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。     

基于Hoek-Brown准则的应变软化模型有限元数值实现研究

研究提出一种Hoek-Brown(H-B)准则应变软化模型的有限元数值实现方法。分析当前不同脆塑性计算方法的合理性,发现塑性位势跌落可正确计算岩石不同类型破坏,而偏应力等比例跌落和最小主应力不变跌落均存在不足。在此基础上,推导写出基于塑性位势跌落的H-B准则脆塑性隐式本构积分算法,及H-B准则理想弹塑性隐式本构积分算法,并采用一系列应力跌落-塑性流动,将H-B准则应变软化模型嵌入有限元软件ABAQUS中。比较应变软化圆隧围岩收敛位移及应力分布的解析解与本文有限元解,发现二者吻合良好,验证了所建H-B准则应变软化模型的正确性。对某薄上覆盖岩层高内水压输水隧洞工程的计算结果表明,相较理想弹塑性模型,所建应变软化模型可正确反映隧洞顶部围岩塑性区贯通引起的整体结构失稳破坏现象,为工程选择衬砌方案提供依据。     

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。     

循环稳定材料的棘轮行为:I.实验和本构模型

在实验分析结果的基础上,对循环稳定材料的室温单轴和非比例多轴循环棘轮行为进行了本构描述,建立了一个简单而合理的、便于工程应用的粘塑性循环棘轮本构模型。给出了模型参数的确定方法,并根据实验获得的单拉应力-非弹性应变关系曲线确定了针对U71Mn 轨道钢材料的参数值。在此基础上,通过对该材料棘轮行为的本构模拟检验了发展模型的预言能力。结果表明,模型具有很好的预测效果,模拟结果与对应的实验结果符合得很好。     

循环稳定材料的棘轮行为：Ⅰ．实验和本构模型

在实验分析结果的基础上，对循环稳定材料的室温单轴和非比例多轴循环棘轮行为进行了本构描述，建立了一个简单而合理的、便于工程应用的粘塑性循环棘轮本构模型。给出了模型参数的确定方法，并根据实验获得的单拉应力．非弹性应变关系曲线确定了针对U71Mn轨道钢材料的参数值。在此基础上，通过对该材料棘轮行为的本构模拟检验了发展模型的预言能力。结果表明，模型具有很好的预测效果，模拟结果与对应的实验结果符合得很好。     

基于Bodner-Partom理论的FGH96合金本构建模研究

为研究某航空发动机涡轮盘典型材料粉末高温合金FGH96高温下的变形特性,基于Bodner-Partom(B-P)统一粘塑性本构理论对其高温下的力学行为进行本构建模。开展了550℃下的单轴拉伸及低周疲劳试验,利用Levenberg-Marquardt算法对模型参数进行了优化识别。采用隐式积分算法将本构方程离散为差分方程组,推导了一致切线刚度矩阵,为提高积分过程的精度和可靠性,引入以非弹性应变增量为度量的积分步长控制策略。通过用户子程序接口UMAT将B-P模型引入到ABAQUS有限元软件中进行数值模拟。结果表明:高温下FGH96材料表现出一定的率相关性及循环软化特性,模拟曲线与试验结果平均相对误差在10%以内,具有较好的一致性,说明B-P模型能够较好地模拟FGH96合金高温下的变形特性,验证了本实验模型与UMAT子程序的准确性。     

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。     

基于不可逆热力学的Ni-Ti合金动态本构模型及其有限元实现

为了准确描述Ni-Ti形状记忆合金在高应变率下的动态压缩力学行为,基于不可逆热力学理论框架假定了两个内变量表征Ni-Ti合金应力诱发马氏体相变与塑性屈服的不可逆变形过程,分别推导了马氏体相变与塑性屈服演化规律的主控方程,构建了Ni-Ti合金的三维动态本构模型。根据材料单轴动态压缩实验的应力-应变曲线并采用最小二乘法对本构参数进行了优化识别,然后采用应力补偿更新算法,通过隐式用户子程序接口UMAT将动态本构模型嵌入ABAQUS有限元软件,实现了Ni-Ti合金在高应变率下动态压缩力学行为的数值模拟。通过比对发现,模拟结果与实验数据吻合良好,验证了动态本构模型与UMAT子程序的准确性。本工作为Ni-Ti合金在高速冲击、切削等极端条件下的工程应用奠定了基础。     

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。     

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。     

考虑界面结合的SiCP/6061Al 复合材料时间相关棘轮行为的三维有限元分析

采用多颗粒三维单胞模型和复合材料细观有限元分析方法,借助先进循环黏塑性本构模型的有限元实现,对SiC颗粒增强6061Al复合材料的室温、高温时间相关单轴棘轮行为进行数值模拟。讨论了颗粒排列方式和界面结合状态的变化对复合材料棘轮行为的影响;同时,分析了复合材料中基体和界面的微观变形特征及其演变规律;最后,选取一组合理的微结构参数,对复合材料的时间相关棘轮行为进行了数值模拟,并通过与已有实验结果的比较,检验了有限元分析的合理性。结果表明：多颗粒代表性体积单元能够反映复合材料更多的微观细节;颗粒排列方式的变化显著影响复合材料的整体棘轮行为;界面结合状态越好,产生的棘轮变形越小;具有合理参数值的弱界面模型给出的时间相关棘轮变形预测结果比完好界面模型的结果更接近实验值。     

