Numerical investigation of matrix cracking propagation in cross‐ply laminated composites subjected to three‐point bending load using concurrent multiscale model

The purpose of the present study is to analyze fiber‐matrix debonding and induced matrix cracking formation as two major micromechanical damage modes in cross‐ply composite laminates using a two‐dimensional numerical approach. To this aim, the cross‐ply laminates containing 90‐degree layers are modeled, where the fibers are arranged randomly in transverse plies. Damage modes in this numerical model are simulated by the cohesive surface method. The performed analyses reveal that in the laminates with 90‐degree layers located in the outer positions, the primary micro damage mode is micro matrix cracking which is initiated from the fiber‐matrix debonding damage mode and will be followed by matrix cracking. The main benefit of the present study in comparison to other numerical methods is proposing a virtual test method for damage analysis of different cross‐ply laminates in which, the matrix cracking formation will emerge physically in a random and antisymmetric pattern similar to the experimental observations.     

Prediction of fragment size and ejection distance of masonry wall under blast load using homogenized masonry material properties

The fragment hazard resulting from a nearby explosion is a major concern in the design of structures which may be subjected to blast loads. This paper presents a predictive method based on the theories of continuum damage mechanics and mechanics of micro-crack development, and numerical simulation to determine the probabilistic fragment size distribution and the launch distances. Theoretical derivations are presented to calculate fragment distribution. The fragmentation process is modeled according to the crack initiation and propagation, which depend on the material damage levels and are estimated using continuum damage mechanics theory. The proposed method involves two steps. First a finite element model is developed to estimate the material damage, fragment distribution and the ejection velocity. Then a simple algorithm is used to predict the fragment trajectory and the launch distance based on the fragment size and the ejection velocity. A masonry wall is used as an example in this study. The wall is modeled with both the distinctive consideration of the brick and mortar material properties and the homogenized masonry material properties. The reliability and efficiency of using the homogenized masonry material model in predicting the masonry wall damage and fragmentation are proven. The program AUTODYN is used in this study to conduct the numerical simulations with the proposed models linked to it as user subroutines. The numerical results indicate that the masonry fragments approximately follow the Weibull distribution, which is consistent with some empirical fragment distributions. The proposed method avoids using erosion technique, which inevitably results in a loss of fragment mass, and avoids discretizing the structure into particles or predefining the failure planes, which may lead to unrealistic prediction of damage propagation and evolution and therefore inaccurate fragmentation process and fragment size distributions.     

Verification of numerical determination of carrying capacity of large rolling bearings with hardened raceway

For the purpose of the numerical analysis of the actual carrying capacity of rolling contacts in large rolling bearings with surface-hardened raceways, an elasto-plastic constitutive model was used which links the mechanics of material damage with the isotropic and kinematic hardening or softening.A damage material model, implemented into a commercial finite element program, allows us to monitor the elastic strain, plastic strain increase, stress changes and material damage growth, which are closely related to the number of load cycles. In this way, the location and the time of occurrence of bearing raceway damage can be determined along with the growth of damage up to the point when a microcrack is formed. In other words, low cycle life of rotational rolling connection can be assessed.The paper presents the material model, numerical analysis of the actual carrying capacity of the rolling contact in single-row ball bearings and the verification of the numerical material model with experimental results of low cycle carrying capacity.     

基于小波包能量曲率差法的桥梁损伤识别试验研究

针对各种损伤识别指标中,小波包能量曲率差法仅有数值仿真、未经试验验证,尤其缺少实际工程验证问题,用数值模拟验证该方法识别结构损伤的有效性;利用沧州子牙河新桥替换下的梁体,进行两种工况损伤模拟。通过测试完好与损伤状态各点加速度响应,用小波包能量曲率差法识别损伤,考察小波函数和分解层数对识别效果的影响。结果表明,该方法有效,并可应用于实际工程。     

Simulation of elevated temperature fatigue damage evolution using the finite element method for near alpha titanium alloy

The numerical estimation of evolving damage under low cycle fatigue loading condition has been performed in the near‐α titanium alloy IMI‐834 at 823 K temperature. By using the experimentally determined parameters as input, numerical simulation of fatigue damage has been performed on round specimens using finite element analysis. Coupled deformation‐damage model has been established for this alloy for simulation of damage evolution in a three‐dimensional cylindrical low cycle fatigue test specimen. The fatigue damage estimates from numerical simulation are observed to be in close agreement with the experimental results.     

