考虑裂纹闭合效应的岩石损伤本构关系

岩石中的预存裂纹只有在一定的法向压应力即裂纹闭合应力的作用下才可能闭合，其闭合过程与其方位和外加应力场有关，并且，即使对于裂纹已经完全闭合的岩石，如果裂纹闭合应力不同，则岩石的应力应交关系也不相同。本文建立了考虑裂纹闭合效应的岩石细观损伤力学模型，分析了裂纹闭合应力对岩石损伤演化过程和应力应变关系的影响。数值结果表明裂纹闭合应力显著地改变岩石的应力应变关系，表现为随裂纹闭合应力的增加，岩石的轴向应变变化较小，侧向应变和体积应变则大为增加。     

陶瓷材料动态压缩损伤本构模型

运用细观损伤力学理论,从动态压缩载荷下陶瓷材料内翼型裂纹的产生和扩展的损伤机理出发,建立了陶瓷材料的弹脆性动态损伤本构模型,给出相应的损伤演化方程.假设裂纹成核满足Weibull分布,讨论了成核分布参数、原始缺陷尺寸对材料动态断裂应力、断裂应变的影响,并用动态损伤演化模型计算了冲击载荷下AD90陶瓷的动态应力应变曲线,计算结果和实验结果符合很好.     

含微裂纹弹性体的应力应变关系

本义建立了考虑裂纹闭合和裂纹表面摩擦影响的含微裂纹弹性体的应力应变关系，给出了柔度张量增量的显式表达式。对于二维平面应力和平面应变状态，给出了等效工程弹性系数。数值计算结果表明，裂纹闭合和裂纹面摩擦对裂纹体的应力应变关系和等效工程弹性系数有重要影响。     

含微裂纹弹性体的应力应变关系

本义建立了考虑裂纹闭合和裂纹表面摩擦影响的含微裂纹弹性体的应力应变关系，给出了柔度张量增量的显式表达式。对于二维平面应力和平面应变状态，给出了等效工程弹性系数。数值计算结果表明，裂纹闭合和裂纹面摩擦对裂纹体的应力应变关系和等效工程弹性系数有重要影响。     

应变损伤材料I型动态扩展裂纹尖端场的渐近分析

研究了应变损伤材料Ｉ型动态扩展的裂纹尖端场。假定材料服从Ｊ２流动理论，且损伤规律以幂律应变软化的规律给出。对于塑性区引进了应力函数φ，ψ０借助于动力学方程的分析，给出了渐近方程及数值解。结果表明，对于可压缩材料Ｉ型平面应变尖端场是完全由塑性区组成，没有弹性卸载区。在裂纹尖端附近，应力和应变分别具有如下的奇异性：σ￣（ｌｎＲ／ｒ）＾－ｎ／ｎ＋１，ε￣（ｌｎＲ／ｒ）＾１／ｎ＋１。     

在线振动监测与故障诊断的一种新途径

文中由应力强度因子导出含裂纹单元的刚度矩阵,从而提出了一种有限元法.将该法用于单边裂纹悬臂梁,计算了应变响应.用时域法识别了模态参数,并考虑了裂纹闭合的影响.分析了应变响应对故障的敏感度,计算结果表明,应变响应相对于位移响应而言,对故障更敏感.本文还提出了一种判别函数,该函数对于损伤检测,比现有几种判别函数更有效.最后,给出了一种在线振动监测与故障诊断新方法.     

脆性损伤材料裂纹尖端的局部解

本文利用Mazars和Lemaitre提出的混凝土脆性损伤模型,求得了裂纹尖端应力、应变及损伤的局部解.对手Ⅲ型及不可压缩平面应变Ⅰ型裂纹,其尖端场的构造和理想塑性材料相类似.指出由于丧失了应力全连续条件,从而损伤边界不能由局部解定出.     

Ⅱ型动态扩展裂纹尖端的弹黏塑性渐近场

考虑材料的黏性效应建立了Ⅱ型动态扩展裂纹尖端的力学模型,假设黏性系数与塑性等效应变率的幂次成反比,通过分析使尖端场的弹、黏、塑性得到合理匹配,并给出边界条件作为扩展裂纹定解的补充条件,对理想塑性材料中平面应变扩展裂纹尖端场进行了弹黏塑性渐近分析,得到了不含间断的连续解,并讨论了Ⅱ型裂纹数值解的性质随各参数的变化规律.分析表明应力和应变均具有幂奇异性,对于Ⅱ型裂纹,裂尖场不含弹性卸载区.引入Airy应力函数,求得了Ⅱ型准静态裂纹尖端场的控制方程,并进行了数值分析,给出了裂纹尖端的应力应变场.当裂纹扩展速度(M→0)趋于零时,动态解趋于准静态解,表明准静态解是动态解的特殊形式.     

