Ⅰ阶梯度损伤理论

从热力学基本定律出发,将应变张量、标量损伤变量、损伤梯度作为Helmholtz自由能函数的状态变量,利用本构泛函展开法在自然状态附近作自由能函数的Taylor展开,未引入附加假设,推导出Ⅰ阶梯度损伤本构方程的一般形式．该形式在损伤为0时可退化为线弹性应力-应变本构方程,在损伤梯度为0时可退化为基于应变等效假设给出的线弹性局部损伤本构方程．一维解析解表明,随着应力增大,损伤场逐步由空间非周期解变为关于空间的类周期解,类周期解的峰值区域形成局部化带．局部化带内的损伤变量将不同于局部化带外的损伤变量,由此可以反映出介质的局部化特征．损伤局部化并不是与损伤同时发生,而是在损伤发生后逐渐显现出来,模型的局部化机制开始启动;损伤局部化的宽度同内部特征长度成正比．     

考虑双拉耦合的复合材料编织物非正交本构模型

基于连续介质力学理论,将复合材料编织物的双轴拉伸效应引入到前期提出的非正交本构模型中,提出了一种考虑双拉耦合的复合材料编织物非正交本构模型.给出了模型参数的确定方法,并通过拟合单轴拉伸、不等比双轴拉伸和偏轴拉伸实验数据,得到了本构模型参数.利用该模型对双轴拉伸和双球冲压实验进行了有限元模拟,并将模拟结果和实验结果进行对比,验证了所提出本构模型的可靠性,该模型能更好地表征复合材料编织物在成形过程中由于大变形所引起的非线性各向异性力学行为.这一本构模型具有结果精确、参数容易确定的优点,为编织复合材料成形的数值模拟和成形工艺优化奠定了理论基础.     

昆虫翼拍动中受载变形的粘弹性本构模型

昆虫翼拍动受载时发生被动变形,被看作为有助于改善飞行性能的机制之一．决定这种被动变形大小的一个关键因素是昆虫翼的材料本构关系,至今缺乏研究．基于蜻蜓翼(离体)的应力松弛实验和模型翼拍动时受载变形的有限元数值分析,揭示了粘弹性本构关系是昆虫翼材料性能的合理描述,并研究了粘弹性参数对被动变形的影响．     

梯度增强的弹塑性损伤非局部本构模型研究

简要介绍了几种主要的梯度增强非局部模型．基于“能量耗散梯度依赖”原则,在连续介质热力学框架内推导了梯度增强损伤与塑性耦合的本构关系,同时给出了一个基于塑性的损伤模型的梯度依赖本构的具体形式．在数值计算方面,结合移动最小二乘法和泰勒级数展开方法,建立了损伤场（有限元高斯积分点上）的Laplace值的近似求解格式,分别给出了二维和三维情况下的相关公式．给出的二维的韧性断裂的梯度依赖损伤塑性的数值应用,表明了格式的有效性和实用性．还讨论了内部长度的意义及取值问题．     

混凝土材料的粘塑性损伤本构模型

基于不可逆热力学,引入运动硬化、等向硬化和损伤内变量,构造了相应的自由能函数和流动势函数,推导出了混凝土材料的粘塑性损伤本构模型．数值模拟的结果表明,该模型能够避开屈服面和破坏准则的基本假设来描述混凝土材料的以下特性:压缩载荷作用下的体积膨胀现象;应变率敏感性;峰值后由损伤和破坏引起的应力软化和刚度退化现象A·D2由于此模型避开了根据各种变形阶段选择与其相应的本构模型的繁琐计算,因此更便于纳入复杂工况下应力分析有限元程序中．     

有限变形下的混凝土动态本构关系研究

讨论有限变形和小变形假设下本构关系的区别,并将其运用于混凝土的弹-粘塑性本构关系研究,提出了一个应变率相关的动态力学模型．模型基于Ottosen的4参数屈服准则,分别考虑混凝土在硬化阶段和软化阶段加载面的不同变化规律,建立冲击荷载下的混凝土本构关系．该模型可以应用于冲击载荷下混凝土材料响应的模拟．引进Green-Naghdi客观率建立有限变形的混凝土模型．根据大量实验结果对应变率和材料强度的关系提出合理假设,使模型可以反映混凝土大变形的动态力学行为,为相关工程问题的研究提供有益的思路和有效的工具．     