SiCP/6061Al合金复合材料高温时相关棘轮行为的数值模拟

基于颗粒增强金属基复合材料的单球形颗粒模型和轴对称二维6节点三角形单元, 利用ABAQUS对T6热处理后的两种体积分数的SiC_P/6061Al合金复合材料的高温(300℃)单轴拉伸行为和单轴棘轮行为进行数值模拟。在有限元模拟中, 对基体采用了新发展的、 能够合理描述材料棘轮行为的黏塑性循环本构模型。数值模拟表明: 本文中建立的有限元分析模型对颗粒增强金属基复合材料的高温单轴棘轮行为及其时间相关特性得到了较为合理的描述, 模拟结果与实验吻合较好。模拟结果同时还揭示了复合材料内循环变形行为在细观层次上的不均匀性和复杂性。      

Numerical integration and FEM-implementation of a viscoplastic Chaboche-model with static recovery

This paper is concerned with the implementation of a viscoplastic material model of the Chaboche type in the framework of the finite element method (FEM). The equations of the used constitutive law, that incorporates isotropic hardening, back stress evolution with static recovery terms and drag stress evolution, are introduced. A representation of their numerical integration using the implicit backward Euler method under the assumption of small deformations and an isothermal formulation follows. The use of the backward Euler method leads to a nonlinear algebraic system of three equations, which is solved by a combination of the Pegasus method and a fixed-point iteration. After considering the accuracy of the presented integration algorithm in form of iso-error maps, the derivation of the consistent viscoplastic tangent operator is shown. The integration scheme and the calculation of the consistent viscoplastic tangent operator are implemented in the commercial finite element code ABAQUS, using the possibility of the user-defined material subroutine (UMAT). Finally a numerical example in form of a notched bar under tension is presented.     

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.     

Aspects of the formulation and finite element implementation of large strain isotropic elasticity

The paper presents a formulation of isotropic large strain elasticity and addresses some computational aspects of its finite element implementation. On the theoretical side, an Eulerian setting of isotropic elasticity is discussed exclusively in terms of the Finger tensor as a strain measure. Noval aspects are a direct representation of the Eulerian elastic moduli in terms of the Finger tensor and their rigorous decomposition into decoupled volumetric and isochoric contributions based on a multiplicative split of the Finger tensor into spherical and unimodular parts. The isochoric stress response is formulated in terms of the eigenvalues of the unimodular part of the Finger tensor. A constitutive algorithm for the computation of the stresses and tangent moduli for plane problems is developed and applied to a model problem of rubber elasticity. On the computational side, the implementation of the constitutive model in three possible finite element formulations is discussed. After pointing out algorithmic techniques for the treatment of incompressible elasticity, several numerical simulations are presented which show the performance of the proposed constitutive algorithm and the convergence behaviour of the different finite element fomulations for compressible and incompressible elasticity.     

An implicit algorithm using explicit correctors for the kinematic hardening model with multiple back stresses

This paper presents an efficient mathematical algorithm for a class of non‐linear kinematic hardening models with multiple back stresses, as an extension of the implicit integration algorithm for a single back stress hardening model. Explicit formulations for general three‐dimensional stress states as well as plane stress and plane strain are given. The new formulation is implemented in a general‐purpose finite element code, ABAQUS, and is verified by comparison with the existing formulation for the single back‐stress constitutive model. Comparison is also made with the experimental results obtained from a plate containing a circular hole subjected to cyclic loading, demonstrating the validity of new method. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite element implementation of a macromolecular viscoplastic polymer model

This paper presents a time‐integration method for a viscoplastic physics‐based polymer model at finite strains. The macromolecular character of the model resides in (i) the viscoplastic law based on a double‐kink molecular mechanism, and (ii) a full chain network model inspired by rubber elasticity to describe the large‐strain orientation hardening. A back stress enters the constitutive model formulation. Essential aspects of a three‐dimensional finite‐element implementation are outlined, the main novelty being in the back stress formulation. The computational efficiency and accuracy of the algorithm are examined in a series of parameter studies. In addition, because a co‐rotational formulation of the constitutive equations is employed using the Jaumann rate in the hypoelastic equation and the back stress evolution equation a detailed analysis of stress oscillations is carried out up to very large strains in simple shear. Subsequently, three‐dimensional FE analyses of compression with friction and instability propagation in tension are used as a means to demonstrate the robustness of the implementation and the potential occurrence of stress oscillations and shear bands in large‐strain analyses. Copyright © 2013 John Wiley & Sons, Ltd.     

Uniaxial and non-proportionally multiaxial ratcheting of U71Mn rail steel: experiments and simulations

The ratcheting and strain cyclic characteristics of U71Mn rail steel were experimentally researched under uniaxial and non-proportionally multiaxial cyclic loading at room temperature. The effects of cyclic strain, stress and their histories on strain cyclic characteristics and ratcheting were studied, respectively. It is shown that: U71Mn rail steel exhibits a cyclic stabilization and non-memorization for previous loading history under strain cycling; however, the ratcheting of the material depends greatly not only on the current values of mean stress and stress amplitude, but also on their histories; the non-proportionality of multiaxial loading path only causes a negligible additional hardening for the material. Based on the Ohno–Wang non-linear kinematic hardening model [Int. J. Plast. 9 (1993) 375, 391], the uniaxial and multiaxial ratcheting behaviours of the material were simulated by a visco-plastic constitutive model. The simulated results are in good consistence with the experimental ones.