Simulation of the stochastic damage evolution process under low cycle fatigue by the finite element method

A numerical simulation of stochastic damage evolution process in the condition of low cycle fatigue loading is discussed. The relations between damage variables and micro-cracks are obtained by means of the micro-mechanics model of the representative volume element proposed by Lemaitre and Dufailly^[10]. The stochastic initial damage values are introduced in consideration of the inherent micro-defects in materials. The model combined with a finite element method is applied to simulate the damage evolution process under low cycle fatigue loading. The micro-cracks on the sur face of a specimen of 19Mn6 alloy steel are measured with a replica technique. The numerical results show that the nonhomogeneity of damage and the localization of the fatigue failure are well shown by the proposed simulations, and the fatigue lives are reasonably predicted.     

Combination of fracture and damage mechanics for numerical failure analysis

A new approach for the analysis of crack propagation in brittle materials is proposed, which is based on a combination of fracture mechanics and continuum damage mechanics within the context of the finite element method. The approach combines the accuracy of singular crack-tip elements from fracture mechanics theories with the flexibility of crack representation by softening zones in damage mechanics formulations. A super element is constructed in which the typical elements are joined together. The crack propagation is decided on either of two fracture criteria; one criterion is based on the energy release rate or the J-integral, the other on the largest principal stress in the crack-tip region. Contrary to many damage mechanics methods, the combined fracture⧹damage approach is not sensitive to variations in the finite element division. Applications to situations of mixed-mode crack propagation in both two- and three-dimensional problems reveal that the calculated crack paths are independent of the element size and the element orientation and are accurate within one element from the theoretical (curvilinear) crack paths.     

低周疲劳随机损伤过程的有限元模拟

讨论了一种低周疲劳下随机损伤演变过程 数值模拟方法，借助于Ｌｅｍａｉｔｒｅ＆Ｄｕｆａｉｌｌｙ给出的代表性体元的微观力学模型，建立了损伤与微裂纹尺寸的关系，采用随机初始损伤反映材料中固的的微缺陷，将所得模型与有限元结合对低周疲劳损伤过程进行了数值模拟。     

New approach based on continuum damage mechanics with simple parameter identification to fretting fatigue life prediction

A new continuum damage mechanics model for fretting fatigue life prediction is established. In this model, the damage evolution rate is described by two kinds of quantities. One is associated with the cyclic stress characteristics obtained by the finite element(FE) analysis, and the other is associated with the material fatigue property identified from the fatigue test data of standard specimens. The wear is modeled by the energy wear law to simulate the contact geometry evolution. A two-dimensional(2D) plane strain FE implementation of the damage mechanics model and the energy wear model is presented in the platform of ABAQUS to simulate the evolutions of the fatigue damage and the wear scar. The effect of the specimen thickness is also investigated. The predicted results of the crack initiation site and the fretting fatigue life agree well with available experimental data. Comparisons are made with the critical plane SmithWatson-Topper(SWT) method.     

基于构型力内变量的界面损伤问题研究

本文基于材料构型力的基本理论和损伤力学中含有内变量的热力学框架,提出了新的损伤变量定义方式,为研究界面损伤问题提供了一种新思路。首先,基于双相弹性体的能量分析,给出界面材料构型力表达式,通过构型力的离散化方法,实现了其在有限元中的数值计算。其次,定义构型力为界面损伤内变量,进而提出一种新的损伤演化模型,并采用刚度劣化的方法,对该界面损伤模型进行数值实现。最后,通过对复合材料界面损伤问题（有裂纹或无裂纹）进行数值模拟,分析了其界面损伤发展趋势,探讨了此模型的合理性和优越性。基于构型力内变量的界面损伤模型,可为研究复合材料的界面损伤失效问题提供一种普适性的方法。     

