弹脆塑性围岩应力和位移的广义SMP准则解

该文基于广义空间准滑动面SMP(Spatial Mobilized Plane)强度准则,对圆形隧洞围岩的应力和位移,得到了可考虑中间主应力和材料脆性软化影响旳弹塑性解和弹-脆-塑性解,给出了隧洞围岩的应力、位移、临界支护力与塑性区半径的表达式。通过将该文的弹塑性解与经典的圆形隧洞弹塑性解(卡斯特纳解)进行对比,验证了建立的公式的正确性,同时通过与基于Mohr-Coulomb强度准则的弹-脆-塑性解析解进行对比:论证了中间主应力和材料脆性软化对围岩稳定性的影响显著,考虑中间主应力的影响可以发挥围岩的强度潜能,能使围岩的强度和变形规律更接近工程实际,所得成果有重要参考价值。     

基于弹塑性损伤本构模型的复合材料层合板破坏荷载预测

在连续损伤力学和塑性力学框架内,建立一个同时考虑塑性效应和损伤累积导致材料属性退化的复合材料弹塑性损伤本构模型。基于最近点投影回映算法,开发本构模型的应变驱动隐式积分算法以更新应力及与解答相关的状态变量,并推导与所开发算法相应的数值一致性切线刚度矩阵,保证有限元分析采用NewtonRaphson迭代法解答非线性问题的计算效率。采用断裂带模型对已开发的本构模型软化段进行规则化,以减轻有限元分析结果的网格相关性问题。对损伤变量进行粘滞规则化,并推导出相应的粘滞规则化数值一致性切线刚度张量,解决了在有限元隐式计算程序中采用含应变软化段本构关系的数值分析由于计算困难而提前终止的问题。开发包含数值积分算法的用户材料子程序UMAT,并嵌于有限元程序Abaqus v6.14中。通过对力学行为展现显著塑性效应的AS4/3501-6V型开口复合材料层合板的渐进失效分析,验证本文提出的材料本构模型的有效性。结果显示,预测结果与已报道的试验结果吻合良好,并且预测精度高于其他已有弹性损伤模型。表明已建立的弹塑性损伤本构模型能够准确预测力学行为,展现显著塑性效应的复合材料层合板的破坏荷载,为其构件和结构设计提供一种有效的分析方法。     

基于双剪统一强度理论应变退化模型的隧道结构稳定性分析

论文基于双剪统一强度准则应变软化模型对圆形隧道稳定性的分析,提出一种简单的数值计算方法来对围岩进行弹塑性分析。该文采用差分法,基于广义形式的双剪应力屈服准则,并采用相关联流动法则,建立本构方程。对于应变软化模型,该文选定塑性应变增量作为软化参数,并且假设强度参数随软化参数成线性函数关系。弹性区的解答引用拉梅解答,而求解塑性区的解答时,将塑性区分成很多微元圆环,并假设每个圆环的径向应力?r沿半径向内均匀递减;其次,建立每个微元圆环的平衡微分方程、本构方程、几何方程及相邻两微元之间的应力增量和应变增量的关系。从弹塑性交界面处的塑性区最外一个圆环开始,求解出每一个微元圆环的解答。并且利用MATLAB进行编程求解出最终的结果:应力场、应变场、径向位移场的数值解。此外还分析讨论了中间主应力影响系数b、软化参数临界值η*对解答的影响,并分析了影响塑性区半径的因素。     

基于广义Hoek-Brown准则的弹塑性本构模型及其数值实现

Hoek-Brown强度准则在岩石及岩体工程中得到了广泛的应用,而目前基于该准则建立起的弹塑性本构模型在理论上还存在着一些不足;考虑到不同围压条件下的岩石材料塑性形变发展特征,提出了基于分段隐式修正塑性势的塑性流动法则,解决了其它基于广义H-B准则所建立的本构模型中塑性流动方向不连续及需额外引入参数等问题;采用基于误差控制的改进欧拉中点积分算法,对该本构模型进行了数值实现并给出了单积分点层次的结果验证;进一步将成果嵌入到了同济曙光岩土工程三维数值平台(GeoFBA3D)当中,并给出了一类经典弹塑性力学问题的计算结果验证以及其在隧道工程中的典型应用算例。     