受热弹性复合球体空化问题的分析

研究了由两种弹性固体材料组成的复合球体,在均匀变温场作用下的空化问题．采用了几何大变形的有限对数应变度量和Hooke弹性固体材料的本构关系,建立了问题的非线性数学模型．求出了复合球体大变形热弹性膨胀的参数形式的解析解．给出了空穴萌生时临界温度随几何参数和材料参数的变化曲线,以及空穴增长的分岔曲线．算例的数值结果指出:超过临界温度后空穴半径将迅速增大,并且空穴萌生时环向应力将成为无限大,这意味着如果内部球体是弹塑性材料,则会在空穴表面附近产生塑性变形而造成材料的局部损伤．另外,当内部球体材料的弹性接近于不可压时,复合球体可以在较低的变温下空化．     

形状记忆合金相变过程三维大变形有限元模拟

形状记忆合金（SMA）一直被作为智能材料开发,并被用于阻尼器、促动器和智能传感器元件．形状记忆合金（SMA）的一项重要特性,是它具有恢复在机械加卸载周期下产生的大变形而不表现出永久变形的能力．该文旨在介绍一种由应力产生的相变且可以描述马氏体和奥氏体之间的超弹性滞回环现象本构方程．形状记忆合金的马氏体系数假设为应力偏张量的函数,因此形状记忆合金在相变过程中锁定体积．本构模型是在大变形有限元的基础上执行的,采用了现时构型Lagrange大变形算法．为了方便地使用Cauchy应力和线性应变本构关系,使用了与旋转无关的Jaumann应力增率计算应力．数值分析结果表明,相变引起的超弹性滞回环可以有效地通过该文提出的本构方程和大变形有限元模拟．     

反映混凝土单边效应的弹塑性损伤本构模型及应用

为了尽可能有效和准确地描述混凝土材料的非线性力学特性,在研究国内外混凝土损伤本构模型的基础上,基于连续介质损伤力学和不可逆热力学的理论框架,采用统一强度理论作为屈服破坏准则,分别定义拉、压双标量损伤来考虑材料的拉、压迥异特性,同时引入反向加载影响因子以修正拉压交替循环加载时材料的单边效应,以及多轴应力状态下拉、压损伤累积的相互影响,最终采用显式积分算法建立了一种改进的混凝土弹塑性损伤本构模型.不同素混凝土加载试验模拟结果初步验证了建议模型的有效性,而通过对含I型裂缝的混凝土简支梁试验进行数值分析,结果表明,所得的荷载 挠度曲线与试验结果吻合良好,进一步检验了模型应用于结构非线性分析的有效性.     

损伤粘弹性Timoshenko梁的拟静态力学行为分析

从考虑损伤的粘弹性材料——一种卷积型本构关系出发,应用Timoshenko梁的基本变形假设,建立损伤粘弹性Timoshenko梁的静、动力学行为研究的数学模型.分析了损伤粘弹性Timoshenko梁在阶跃载荷作用下的准静态力学行为,在Laplace域中得到了挠度和损伤的解析表达式．应用数值逆变换技术,考察了材料粘性参数对梁的挠度和损伤的影响,得到不同时刻损伤和挠度随时间的变化曲线．     

考虑损伤的修正梯度弹性理论

梯度弹性理论在描述材料微结构起主导作用的力学行为时具有显著优势,将其与损伤理论相结合,可在材料破坏研究中考虑微结构的影响.基于修正梯度弹性理论,将应变张量、应变梯度张量和损伤变量作为Helmholtz自由能函数的状态变量,并在自然状态附近对自由能函数作Taylor展开,进而由热力学基本定律,推导出修正梯度弹性损伤理论本构方程的一般形式.编制有限元程序,模拟土样损伤局部化带的发展演化过程.结果表明,修正梯度弹性损伤理论消除了网格依赖性;损伤局部化带不是与损伤同时发生,而是在损伤发展到一定程度后再逐渐显现出来.     

Structural damage identification based on best achievable flexibility change

A new method based on best achievable flexibility change is presented in this paper to localize and quantify damage in structures. Central to the damage localization approach is the computation of the Euclidean distances between the measured flexibility change and the best achievable flexibility changes. The location of damage can be identified by searching for a value that is considerably smaller than others in these distances. With location determined, a simple extent algorithm is then developed. Three examples are used to demonstrate the efficiency of the method. Results indicate that the proposed procedure may be useful for structural damage identification.     

Incremental Variational Principles in Damage Mechanics

We propose a new kind of damage formulation which leads, in connection with relaxation techniques known in literature, to a well posed problem suitable for finite element calculations. The model is rate‐dependent and allows a consistent treatment of micro‐structures and localization phenomena.     

