Generalization of Hill’s yield criterion to tension-compression asymmetry materials

This paper is devoted to developing a yield criterion that can model the asymmetry and anisotropy in yielding of pressure insensitive metals,in terms of accuracy and simplicity of formulation.First,a new isotropic yield criterion,which can model the asymmetry in yielding of pressure insensitive metals,is proposed.Further,using Cazacu’s generalizations to anisotropic conditions of the invariants of the deviatoric stress,the proposed isotropic yield criterion is extended to orthotropy.The proposed anisotropic criterion has a quite simple form,and the number of material constants involved is only half of that of Cazacu’s(2004) yield criterion.Compared to Hill’s(1948) yield criterion,the proposed anisotropic yield criterion has three additional constants,which are used to model the tension-compression asymmetry of materials.All the material constants involved in the criterion can be determined by simple tests.The proposed criterion reduces to Hill’s(1948) yield criterion if the tensile and compressive yield stresses are equal.In other words,the proposed anisotropic yield criterion can be considered as an extension of Hill’s(1948) criterion to tension-compression asymmetry materials.The anisotropic yield criterion is used to describe the plastic response of Cu-Al-Be shape memory alloy(data after Laydi and Lexcellent) and Ni3Al based intermetallic alloy IC10 sheets.It is shown that the proposed yield criterion can describe very well the asymmetry and anisotropy observed in those materials.     

Three-dimensional dissipative stress space considering yield behavior in deviatoric plane

Naturally deposited soils are always found in the complex three-dimensional stress state.Constitutive models developed for modeling the three-dimensional mechanical behavior of soils should obey the basic laws of thermo-mechanical principles.Based on the incremental dissipation function,a new deviatoric shift stress is derived and then introduced into the existing constitutive models to describe the yield behavior in the deviatoric plane for geomaterials.By adopting the proposed shift stress,the relationship between dissipative stress tensors and true stress tensors can be established.Therefore,the threedimensional plastic strain can be calculated reasonably through the associated flow rule in the three-dimensional dissipative stress space.At the same time,three methods that are conventionally adopted for generalizing constitutive models to model the three-dimensional stress-strain relationships are examined under the thermo-mechanical framework.The TS(transformed stress)method is shown to obey the thermo-mechanical rules and the TS space adopted in TS method is actually a translational three-dimensional dissipative stress space.However,it is illustrated that the other two approaches,the method of using failure criterion directly and the method of using g()function,violate the basic rules of thermo-mechanical theories although they may bring convenience and simplicity to numerical analysis for geotechnical engineering.Comparison between model predictions and experimental data confirms the validity of the proposed three-dimensional dissipative stress space.     

A new numerical method for determining collapse load-carrying capacity of structure made of elasto-plastic material简

Determination of collapse load-carrying capacity of elasto-plastic material is very important in designing structure. The problem is commonly solved by elasto-plastic finite element method （FEM）. In order to deal with material nonlinear problem involving strain softening problem effectively, a new numerical method-damped Newton method was proposed. The iterative schemes are discussed in detail for pure equilibrium models. In the equilibrium model, the plasticity criterion and the compatibility of the strains are verified, and the strain increment and plastic factor are treated as independent unknowns. To avoid the stiffness matrix being singularity or condition of matrix being ill, a damping factor a was introduced to adjust the value of plastic consistent parameter automatically during the iterations. According to the algorithm, the nonlinear finite element program was complied and its numerical example was calculated. The numerical results indicate that this method converges very fast for both small load steps and large load steps. Compared with those results obtained by analysis and experiment, the predicted ultimate bearing capacity from the proposed method is identical.     

Practical elasto-plastic damage model for dynamic loading and nonlinear analysis of Koyna concrete dam

The elasto-plastic damage model for concrete under static loading,previously proposed,was extended to account for the concrete strain-rate through viscous regularization of the evolution of the damage variables.In order to describe the energy dissipation by the motion of the structure under dynamic loading,a damping model which only includes stiffness damp stress was proposed and incorporated into the proposed rate dependent model to consider the energy dissipation at the material scale.The proposed model was developed in ABAQUS via UMAT and was verified by the simulations of concrete specimens under both tension and compression uniaxial loading at different strain rates.The nonlinear analysis of Koyna concrete dam under earthquake motions indicates that adding stiffness damp into the constitutive model can significantly enhance the calculation efficiency of the dynamic implicit analysis for greatly improving the numerical stability of the model.Considering strain rate effect in the model can affect the displacement reflection of this structure for slightly enhancing the displacement of the top,and can improve the calculation efficiency for greatly reducing the cost time.     

Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.     

Fluid-solid coupling model based on endochronic damage for roller compacted concrete dam

According to the characteristics of thin-layer rolling and pouting construction technology and the complicated mechanical behavior of the roller compacted concrete dam （RCCD） construction interface, a constitutive model of endochronic damage was established based on the endochronic theory and damage mechanics. The proposed model abandons the traditional concept of elastic-plastic yield surface and can better reflect the real behavior of rolled control concrete. Basic equations were proposed for the fluid-solid coupling analysis, and the relationships among the corresponding key physical parameters were also put forward. One three-dimensional finite element method （FEM） program was obtained by studying the FEM type of the seepage-stress coupling intersection of the RCCD. The method was applied to an actual project, and the results show that the fluid-solid interaction influences dam deformation and dam abutment stability, which is in accordance with practice. Therefore, this model provides a new method for revealing the mechanical behavior of RCCD under the coupling field.     

Entire deformational characteristics and strain localization of jointed rock specimen in plane strain compression

Shear band （SB）, axial, lateral and volumetric strains as well as Poisson＇s ratio of anisotropic jointed rock specimen （JRS） were modeled by Fast Lagrangian Analysis of Continua （FLAC）. Failure criterion of rock was a composited Mohr-Coulomb criterion with tension cut-off. An inclined joint was treated as square elements of ideal plastic material beyond the peak strength. Several FISH functions were written to automatically find the addresses of elements in the joint and to calculate the entire deformational characteristics of plane strain JRS. The results show that for moderate joint inclination （JI） , strain is only concentrated into the joint governing the behavior of JRS, leading to ideal plastic responses in axial and lateral directions. For higher JI, the post-peak stress-axial and lateral strain curves become steeper as JI increases owing to the increase of new SB＇s length. Lateral expansion and precursor to the unstable failure are the most apparent, resulting in the highest Poisson＇s ratio and even negative volumetric strain. For lower JI, the entire post-peak deformational characteristics are independent of JI. The lowest lateral expansion occurs, leading to the lowest Poisson＇s ratio and positive volumetric strain all along. The present prediction on anisotropic strength in plane strain compression qualitatively agrees with the results in triaxial tests of rocks. The JI calculated by Jaeger＇s formula overestimates that related to the minimum strength. Advantages of the present numerical model over the Jaeger＇s model are pointed out.     

Fatigue life prediction and experiment research for composite laminates with circular hole

Based on the fatigue prediction model of exponential function and Whitney-Nuismer(WN) criterion of static strength for the composite material laminate with a circular hole, the stress correct factor (β) was put forward and a new fatigue prediction model for composite material laminate was set up. T300/KH304, which is recently studied and is a high capability composite material, was used as the raw material. In order to gain the factor β, the fatigue experiments of the laminates with holes in different diameters and the same ratio of width to diameter were conducted. The fatigue analysis and tests of the laminates with a hole 5 mm in diameter are carried out at different stress levels, and the results meet the engineering requirement. The simple, prompt and practical method is provided for the prediction of S-N curve of composite laminate with a circular hole.     

Equal perimeter yield criterion and its specific plastic work rate: Development,validation and application

In order to overcome the nonlinearity of Mises criterion, a new linear yield criterion with a dodecagon shape of the same perimeter as Mises criterion was derived by means of geometrical analysis. Its specific plastic work rate expressed as a linear function of the yield stress, the maximum and minimum strains was also deduced and compared with that of Mises criterion. The physical meaning of the proposed yield criterion is that yielding of materials begins when the shear yield stress τs reaches the magnitude of 0.594σs. By introducing the Lode parameter, validation of evolution expressions of the proposed yield criterion with those based on Tresca, Mises and TSS criteria as well as available classical yield experimental results of various metals shows that the present results intersect with Mises results and coincide well with experimental data. Moreover, further application to the limit analysis of circle plate as an example is performed to demonstrate the effectiveness of the proposed yield criterion, and the subsequent comparison of limit loads with the Tresca analytical solutions and Mises numerical results shows that the present results are higher than the Tresca analytical results, and are in good agreement with the Mises numerical results.     