一个修正的金属材料低周疲劳损伤模型

疲劳破坏是金属最常见的失效形式之一。基于连续损伤力学理论和能量原理,本文提出了一个修正的金属材料低周疲劳损伤演化方程,该方程综合考虑了材料的塑性强化、微裂纹闭合效应等因素对损伤累积的影响。将修正后的损伤演化方程以UMAT子程序的形式导入有限元计算软件ABAQUS之中,建立了疲劳损伤的计算模型,并以铝合金7050-T7451为例对该模型的有效性和适用性进行了验证。     

基于连续体损伤理论的硼钢高温成形极限确定法

为了应对节能减排及汽车安全性的双重要求,先进高强钢的开发和应用受到愈来愈高的重视. 超高强度钢板热冲压成形技术是减轻车身重量、提高汽车抗冲击和防撞性能的重要途径,目前已经成为世界汽车制造行业的热门技术. 成形极限是硼钢热冲压成形过程中一个非常重要的表征参数,但由于高温半球形凸模胀形试验(Nakazima) 的复杂性造成实验测试面临诸多困难. 针对硼钢热冲压成形过程特点,提出将韧性损伤模型与有限元数值模拟技术结合起来预测硼钢高温成形极限的方法. 在连续体损伤力学基础上,建立了考虑有效应力和等效塑性应变对微孔损伤影响的勒迈特(Lemaitre) 韧性损伤演化方程,在损伤耗散势函数中引入了等效塑性应变因子,从而寻找到能够准确反映硼钢在奥氏体状态下的成形特性的勒迈特耗散势函数. 选取基于遗传算法的基于非支配排序的多目标优化算法(NSGA-II) 与有限元分析软件“FORGETM” 相结合的方法优化韧性损伤模型中材料的损伤因子,并利用优化后的损伤因子准确预测到板料成形过程的拉伸失稳和断裂现象. 将建立的韧性损伤模型引入到硼钢高温半球形凸模胀形有限元仿真模型中,通过预测的成形极限与实验测定结果的比较,验证了所提韧性损伤模型预测硼钢高温成形极限的可靠性.      

混凝土冻融损伤本构模型研究

基于各向同性连续损伤力学理论,以损伤条件下的弹性模量和泊松比为变量,基于Ottosen理论模型建立了混凝土冻融损伤破坏准则,并以Ottosen本构理论模型为基础,利用建立的冻融损伤破坏准则构建了混凝土冻融损伤本构模型,并编制了本构模型有限元程序,经过试验验证模型计算结果较为准确,为有限元计算和冻融作用后混凝土结构模拟应...     

基于一类非局部宏-微观损伤模型的裂纹模拟

结合近场动力学和统一相场理论的基本思想, 最近提出了一类非局部宏-微观损伤模型, 为固体裂纹扩展模拟提供了新途径. 本文在此基础上改进了微观损伤准则, 并给出损伤的$\bar{\lambda}-\ell$语言以刻画固体破坏过程中位移场的不连续程度. 在改进模型中, 首先根据两物质点(即物质点对)之间的变形量, 基于相对临界伸长量的历史最大超越程度, 给出表征物质键性能退化的微细观损伤. 进而, 对影响域内的物质键损伤进行空间局部加权平均, 获得宏观拓扑损伤. 通过引入能量退化函数, 建立基于能量的损伤与宏观拓扑损伤之间的关系, 由此将其嵌入连续损伤力学基本框架, 形成了问题求解的基本方程. 该模型是一类非局部化模型, 可采用有限单元法进行离散求解, 避免了经典局部损伤力学所面临的网格敏感性问题. 文中, 进一步将其应用于具有强非线性回弹特性的裂纹扩展模拟问题. 实例分析表明, 本文方法不仅可以把握裂纹扩展模式, 而且能够定量刻画裂纹扩展过程中的载荷-变形关系. 最后指出了需要进一步研究的问题.      