某抽水蓄能电站地下洞室围岩岩体质量特征分析

考虑材料的黏性效应建立了II型动态扩展裂纹尖端的力学模型,假设黏性 系数与塑性等效应变率的幂次成反比,通过分析使尖端场的弹、黏、塑性得到合理匹配,并 给出边界条件作为扩展裂纹定解的补充条件,对理想塑性材料中平面应变扩展裂纹尖端场进 行了弹黏塑性渐近分析,得到了不含间断的连续解,并讨论了II型裂纹数值解的性质随各参 数的变化规律. 分析表明应力和应变均具有幂奇异性,对于II型裂纹,裂尖场不含弹性卸载 区. 引入Airy应力函数,求得了II型准静态裂纹尖端场的控制方程,并进行了数值分析, 给出了裂纹尖端的应力应变场. 当裂纹扩展速度($M\to 0$)趋于零时,动态解趋 于准静态解,表明准静态解是动态解的特殊形式.     

Reissner型板裂纹尖端应力应变场及应力强度因子计算

本文采用考虑横向剪应变的Reissner理论,给出了含裂纹平板在弯曲情况下裂纹尖端应力应变场的一般解。作为算例,应用此展开式对于在对称和反对称情况下的有限尺寸板进行了应力强度因子计算并给出相应的曲线。     

裂隙岩体损伤局部化破坏分岔模型及其应用

采用概率统计方法分析节理裂隙岩体的几何特征，定义了反映裂隙岩体几何特征的组构张量．基于不可逆热力学理论，通过裂纹扩展的细观分析，得出了损伤的发展机理和演化方程，把损伤演化和裂隙的几何特征的变化联系起来，建立了弹塑性损伤本构关系．为分析含有节理裂隙岩体在发生局部化破坏时的特征，通过对发生局部化时的裂隙岩体的分析。构造了适用于节理裂隙岩体局部化分析的不连续分岔模型．利用非线性规划数值解法，可以得出局部化破坏的方向特征．在有限元方法中，根据该模型给出了节理裂隙岩体相关的算例，分析表明该模型用于分析裂隙岩体的局部化破坏是有效的．     

A physico-mechanical approach to modeling of metal forming processes—part I: theoretical framework

A combined physico-mechanical approach to research and modeling of forming processes for metals with predictable properties is developed. The constitutive equations describing large plastic deformations under complex loading are based on both plastic flow theory and continuum damage mechanics. The model which is developed in order to study strongly plastically deformed materials represents their mechanical behavior by taking micro-structural damage induced by strain micro-defects into account. The symmetric second-rank order tensor of damage is applied for the estimation of the material damage connected with volume, shape, and orientation of micro-defects. The definition offered for this tensor is physically motivated since its hydrostatic and deviatoric parts describe the evolution of damage connected with a change in volume and shape of micro-defects, respectively. Such a representation of damage kinetics allows us to use two integral measures for the calculation of damage in deformed materials. The first measure determines plastic dilatation related to an increase in void volume. A critical amount of plastic dilatation enables a quantitative assessment of the risk of fracture of the deformed metal. By means of an experimental analysis we can determine the function of plastic dilatation which depends on the strain accumulated by material particles under various stress and temperature-rate conditions of forming. The second measure accounts for the deviatoric strain of voids which is connected with a change in their shape. The critical deformation of ellipsoidal voids corresponds to their intense coalescence and to formation of large cavernous defects. These two damage measures are important for the prediction of the meso-structure quality of metalware produced by metal forming techniques. Experimental results of various previous investigations are used during modeling of the damage process.      

Anisotropic damage law of evolution

A formulation for anisotropic damage is established in the framework of the principle of strain equivalence. The damage variable is still related to the surface density of microcracks and microvoids and, as its evolution is governed by the plastic strain, it is represented by a second order tensor and is orthotropic. The coupling of damage with elasticity is written through a tensor on the deviatoric part of the energy and through a scalar taken as its trace on the hydrostatic part. The kinetic law of damage evolution is an extension of the isotropic case. Here, the principal components of the damage rate tensor are proportional to the absolute value of principal components of the plastic strain rate tensor and are a nonlinear function of the effective elastic strain energy. The proposed damage evolution law does not introduce any other material parameter. Several series of experiments on metals give a good validation of this theory. The coupling of damage with plasticity and the quasi-unilateral conditions of partial closure of microcracks naturally derive from the concept of effective stress. Finally, a study of strain localization makes it possible to determine the critical value of the damage at mesocrack initiation.     