A numerical technique for structural damage detection

A computationally attractive method is proposed in this study to provide an insight to the location and extent of structural damage. The proposed method makes use of the matrix disassembly technique and approaches the damage location and extent problem in a decoupled fashion. First, a scheme is developed to determine the damage location by calculating a damage localization vector, which is derived from the modal residual force criteria. With location determined, the corresponding damage extent can be easily obtained only by the processes of division. The algorithm is applied to a numerical example and its efficiency is demonstrated through damage simulations.     

Two-phase damage detection of beam structures under moving load using multi-scale wavelet signal processing and wavelet finite element model

This paper proposes a damage detection method with two phases, namely, localization and quantification, for beam structures subjected to moving load and successfully validates it via a laboratory experiment. Firstly, the discrete wavelet transform (DWT) is applied to decompose the displacement response change induced by a moving vehicle and locate potential structural damages. Then adaptive-scale wavelet finite element model (WFEM) updating is employed to estimate the damage severity in the identified damage regions in a progressive fashion. The elemental scales of WFEM are adaptively changed according to not only the moving vehicle position but also the progressively identified damage regions. Such a method can effectively minimize the number of modeling degree-of-freedoms (DOFs) and updating parameters during optimization. The feasibility and effectiveness of the proposed method is examined through a laboratory experiment with different damage scenarios. The results indicate the proposed method can achieve good consistency between structural modeling, damage scenarios, and load conditions, as well as an optimal tradeoff between damage detection accuracy and efficiency.     

An enhanced tensorial formulation for elastic degradation in micropolar continua

In the past, a lot of applications of the micropolar (or Cosserat) continuum theory have been proposed, especially in the field of granular materials analysis and for strain localization problems in elasto-plasticity, due to its regularization properties. In order to make possible the application of the micropolar theory to different constitutive models and to extend its regularization properties also to damage models, in this work a general formulation for elastic degradation based on the micropolar theory is proposed. Such formulation is presented in a unified format, able to enclose different kinds of elasto-plastic, elastic-degrading and damage constitutive models. A peculiar tensor-based representation is introduced, in order to guarantee the conformity with analogous theories based on the classic continuum, in such a way as to make possible the application to the micropolar theory of theoretical and numerical resources already defined for the classic theory. Peculiar micropolar scalar damage models are also proposed, and derived within the new general formulation.     

Locating damaged storeys in a structure based on its identified modal parameters in Cauchy wavelet domain

Structural damage detection based on the changes of dynamic properties is a major topic for structural health monitoring. In this paper, efforts are made to extend the flexibility-based damage localization methods, especially the damage locating vectors (DLVs) method, to the case of earthquake vibration, where the finite element model and mass matrices are not available. First, a new method using continuous Cauchy wavelet transform (CCWT) and state-variable time series model is proposed to identify the modal parameters of a structure. Then the flexibility matrix can be constructed from the identified modal parameters. Second, a modified DLVs damage assessment approach is also proposed to locate damage positions in the structure through a weighted relative displacement index (WRDI). This index is calculated by using DLVs vectors determined from the change of flexibility matrix before and after damage of the structure. Numerical analyses demonstrate that the proposed process can indeed monitor the variation of stiffness for each storey. These two approaches are further applied to process the dynamic responses of three-storey and eight-storey steel frames in shaking table tests. The proposed scheme is also proved to be superior to mode shape based methods (CMS, COMAC) in monitoring the variation of stiffness for each storey.     

Local and non‐local ductile damage and failure modelling at large deformation with applications to engineering

The numerical analysis of ductile damage and failure in engineering materials is often based on the micromechanical model of Gurson [1]. Numerical studies in the context of the finite‐element method demonstrate that, as with other such types of local damage models, the numerical simulation of the initiation and propagation of damage zones is strongly mesh‐dependent and thus unreliable. The numerical problems concern the global load‐displacement response as well as the onset, size and orientation of damage zones. From a mathematical point of view, this problem is caused by the loss of ellipticity of the set of partial di.erential equations determining the (rate of) deformation field. One possible way to overcome these problems with and shortcomings of the local modelling is the application of so‐called non‐local damage models. In particular, these are based on the introduction of a gradient type evolution equation of the damage variable regarding the spatial distribution of damage. In this work, we investigate the (material) stability behaviour of local Gurson‐based damage modelling and a gradient‐extension of this modelling at large deformation in order to be able to model the width and other physical aspects of the localization of the damage and failure process in metallic materials.