Monitoring structural damage of components using an effective modulus approach

This paper describes a novel nondestructive damage detection method that was developed to study the influence of a crack on the dynamic properties of a cantilever beam subjected to bending. Experimental measurements of transfer functions for the cracked cantilever beam revealed a change in the natural frequency with increasing crack length. A finite element model of a cracked element was created to compute the influence of severity and location of damage on the structural stiffness. The proposed model is based on the response of the cracked beam element under a static load. The change in beam deflection as a result of the crack is used to calculate the reduction in the global component stiffness. The reduction of the beam stiffness is then used to determine its dynamic response employing a modal analysis computational model. Euler–Bernoulli and Timoshenko beam theories are used to quantify the elastic stiffness matrix of a finite element. The transfer functions from both theories compare well with the experimental results. The experimental and computational natural frequencies decreased with increasing crack length. Furthermore the Euler–Bernoulli and Timoshenko beam theories resulted in approximately the same decrease in the natural frequency with increasing crack length as experimentally measured.     

延性金属层裂模型比较

在平面一维弹塑性流动有限差分计算程序中加入4种延性金属层裂模型，对平板撞击层裂实验进行数值模拟。结果表明:简单最大拉伸应力模型和简单损伤累积模型能定性反映层裂的物理现象，由于忽略损伤对本构的影响，计算结果和实验有偏差，但模型要求参数较少，对于一些精度要求不是很高的工程问题，可以采用；从材料损伤断裂物理本质出发，采用微损伤统计方法得到的NAG模型和封加波损伤度函数模型，能很好地再现实测的自由面速度剖面,数值计算结果与实验吻合很好。     

Coupled viscoplasticity damage constitutive model for concrete materials

A coupled viscoplasticity damage constitutive model for concrete materials is developed within the framework of irreversible thermodynamics.Simultaneously the Helmholtz free energy function and a non-associated flow potential function are given, which include the internal variables of kinematic hardening,isotropic hardening and dam- age.Results from the numerical simulation show that the model presented can describe the deformation properties of the concrete without the formal hypotheses of yield criterion and failure criteria,such as the volume dilatancy under the compression,strain-rate sen- sitivity,stiffness degradation and stress-softening behavior beyond the peak stress which are brought by damages and fractures.Moreover,we could benefit from the application of the finite element method based on this model under complex loading because of not having to choose different constitutive models based on the deformation level.     

基于微态方法的耦合韧性损伤的弹塑性本构模型

基于广义连续介质力学提出了一个热力学一致性的耦合微态韧性损伤的弹塑性本构模型。该模型遵循Forest的微态方法,在有限变形中提出引入额外的微态损伤因子及其一阶梯度以考虑材料的内部特征尺度。通过广义虚功原理得到了微态损伤的补充控制方程,对亥姆霍兹自由能进行扩展,得到了新的包含微态损伤变量的损伤能量释放率,在微态损伤的正则化作用下,采用隐式迭代更新局部损伤和应力等状态变量。基于Galerkin加权余量法,推导了以传统位移和微态损伤为基本未知量的有限元列式。利用该数值模型,对DP1000材料的单向拉伸实验和十字形零件的冲压实验进行了应变局部化与材料断裂的有限元分析。结果表明,该微态弹塑性损伤模型可以得到一致的有限元模拟响应曲线并收敛到实验曲线,从而避免发生网格依赖性问题。     

Statistical detection of structural damage based on model reduction

This paper proposes a statistical method for damage detection based on the finite element （FE） model reduction technique that utilizes measured modal data with a limited number of sensors. A deterministic damage detection process is formulated based on the model reduction technique. The probabilistie process is integrated into the deterministic damage detection process using a perturbation technique, resulting in a statistical structural damage detection method. This is achieved by deriving the first- and second-order partial derivatives of uncertain parameters, such as elasticity of the damaged member, with respect to the measurement noise, which allows expectation and covariance matrix of the uncertain parameters to be calculated. Besides the theoretical development, this paper reports numerical verification of the proposed method using a portal frame example and Monte Carlo simulation.     