循环稳定材料的棘轮行为:II.隐式应力积分算法和有限元实现

针对第一部分发展的、能够合理描述循环稳定材料棘轮行为的粘塑性本构模型,详细讨论该模型的数值计算方法和有限元实现。在径向回退(RadialReturn)和向后欧拉积分方法的基础上,结合连续迭代(SuccessiveSubstitution)方法,推导并建立了针对循环粘塑性本构模型的、新的隐式应力积分算法。为了本构模型在大型有限元分析程序(如ABAQUS等)中的实现,针对有限元的整体节点迭代计算,推导和确立了一个新的、考虑率相关塑性的一致切线刚度矩阵(ConsistentTangentModulus)表达式。通过对一些算例的有限元分析,讨论了建立的隐式应力积分算法的优越性,同时对特定构件的棘轮行为进行了数值模拟,进而检验了有限元实现的合理性和必要性。     

循环稳定材料的棘轮行为:Ⅱ.隐式应力积分算法和有限元实现

针对第一部分发展的、能够合理描述循环稳定材料棘轮行为的粘塑性本构模型,详细讨论该模型的数值计算方法和有限元实现。在径向回退(Radial Retulm)和向后欧拉积分方法的基础上,结合连续迭代(Successive Substimtionl方法,推导并建立了针对循环粘塑性本构模型的、新的隐式应力积分算法。为了本构模型在大型有限元分析程序(如ABAQUS等)中的实现,针对有限元的整体节点迭代计算,推导和确立了一个新的、考虑率相关塑性的一致切线刚度矩阵(Consistent Tangent Modulus)表达式。通过对一些算例的有限元分析,讨论了建立的隐式应力积分算法的优越性,同时对特定构件的棘轮行为进行了数值模拟,进而检验了有限元实现的合理性和必要性。     

Lemaitre等向硬化弹塑性损伤耦合本构模型积分算法及程序实现EI北大核心CSCD

涉及复杂材料弹塑性损伤问题数值计算研究时,不仅需要选择恰当预测损伤和破坏的本构模型,还需要有效和稳健的本构积分算法。首先,阐述了在热力学和连续介质力学框架下建立弹塑性损伤本构模型的基本步骤;其次,基于Lemaitre等向硬化弹塑性损伤耦合本构模型、相应的本构积分算法-完全隐式返回映射算法(Fully Return Mapping Algorithm)和一致切线模量,采用C++语言在Visual 6.0环境下编制有限元本构求解程序,在塑性损伤修正步中求解返回映射方程时,选取一种简单的形式,只需迭代求解一个标量非线性方程,计算效率较高。最后,通过缺口圆棒数值算例初步验证了程序的正确性,并编制接口程序对计算结果进行可视化。研究结果表明积分算法的有效性及程序的正确性,Lemaitre等向硬化弹塑性损伤耦合本构模型能够较好地模拟韧性材料的破坏发展过程,可以求解类似的有限元边界值问题,为考虑损伤特性的韧性材料结构研究和设计奠定基础。     

Lemaitre等向硬化弹塑性损伤耦合本构模型积分算法及程序实现

涉及复杂材料弹塑性损伤问题数值计算研究时,不仅需要选择恰当预测损伤和破坏的本构模型,还需要有效和稳健的本构积分算法。首先,阐述了在热力学和连续介质力学框架下建立弹塑性损伤本构模型的基本步骤;其次,基于Lemaitre等向硬化弹塑性损伤耦合本构模型、相应的本构积分算法-完全隐式返回映射算法(Fully Return Mapping Algorithm)和一致切线模量,采用C++语言在Visual 6.0 环境下编制有限元本构求解程序,在塑性损伤修正步中求解返回映射方程时,选取一种简单的形式,只需迭代求解一个标量非线性方程,计算效率较高。最后,通过缺口圆棒数值算例初步验证了程序的正确性,并编制接口程序对计算结果进行可视化。研究结果表明积分算法的有效性及程序的正确性,Lemaitre等向硬化弹塑性损伤耦合本构模型能够较好地模拟韧性材料的破坏发展过程,可以求解类似的有限元边界值问题,为考虑损伤特性的韧性材料结构研究和设计奠定基础。     