砌石坝非线性应力重分布与断裂分析的探索(结合山东东风砌石拱坝)

晚近二十年来我国兴建的砌石坝已逾千座。一般设计只考虑弹性问题,作简单的计算。砌石坝常有成层的水平通缝。水平通缝的软弱面作用是受到工程界注意的,但尚缺少具体的分析研究。本文将砌石体当做两种材料的结合体,由线弹性石料与非线弹性水平通缝所组成。考虑了水平通缝在理想弹塑性状态下应力重分布与通缝部分破坏两种状态。因东风大坝工程待鉴定验收,还对该砌石坝的断裂计算进行了探索。     

FRP增强砖砌体墙在平面内荷载作用下有限元模型

为研究承受平面内荷载的FRP增强砖砌体墙片的力学行为,建立了分离式平面有限元模型,分别用四节点平面单元,联结单元和膜单元模拟块体,砂浆和FRP.块体材料采用增量弹塑性本构模型以及Mises屈服准则结合最大拉应力准则,砂浆材料采用弹性本构模型以及Mohr-Coulomb屈服准则,FRP采用一维线弹性本构模型,有限元模型的求解采用增量初应力法.最后,利用两个算例对模型进行了验证,计算结果与试验结果的对比表明二者符合程度较好,说明模型是有效的.     

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.     

混凝土注芯砌块砌体材料本构关系试验

与普通混凝土材料相比较,混凝土砌块砌体由于构成材料的性质迥异、规则性布置方式以及块体自身具有的方向性差别而表现出明显的各向异性.在宏观层次上,将各组成相材料的影响视为整体的平均表观性能考虑,把具有实际尺寸的宏单元体作为基本研究对象,采用唯象方法,通过设置减摩层,进行单元体在平面应力状态下的单、双轴试验.利用应力比、异化参数和等效单轴应变的概念,建立混凝土注芯砌块砌体材料的平面应力状态的非线性本构关系,并与试验曲线进行比较,能够很好地表征混凝土砌块砌体所具有的非线性各向异性特点.     

砖砌体的非线性计算

在分析总结近年来国内外对砖砌体的本构关系和破坏准则的理论研究成果的基础上,找出了较合理、适用的本构关系和破坏准则的组合,能较好地描述砖砌体受力破坏的力学特性。并通过自行编制的“砖混结构平面有限元分析程序”对一些算例进行了验算,得到较好的结果。     

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。     

水工隧洞支护特性研究

以某水工隧洞为工程背景,采用D-P屈服准则,考虑了水应力的影响范围,利用ANSYS软件进行了水工隧洞三维弹塑性有限元计算分析.分别研究了衬砌支护材料的选择对隧洞稳定性的影响、开挖过程和应力旋转对支护时机选择的影响.计算结果表明:随着衬砌支护材料弹性模量的提高,隧洞顶部和底部分别有上弹和下沉的趋势,隧洞的稳定性有所提高;隧洞的开挖步骤和应力旋转对衬砌支护施做时机的选择有重要影响.     

Ultimate end bearing capacity of rock-socketed pile based on generalized nonlinear unified strength criterion

In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems which govern the stress field were applied to derive the ultimate end bearing capacity based on some reasonable hypothesis and failure plane model. Both numerical simulation and test results were compared with the theoretic solution. The results show good consistency with each other and verify the validity of the present approach. The depth effect with respective to embedment ratio and other influence factors like geological strength index, intermediate principal stress, overburden factor, and damage on end bearing capacity were discussed in the analytical solution. The results show that the proposed yield criterion can be much better for investigating the ultimate end bearing performance of rock-socketed pile. The end bearing capacity increases with embedment ratio and the increasing degree is influenced intensely by the above parameters. Furthermore, ignoring intermediate stress effect would underestimate the strength properties of the rock material and lead to a very conservative estimation value.     

广义Hoek Brown破坏准则平面应变问题的滑移线场理论

根据弹塑性力学平面应变问题的特点,推导广义Hoek-Brown破坏准则平面应变问题应力分量的双参数表达式。代入静力平衡微分方程,得到双曲型一阶拟线性偏微分方程组。运用行列式方法,在适当的变量代换后,获得应力偏微分方程组的特征方向和特征上的微分关系。特征方向表明塑性区中的共轭斜交剪切滑移面形成两族非正交滑移线,其共轭角随极限应力状态和Hoek—Brown岩体材料物性参数而变化。由于对称初始应力场条件下圆形硐室理想弹塑性围岩塑性区内最大主应力方向为环向,而滑移线切线方向与最大主应力方向的夹角是最小主应力（径向应力）的函数,结合圆形硐室理想弹塑性围岩的应力分布的分析解,获得滑移线的极坐标曲线所满足的微分方程,进而得到其极坐标曲线方程。