffness degradation and large deformation, a modified constitutive model of rock considering stiffness degradation and dilatation behavior at large deformation was proposed in this study. This study analyzes and discusses various attenuation parameters in the proposed nonlinear plastic constitutive model using FLAC~(3D) software. The excavation-induced stress in rocks was calculated by FLAC~(3D) using the Mohr-Coulomb model, conventional strain model, and the proposed modified model. The obtained results of these models were analyzed and compared with field data. This study shows that the simulated results using the proposed new constitutive model matched much more closely with the measured field data, with an average error less than 5%. This new model can successfully reflect the damage-induced stiffness degradation at large deformation, and can provide a theoretical basis for stability design and evaluation of underground excavation.     

衬砌压力隧洞的弹塑性分析

基于岩体应变非线性软化本构模型,考虑中间主应力的影响,对衬砌圆形压力隧洞在等压荷载下进行弹塑性分析,对弹塑性边界位置在衬砌范围内和围岩范围内分别进行了讨论,指出根据弹塑性边界位置的不同应采用不同的计算公式,并得到了由隧洞开挖卸荷引起的、围岩开始屈服时的极限压力以及内压力作用下分别使衬砌、围岩开始屈服时的极限压力。     

Digitalization Modeling System for Constitutive Relation of Geomaterial

1 Introduction The classic theory of plasticity for metal is just a particular case of the general constitutive model for geomaterials[1]. It’s very difficult to acquire an effective constitutive model because its validity rests with many characteristics of geomaterials. It’s very difficult to make certain deformation of specimens in conventional soil tri-axial compression tests because some disadvantages exist in the experiment principles, approaches and instruments [2–3]. The axial deform…     

基于最小能量原理计算高速切削过程中的剪切角

以Oxley模型的切削力和切削几何关系为基础,提出通过计算切削过程中第一形变区、第二形变区的应力和应变来计算塑性变形功,从而构建随着切削过程中剪切角的变化,系统总能量变化规律的计算模型。基于最小能量原理,确定对应切削过程中塑性变形功最低时的剪切角为平衡剪切角。在模型中引入Johnson-Cook本构方程与动态流变应力本构方程,以文献中45钢的切削实验数据为依据,分别计算引入2种本构方程的基于最小能量原理模型的剪切角,并将计算结果与Oxley模型的计算结果进行对比分析,结果表明文中构建模型的计算结果与实验结果吻合较好。     

等主应力比路径下砂土弹塑性本构关系的数值建模

按照数值建模理论,建立了砂土在等主应力比路径下的弹塑性本构模型,给出了塑性体应变和塑性剪应变两组屈服轨迹,模型的建立为工程提供了一个符合土体中实际发生的应力路径的本构方程.同时,通过与常规三轴压缩路径和等p路径(TC)下的应力应变关系曲面和屈服轨迹的对比,发现三者之间存在着显著差别,证实了应力路径对本构关系的影响是不可忽略的.     

基于热力学原理的混凝土热-力耦合本构模型

为了解决高温条件下混凝土材料力学性质描述的问题,基于热力学理论,将损伤理论与经典弹塑性理论结合,建立了一个考虑温度影响的混凝土热-力耦合本构模型,用于描述高温条件下混凝土材料的力学性质。基于热力学原理推导了考虑温度影响的弹性应变增量的表达式,并基于经典塑性理论,构造了一个考虑温度影响的硬化参数,推导出相应的塑性应变增量表达式,将上述2部分应变增量叠加得到混凝土热-力耦合本构模型的表达式。将模型预测结果与试验结果进行对比,符合良好,表明上述热-力耦合本构模型能够对高温条件下混凝土材料的力学性质进行较为准确的描述与预测。     

韧性断裂准则参数标定及其在DP590中的应用

为研究DP590高强钢板材的韧性断裂力学性能,以DF2012韧性断裂准则为理论基础,设计6种包含不同应力状态的拉伸试样来获取材料的塑性流动和断裂参数,采用一种实验-模拟混合方法标定韧性断裂准则的参数.准确地描述材料发生断裂前的塑性行为是韧性断裂准则参数标定的关键,以新提出的各向异性Drucker屈服准则和一种修正的Voce硬化准则表征DP590的塑性行为,使用Fortran语言将该本构模型编译为VUMAT子程序嵌入ABAQUS仿真软件中进行试样的拉伸模拟.实验和模拟对比表明,所构建的本构模型可以准确地预测不同试样沿着轧制方向各个角度的力程曲线.在拉伸实验和标定的本构模型基础上,标定DF2012韧性断裂准则的参数并构建DP590在应力三轴度和断裂应变二维空间中的断裂轨迹.与3种经典的韧性断裂准则Cockcroft-Latham、Clift和Rice-Tracey进行比较,使用Fortran语言将DF2012韧性断裂准则和本构模型一起嵌入ABAQUS仿真软件对不同试样的断裂进行模拟,结果表明:基于实验-模拟混合法标定的DF2012韧性断裂准则能够合理地构建DP590的断裂轨迹曲线和准确地预测不同应力状态下拉伸试样断裂的发生.