完全隐式返回映射算法对岩土地基问题的求解

针对岩土工程中的复杂力学问题,在弹塑性力学理论框架和非线性有限元理论基础上,采用非关联等向硬化Drucker-Prager模型的完全隐式积分算法—返回映射算法(Return Mapping Algorithm)编制了有限元求解程序。该算法可以避免预测应力漂移屈服面的现象,对准静态变形条件下的本构方程可以获得准确解,在迭代中使用Newton-Raphson法获得近似平方的收敛速率,具有较高的精确性和稳定性。对岩土工程中的地基问题进行求解,计算得出位移、应力等结果,模拟了塑性区随载荷步增加的演化过程,对地基极限承载力进行了解析解和数值解的对比。结果表明了算法的优越性、程序的正确性和实用性。     

双层组合厚壁圆筒弹脆塑性极限内压统一解

基于三剪统一强度准则和弹脆塑性软化模型,考虑材料的脆性软化和中间主应力效应,推导了双层组合厚壁圆筒弹脆塑性极限内压统一解,探讨了粘聚力、内摩擦角、半径比、强度理论参数和中间主应力系数的影响特性,克服了以往基于Tresca屈服准则、Mises屈服准则或双剪强度理论的理想弹塑性解的不足。研究结果表明:中间主应力、材料模型和脆性软化对厚壁圆筒的极限内压均有显著影响。该文所得统一解具有广泛的适用性和理论意义,不但可退化为现有公式,而且还能得到系列化的新解答,对组合厚壁圆筒的设计及工程应用有重要参考价值。     

扩容角对圆形巷道岩爆过程的影响

利用FLAC模拟了不同扩容角时圆形巷道的岩爆过程。为了模拟巷道开挖,利用编写的FISH函数删除巷道内部的单元。岩石服从莫尔库仑剪破坏与拉破坏复合的破坏准则,破坏之后呈现应变软化—理想塑性行为。文章的模拟分为3步:首先,将静水压力施加在模型上,直到达到静力平衡状态;然后,利用编写的FISH函数,开挖巷道;最后,计算重新开始,直到达到静力平衡状态。模拟结果表明,随着扩容角的增加,剪切带变宽,岩爆坑变深,破坏单元数目增多,破坏区变大。当扩容角较低时,高剪切应变集中于"狗耳"形岩爆坑位置,剪切带与巷道周边切线之间的夹角较大;当扩容角较高时,高剪切应变集中于巷道周边的一些位置上,剪切带与巷道周边切线之间的夹角较小。该研究结果与Roscoe,Arthur理论相符。     

基于Hoek-Brown准则的岩体弹塑性损伤模型及其应力回映算法研究

为了克服一般弹塑性损伤模型不能反映岩体结构、岩块强度、应力状态的影响以及非线性破坏特征等问题,该文基于广义的Hoek-Brown(HB)屈服准则,考虑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,同时引入修正有效应力原理来考虑孔隙水压力的作用,建立了岩体弹塑性损伤本构模型,给出了损伤变量定义及演化方程。针对该模型在数值求解过程中存在的奇异点问题,从主应力空间推导了弹塑性损伤模型的完全隐式返回映射求解算法,包括弹性预测、塑性修正和损伤修正三个步骤。通过ABAQUS软件的用户子程序接口Umat,实现了弹塑性损伤模型的数值求解过程。采用单轴、三轴压缩试验和隧道算例对模型算法进行验证和分析,结果表明,所建立的HB损伤本构模型能够很好地描述岩体材料的力学特性,在实际岩体工程的损伤模拟中效果令人满意,计算结果对工程有指导意义。     