基于能量的弹塑性损伤实用本构模型

建立一个实用的弹塑性损伤本构模型。在有效应力空间采用经验公式计算塑性变形,能将模型塑性部分与损伤部分解耦,降低模型的数值处理复杂性,同时大大简化模型塑性应变的计算。结合不可逆热力学理论,基于损伤能量释放率建立损伤准则,损伤能量释放率由修正后的弹性Helmholtz自由能导出,模型中将弹性Helmholtz自由能分解为应力球量部分和应力偏量部分,将其应力球量部分产生的损伤取为零,同时根据应力状态引入折减系数对其应力偏量部分进行修正,使得模型能较为准确的模拟混凝土材料在双轴加载下的本构行为。将应力张量谱分解为正、负两部分以分别定义材料受拉、受压损伤演化,并采用受拉损伤变量、受压损伤变量分别模拟混凝土材料在拉、压加载下的本构特性。引入一个加权损伤变量使得模型能较准确的反映混凝土材料的“拉-压软化效应”。最后该文给出初步试验验证,证明了该文模型的有效性。     

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

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。     

Modelling large crack propagation: from gradient damage to cohesive zone models

Continuum Damage Mechanics and cohesive zone models are both prone to model large crack propagation inside quasi-brittle materials. Comparing the advantages of the formulations, the latter could be advantageously applied in cases where the crack path is known a priori while the former implicitly encompasses crack path prediction but requires more complex computations involving nonlocal interactions. In order to assess the acceptability of such a hierarchy for industrial studies, it is necessary that the predictions coincide quantitatively. Starting from a gradient damage model in a one-dimensional context, a cohesive law is derived as the asymptotic response of the damage model for vanishing nonlocal length scale. The cohesive law is hence independent of the nonlocal length scale, which is consistent with the fact that it ignores details characteristic of the ??best-estimate?? damage approach. Besides, the existence of such a limit ensures that the damage model is not much sensitive to a small nonlocal length scale, which then appears rather as a numerical regularisation parameter. A numerical comparison between the damage model and its asymptotic cohesive law is then carried out for large bi-dimensional crack propagation. The computed responses remain close to each other although some small discrepancies arise probably related to the damage spread resulting from the stress distribution in the vicinity of the crack tip: the hierarchy strategy is thus validated.     

框架结构损伤定位的比例柔度矩阵分解法试验研究

提出了基于比例柔度矩阵LU分解的结构损伤定位方法。该方法从结构振动响应入手,首先识别出结构前几阶模态振型和频率,构建结构比例柔度矩阵;然后对损伤前后的比例柔度矩阵差进行LU分解;最后基于U矩阵和曲率方法构建损伤指标对损伤进行定位。基于某20层框架结构进行了数值模拟损伤定位研究;并在实验室设计、建造一个6层集中质量剪切型框架模型,基于该模型分别进行了振动台试验和脉冲激励试验。模拟和试验下的单损伤和多损伤工况结果均表明:提出的方法能准确地对结构损伤进行定位。该方法只需要损伤前后测点的振动响应数据,不需要结构有限元模型,避免了复杂的结构有限元模型建模和模型修正工作;并且构建一个满足精确度的比例柔度矩阵只需要结构的前几阶低阶模态参数,而低阶参数的识别准确性相对较高,这些优点均为该方法的工程应用奠定了基础。     

A continuum damage mechanics method for fracture simulation of quasi‐brittle materials

This paper addresses a novel continuum damage‐based method for simulating failure process of quasi‐brittle materials starting from local damage initiation to final fracture. In the developed method, the preset characteristic length field is used to evaluate damage instead of element, which is used to reduce the spurious sensitivity. In addition, damage is only updated in the most dangerous location at a time for considering stress redistribution due to damage evolution, which is used to simulate competitive fracture process. As cases study, representative numerical simulations of two benchmark tests are given to verify the performance of the developed continuum damage‐based method together with a used damage model. The simulation results of the crack paths for two concrete specimens obtained from the developed method matched well with the corresponding experimental results. The results show that the developed continuum damage‐based method is effective and can be used to simulate damage and fracture process of brittle or quasi‐brittle materials. And the simulation results based on the developed method depend only the preset characteristic length field and not grid mesh.     