Load-induced oriented damage and anisotropy of rock-like materials

Theoretical model for deformability of brittle rock-like materials in the presence of an oriented damage of their internal structure is formulated and verified experimentally. This model is based on the assumption that non-linearity of the stress–strain curves of these materials is a result of irreversible process of oriented damage growth. It was also assumed that a material response, represented by the strain tensor, is a function of two tensorial variables: the stress tensor and the damage effect tensor that is responsible for the current state of the internal structure of the material. The explicit form of the respective non-linear stress–strain relations that account for the appropriate damage evolution equation was obtained by employing the theory of tensor function representations and by using the results of own experiments on damage growth. Such an oriented damage that grows in the material, described by the second order symmetric damage effect tensor, results in gradual development of the material anisotropy. The validity of the constitutive equations proposed was verified by using the available experimental results for concrete subjected to the plane state of stress. The relevant experimental data for sandstone and concrete subjected to tri-axial state of stress were also used.     

A microstructure-based viscoplastic model for asphalt concrete

A microstructure-based viscoplastic continuum model is developed for the permanent deformation of asphalt concrete (AC). The model accounts for several phenomena that influence the permanent deformation of AC at high temperatures. These phenomena include strain rate dependency, confining pressure dependency, dilation, aggregate friction, anisotropy, and damage.The material anisotropy was included in the model by replacing the stress invariants in the yield function with invariants of both the stress and a microstructure tensor, which describes the aggregate orientation distribution. The components of the microstructure tensor were determined using image analysis techniques (IAT) conducted on digital images taken from two-dimensional cut sections of AC. Furthermore, damage was included in the model based on the effective stress theory to account for crack and air void growth that significantly reduces the load-carrying capacity of the material.Experimental data from triaxial compressive strength tests conducted at five strain rates and three confining pressures were used to develop a methodology to determine the material parameters that characterize AC permanent deformation. The model predictions were in a good agreement with the experimental measurements.     

Dissymétrie de comportement élastique anisotrope couplé ou non à l'endommagement

A thermodynamic framework is proposed to model anisotropic elasticity different in tension and in compression. Based on Kelvin decomposition of the compliance tensor, it applies to any 3D loading. Coupling with damage is made considering fourth- and second-order damage tensors. The proposed formulation automatically satisfies the continuity of the stress tensor and of the energy release rate tensor. The particular case of initially isotropic materials is exposed.     

单轴压缩下断续节理岩体动态损伤本构模型

断续节理将对工程岩体的强度及变形等力学特性产生显著影响,损伤力学中视节理为岩体的一种宏观损伤,因而采用损伤张量来刻画其对岩体的影响。目前学术界提出了用节理的几何、强度及变形等3类参数来描述节理的物理力学性质,而目前的岩体损伤张量计算方法都只涉及前2类参数,均没有涉及其变形参数即法向及切向刚度。为此,在前人研究的基础上,基于断裂及损伤理论提出了考虑节理法向及切向刚度的单轴压缩下单条断续节理引起的损伤张量计算公式,进而通过考虑节理间相互作用给出了单组单排或多排节理岩体损伤张量计算公式。其次,以岩石细观动态损伤模型为基础,结合宏细观损伤耦合观点提出了一个能够同时考虑节理几何、强度及变形参数的断续节理岩体动态损伤本构模型。最后,利用该模型讨论了节理参数及载荷应变率等对岩体动态力学特性的影响,认为节理长度减小及摩擦角增大将导致岩体动态峰值强度及弹性模量增大;岩体动态峰值强度及弹性模量则随着节理法向及切向刚度的增大分别减小或增大;而当节理法向及切向刚度按照同一比例增大时,岩体动态峰值强度及弹性模量则是增大的。岩体动态峰值强度与载荷应变率呈正相关。     

含正交排列夹杂和缺陷材料的等效弹性模量和损伤

研究含正交排列夹杂和缺陷材料的等效弹性模量和损伤,推导了以Eshelby－Mori－Tanaka方法求解多相各向异性复合材料等效弹性模量的简便计算公式,针对含三相正交椭球状夹杂的正交各向异性材料,得到了由细观参量（夹杂的形状、方位和体积分数）表示的等效弹性模量的解析表达式．在此基础上,提出了一个宏细观结合的正交各向异性损伤模型,从而建立了以细观量为参量的含损伤材料的应力应变关系．最后,对影响材料损伤的细观结构参数进行了分析．