Bi-variable damage model for fatigue life prediction of metal components

Based on the theory of continuum damage mechanics,a bi-variable damage mechanics model is developed,which,according to thermodynamics,is accessible to derivation of damage driving force,damage evolution equation and damage evolution criteria. Furthermore,damage evolution equations of time rate are established by the generalized Drucker’s postulate. The damage evolution equation of cycle rate is obtained by integrating the time damage evolution equations,and the fatigue life prediction method for smooth specimens under repeated loading with constant strain amplitude is constructed. Likewise,for notched specimens under the repeated loading with constant strain amplitude,the fatigue life prediction method is obtained on the ground of the theory of conservative integral in damage mechanics. Thus,the material parameters in the damage evolution equation can be obtained by reference to the fatigue test results of standard specimens with stress concentration factor equal to 1,2 and 3.     

Ductile damage evolution under triaxial state of stress: theory and experiments

In this paper, the continuum damage mechanics (CDM) model formulation proposed by [Eng. Fract. Mech. 58(1/2) (1997) 11] has been validated against ductile damage evolution experimentally measured in A533B low alloy steel under various stress triaxiality conditions. A procedure to identify the model parameters has been defined first. Then, the model has been used to simulate, via finite element analysis (FEA), tests on notched flat rectangular bars with different notch radii. The experiments and the FEA predictions are finally compared with each other. The results presented here confirm the transferability of damage parameters definition and the potential of the proposed damage model in predicting ductile failure occurrence in structures and components under multi-axial state of stress loading conditions.     

Variational modelling of diffused and localized damage with applications to fiber-reinforced concretes

A variational model for the evolution of damage in elastic materials is proposed, which is based on incremental energy minimization. Analytical solutions are determined in the one-dimensional case of a tensile bar, and the issue of their stability is addressed. Analytical results have given insights into the properties that elastic and damage energies must have in order that specific evolution processes are captured, such as diffuse damaging, progressive damage localization or brutal failure. Accordingly, expressions of elastic and damage energies are proposed aimed at reproducing the evolution of damage observed in high-performance fiber-reinforced concretes, which typically exhibit initial micro-cracking and subsequent macro-crack opening. Tensile tests on bone-shaped samples and three-points bending tests are reproduced, by implementing the model in a finite element code, and numerical results are compared with experimental evidences.     

基于卷积非粘滞阻尼模型的超高层结构风效应分析

有限元方法中相对于对结构质量与刚度特性的描述,结构阻尼的描述仍具有较大的模糊性。随着新型建筑材料与复杂结构体系的发展,以及对计算机模拟要求的提高,阻尼作用的机理与相应阻尼模型的研究成为值得关注的问题。基于一种阻尼力与质点速度历程相关的卷积非粘滞阻尼模型,采用微分求积求解算法,对一个大型复杂超高层建筑结构的风振响应进行了分析,并与常用的比例粘滞阻尼模型进行了对比。对卷积非粘滞阻尼力模型系统的响应特征进行了分析,特别是该模型的松弛效应对结构响应的影响。另外,作为将这种新阻尼模型应用于实际工程的一次探索,本文采用微分求积算法,建立了一套可将该阻尼模型及其求解算法嵌入通用有限元软件的求解系统,可用于复杂结构的动力响应分析。     

Three-dimensional analysis of reinforced concrete frames based on lumped damage mechanics

This paper presents a general formulation for the analysis of reinforced concrete frames. The model has been developed within the framework of lumped damage mechanics. This is a theory based on the methods of continuum damage mechanics, fracture mechanics and the concept of plastic hinge. The paper also describes the numerical implementation of the model in the finite element programs. The model is evaluated by the numerical simulation of three tests reported in the literature. Two of them deal with a column subjected to variable axial loads and biaxial flexure. The third is a two-story three-dimensional frame subjected to earthquake loadings outside the principal directions of the frame.