Numerical analysis of low cycle fatigue for welded joints considering welding residual stress and plastic damage under combined bending and local compressive loads

The numerical analysis of low cycle fatigue of HTS‐A steel welded joints under combined bending and local compressive loads are implemented using the damage mechanics approach. First, a finite element numerical simulation of the welding process is employed to extract the welding residual stresses, which are then imported as initial stresses in the subsequent fatigue analysis. Second, a multiaxial fatigue damage model including damage coupled elasto‐plastic constitutive equations and plastic damage evolution formulation is applied to evaluate the mechanical degradation of the material under biaxial fatigue loads. Further, the fatigue lives of the HTS‐A steel welded joints are computed and compared with the experimental results from literature. A series of predicted load‐life curves clearly illustrates the variation of fatigue lives along with the combined loadings. Finally, the effects of local compression on accumulated plastic strain and fatigue damage are studied in detail. It is revealed that the local compression induces a damage competition between two critical zones.     

Damage process in heterogeneous materials analyzed by a lattice model simulation

Several materials of technological interest could be considered as heterogeneous and their random nature can be accounted to be the cause of the nonlinear behavior. The quantitative evaluation of damage in materials subjected to stress or strain states has great importance due to the critical character of these phenomena, which, at a certain point, may suddenly give rise to catastrophic failure. In previous studies, Carpinteri and his coworkers have presented different aspects of the damage process characterization in heterogeneous materials. Three of these aspects demand our attention: (i) the brittleness number to measure the brittleness level of the structure under investigation; (ii) the fractal dimension in which the damage process develops; and (iii) the global indexes obtained for the Acoustic Emission (AE) analysis. In the present work, a version of the discrete element method formed by bars is used to explore these concepts. A set of quasi-brittle material specimens is simulated and, when it is possible, the numerical results are compared with experimental data. Moreover, a discussion of the obtained results aids to better understand the behavior of this kind of materials, describing the numerical method as a viable tool to extract information from experimental tests on the damage process.     

基于分布式应变模态残差统计趋势的大跨斜拉桥损伤识别策略

近几年新兴的分布式测试技术得到了飞速发展,使得基于这类应变测试数据的损伤识别方法的研发显得尤为迫切。本文首先引入了分布式应变模态差损伤指标,并利用此指标对一大跨斜拉桥进行了损伤识别研究,分析了不同的测试环境、随机激励及损伤程度等因素对损伤识别效果的影响。然后对同种健康状态下的结构在不同测试环境条件下进行多次辨识,利用统计趋势分析和概率置信准则,提出了基于准分布式应变模态残差统计趋势的损伤识别策略。数值计算表明：所提策略很好的降低了各种随机干扰的不利影响,对斜拉桥主箱梁上发生损伤的多处单元都能准确识别出来,很好的解决了传统模态法损伤指标对结构早期轻微损伤不敏感的缺陷,避免了损伤淹没和误判现象。     

基于不变环境振动的结构损伤识别方法

建立了受随机外力激励作用的损伤识别理论模型和计算方法 ,提出一种在线结构损伤识别方法。讨论一个15层框架结构 ,数值仿真结果表明 ,该方法具有较高的辨别率和计算精度。它能够使用在桥梁和建筑的健康监测中。     