Implicit stress integration procedure for small and large strains of the Gurson material model

The Gurson material model has broad applications in fracture mechanics, large strain deformations and failure of metals. Void growth and void nucleation are included in the model considered in this paper. An implicit stress integration procedure with calculation of the consistent tangent moduli is developed for the Gurson model. The general 3D deformations and the plane stress conditions are considered. The procedure is robust, simple and computationally efficient, suitable for use within the finite element method (FEM). It represents an application of the governing parameter method (GPM) for stress integration in case of inelastic material deformation. A large strain formulation, based on the multiplicative decomposition of the deformation gradient for material with plastic change of volume and logarithmic strains, is used in the paper. The developed numerical procedure for stress integration is applicable to small and large strains conditions. Solved examples illustrate the main features of the developed numerical algorithm. Copyright © 2002 John Wiley & Sons, Ltd.     

On the elastic plastic initial-boundary value problem and its numerical integration

An interative approach is proposed for the numerical analysis of elastic–plastic continua. This approach gives after convergence an implicit scheme of integration of the evolution problem, and is concerned with elastic-perfectly plastic materials and with hardening standard materials. Under a generalized assumption of positive hardening, the proof of convergence of the iterative solutions is given. Some numerical examples by the finite element method are also discussed.     

A semi‐implicit integration scheme for a combined viscoelastic‐damage model of plastic bonded explosives

This paper presents a new implementation of a constitutive model commonly used to represent plastic bonded explosives in finite element simulations of thermomechanical response. The constitutive model, viscoSCRAM, combines linear viscoelasticity with isotropic damage evolution. The original implementation was focused on short duration transient events; thus, an explicit update scheme was used. For longer duration simulations that employ significantly larger time step sizes, the explicit update scheme is inadequate. This work presents a new semi‐implicit update scheme suitable for simulations using relatively large time steps. The algorithm solves a nonlinear system of equations to ensure that the stress, damaged state, and internal stresses are in agreement with implicit update equations at the end of each increment. The crack growth is advanced in time using a sub‐incremental explicit scheme; thus, the entire implementation is semi‐implicit. The theory is briefly discussed along with previous explicit integration schemes. The new integration algorithm and its implementation into the finite element code, Abaqus, are detailed. Finally, the new and old algorithms are compared via simulations of uniaxial compression and beam bending. The semi‐implicit scheme has been demonstrated to provide higher accuracy for a given allocated computational time for the quasistatic cases considered here. Published 2014. This article is a US Government work and is in the public domain in the USA.     

Research on the stability analysis and design of soil tunnel surrounding rock

The paper first analyzes the failure mechanism and mode of tunnel according to model experiments and mechanical calculation, then discusses the deficiency of taking the limit value of displacement around the tunnel and the size of the plastic zone of surrounding rock as the criterion of stability. So the writers put forward to regard the safety factor of surrounding rock calculated through strength reduction FEM as the criterion of stability, which has strict mechanical basis and unified standard and would not be influenced by other factors. The paper also studies the safety factors of tunnel surrounding rock (safety factors of shear and tension failure) and lining and some methods of designing and calculating tunnels. At last, the writers take the loess tunnel for instance and show the design and calculation results of two-lane railway tunnel.     

Failure analysis of natural gas buried X65 steel pipeline under deflection load using finite element method

A 3D parametric finite element model of the pipeline and soil is established using finite element method to perform the failure analysis of natural gas buried X65 steel pipeline under deflection load. The pipeline is assumed to be loaded in a parabolic deflection displacement along the axial direction. Based on the true stress–strain constitutive relationship of X65 steel, the elastic–plastic finite element analysis employs the arc-length algorithm and non-linear stabilization algorithm respectively to simulate the strain softening properties of pipeline after plastic collapse. Besides, effects of the soil types and model sizes on the maximum deflection displacement of pipeline are investigated. The proposed finite element method serves as a base available for the safety design and evaluation as well as engineering acceptance criterion for the failure of pipeline due to deflection.