一种新的混凝土各向异性弹塑性损伤本构模型及其数值实施

该文的目的是建立一种新的、相对简单的混凝土各向异性塑性损伤本构模型,以方便的模拟混凝土结构的破坏行为。为了更好地描述混凝土在拉、压荷载作用下的不同损伤机制,建立了拉、压不同的两种损伤演化方程,用于确定各向异性的拉、压损伤变量。另外,根据应变等效假设,假定有效构型和损伤构型的应变相等,该方法不仅大大简化了模型的推导过程,而且可方便的通过解耦算法进行有效应力和损伤及名义应力的计算,也即塑性部分计算可通过现有的隐式算法实现,损伤部分及名义应力的计算则可通过较为简便的显式算法实现,从而可大大提高计算效率。模型结果与试验结果的对比分析表明：该模型能较好地描述混凝土在三维应力状态下的非线性行为;对双边开口四点弯曲梁试件的模拟也表明：该模型能反应混凝土损伤各向异性的特点,计算结果相比ABAQUS软件自带的混凝土损伤塑性本构模型(CDP模型)更符合实际情况,计算效率也更高。     

基于伪谱法合成零偏移距记录的结构损伤探测与成像

该文讨论了如何利用伪谱法合成零偏移距记录进行结构损伤探测与偏移成像。从二维标量波动方程出发推导了不同情况下的数值计算公式。采用反周期扩展法对边界吸收问题做了有效处理,消除了边界反射产生的假象和干扰波场。用波场外推法合成得到了能适应复杂损伤形态和横向变速介质的零偏移距记录。根据波动方程分析了伪谱法的数值频散性、奇异性以及波场形态、位移、振幅、能量、动应力集中系数等力学特征,通过波动方程的位移解得到波场快照图和时间剖面图,实现了结构损伤可视化探测与识别。数值算例证明了伪谱法偏移成像的适用性。     

Numerical simulation of cementitious materials degradation under external sulfate attack

A numerical methodology is proposed in this paper to simulate the degradation of cementitious materials under external sulfate attack. The methodology includes diffusion of ions in and out of the structure, chemical reactions which lead to dissolution and precipitation of solids, and mechanical damage accumulation using a continuum damage mechanics approach. Diffusion of ions is assumed to occur under a concentration gradient as well as under a chemical activity gradient. Chemical reactions are assumed to occur under a local equilibrium condition which is considered to be valid for diffusion controlled reaction mechanisms. A macro-scale representation of mechanical damage is used in this model which reflects the cracking state of the structure. The mechanical and diffusion properties are modified at each time step based on the accumulated damage. The model is calibrated and validated using experimental results obtained from the literature. The usefulness of the model in evaluating the mineralogical evolution and mechanical deterioration of the structure is demonstrated.     

基于小波包的数值积分误差分析及消除方法

在结构损伤识别的时域法研究中，数值积分的误差将直接影响反演参数结果的精度。积分初值的未知、消除数值积分引入的误差是结构损伤反演计算中信号处理的难题。针对积分初值、数值积分积累误差和数值积分引入的偏移误差进行了理论分析，得出此类误差均具有低频特性的性质，可作为信号低频噪声进行处理。根据数值计算误差的特点分析及小波包多尺度、高分辨的特性，设计了一种基于小波包的滤波器，较好地解决了消除数值积分计算引入误差的问题。通过四层剪切结构模型算例验证，结构刚度反演误差由73％-32．2％降低到0．6％-0．24％，获得了较理想的效果。该方法同样可以用于其它领域的数值处理。     

A non‐local continuum damage approach to model dynamic crack branching

Dynamic crack‐branching instabilities in a brittle material are studied numerically by using a non‐local damage model. PMMA is taken as our model brittle material. The simulated crack patterns, crack velocities, and dissipated energies compare favorably with experimental data gathered from the literature, as long as the critical strain for damage initiation as well as the parameters for a rate‐dependent damage law are carefully selected. Nonetheless, the transition from a straight crack propagation to the emergence of crack branches is very sensitive to the damage initiation threshold. The transition regime is thus a particularly interesting challenge for numerical approaches. We advocate using the present numerical study as a benchmark to test the robustness of alternative non‐local numerical approaches. Copyright © 2014 John Wiley & Sons, Ltd.