深部节理岩体塑性损伤耦合微面模型

采用微面模型理论和损伤力学方法,建立了节理岩体的弹塑性损伤耦合微面模型. 在节理岩体的微面上,将岩体视为由节理面与岩石组成的二元介质,以节理连通率作为岩体沿该方向的面积损伤变量,考虑微面法向拉应力和压应力下的不同塑性变形和损伤耦合作用机制,基于塑性理论建立了节理岩体的微面塑性损伤增量本构关系. 采用微面物理量与宏观物理量的几何约束模型,根据微面方向积分导出了节理岩体的宏观弹塑性增量本构关系. 编制了节理岩体微面模型的MARC有限元子程序,对节理岩体的单轴拉伸、压缩试验和泥浆压力作用下的井壁稳定问题进行了数值模拟研究. 数值计算结果表明,该模型能很好地揭示载荷作用下节理岩体的各向异性非弹性变形和次生节理演化过程.      

隧道围岩强度不均地段塌方成因及其处理方法

采用微面模型理论和损伤力学方法,建立了节理岩体的弹塑性损伤耦合微面模型. 在节理岩体的微 面上,将岩体视为由节理面与岩石组成的二元介质,以节理连通率作为岩体沿该方向的面积 损伤变量,考虑微面法向拉应力和压应力下的不同塑性变形和损伤耦合作用机制,基于塑性 理论建立了节理岩体的微面塑性损伤增量本构关系. 采用微面物理量与宏观物理量的几何约 束模型,根据微面方向积分导出了节理岩体的宏观弹塑性增量本构关系. 编制了节理岩体微 面模型的MARC有限元子程序,对节理岩体的单轴拉伸、压缩试验和泥浆压力作用下的井壁稳 定问题进行了数值模拟研究. 数值计算结果表明,该模型能很好地揭示载荷作用下节理岩体 的各向异性非弹性变形和次生节理演化过程.     

具确定弱区域正交各向异性薄板的弹塑性屈曲分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的具损伤正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,在此基础上,建立了正交各向异性材料的增量型和全量型弹塑性损伤本构方程,并以具确定弱区域正交各向异性矩形薄板为例,根据屈曲时的能量准则和全量理论,以等效塑性应变为内变量,对其弹塑性屈曲问题进行了分析,讨论了几何参数和弱区域对正交各向异性薄板弹塑性屈曲临界应力的影响.     

材料构型力学及其在复杂缺陷系统中的应用

基于材料构型力学描述复杂缺陷力学系统中的破坏行为, 可以为预测材料临界失效载荷和评估结构完整性提供新的思路. 首先, 通过对拉格朗日能量密度函数的梯度、散度、旋度操作分别获取3 类材料构型应力张量的定义式、平衡方程、物理意义以及其对应的守恒积分表达式. 其次, 基于材料构型力学概念建立描述材料屈服的屈服准则、预测裂纹起裂的断裂准则、以及评估复杂缺陷系统最终失效的破坏准则. 然后, 利用数字散斑图像相关技术, 开发材料构型力学相关参量的无损测量方法. 最后, 将材料构型力学概念应用于纳米损伤力学和铁电多晶材料的断裂力学中, 为此类新型材料的损伤水平评估提供理论支撑.      

立方晶体单晶材料屈服面的研究

将Hill屈服准则用于DD3镍基单晶合金屈服应力的预测，通过与试验结果比较发现，在760℃时的误差较大，根据立方单晶材料的屈服特点，用正应力偏张量平方与剪应力偏张量平方乘积项构成的应力不变量考虑单晶合金偏轴受载时存在的拉、剪应力耦合效应，提出了一个在工程上实用的新屈服准则．在新屈服准则中出现的参数可以通过单向拉伸试验确定，给出了确定这些参数的方法，并重新定义了适合新屈服准则的等效应力和等效应变，对各向同性材料，新屈服准则退化为Von Mises屈服准则，新定义的等效应力和等效应变退化为Von，Mises等效应力和等效应变，用新屈服准则对国产DD3单晶合金的屈服应力进行预测，能很好地符合试验结果；与Hill屈服准则比较，在760℃时的预测精度显提高。     

各向异性屈服准则的发展及实验验证综述

鉴于材料的屈服行为对板料成形的重要性, 人们对各向异性屈服准则进行了长期研究. 本文对各向异性屈服准则的发展进行了较为全面的回顾, 对Hill系列、Hosford系列和Drucker系列3类屈服准则分别进行归纳. 重点介绍不同类型屈服准则的适用范围及缺陷, 总结目前国内外所采用的不同的实验验证方法, 最后指出各向异性屈服准则在数值模拟中应用的难点及今后的研究方向.      

正交各向异性材料的弹塑性损伤本构关系

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,在此基础上,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程,并以具局部损伤的正交各向异性矩形薄板为例,采用Galerkin法和迭代法,对其弹塑性屈曲问题进行了分析,讨论了局部损伤对正交各向异性矩形薄板弹塑性屈曲临界应力的影响.      

基于正则结构的各向异性损伤演化律

在Rice的正则结构框架下，推导出基于共轭力的各向异性损伤演化律。其中损伤变量采用二阶裂隙张量，它是固体内微裂纹的一个宏观测度。推导过程不涉及自由能的具体形式，主要结果包括损伤势函数及演化方程的解析表达式。在唯象的损伤力学模型里，损伤演化方程经常以唯象方程的形式出现。研究了唯象方程成立的条件及损伤特征张量的解析表达式。引入了广义裂隙张量及脆性指数的概念，并介绍了它们的作用和意义。     

一种适用于岩土的扩展强度及屈服准则

土壤材料是一种典型的摩擦型材料,然而天然岩石却具有一定的凝聚力,而金属材料则完全是凝聚型材料.在分析三种典型的材料强度准则表达式基础上,即SMP,Lade-Duncan以及广义Von-Mises准则,通过利用应力张量的不变量表达形式,提出了一种扩展准则即VML准则,该准则能够分别退化为上述3种典型准则.在偏平面上,新准则能够描述从曲边三角形到圆形在内的多种开口形态;在子午面上,采用幂函数作为破坏准则公式,能够描述静水压力对于强度特性影响的非线性性质.而对于土壤的屈服性质,岩土材料具有典型的压剪耦合特性,因此,为了描述剪切与等方向压缩两种路径下的体积耦合现象,采用水滴型屈服面作为屈服准则.对于偏平面上的截面形状,讨论了给定球应力下偏应力强度值的分布形式及特点,讨论了应力罗德角对于偏平面上强度曲线的凹凸性的影响.最后,通过多种材料的破坏与屈服试验成果,用所提新准则进行了验证.通过强度以及屈服特性测试对比,验证了所提VML准则的合理性.     

准脆性材料的弹塑性各向异性损伤耦合本构模型研究

针对准脆性材料的非线性特征：强度软化和刚度退化、单边效应、侧限强化和拉压软化、不可恢复变形、剪胀及非弹性体胀,在热动力学框架内,建立了准脆性材料的弹塑性与各向异性损伤耦合的本构关系。对准脆性材料的变形机理和损伤诱发的各向异性进行了诠释,并给出了损伤构形和有效构形中各物理量之间的关系。在有效应力空间内,建立了塑性屈服准则、拉压不同的塑性随动强化法则和各向同性强化法则。在损伤构形中,采用应变能释放率,建立了拉压损伤准则、拉压不同的损伤随动强化法则和各向同性强化法则。基于塑性屈服准则和损伤准则,构建了塑性势泛函和损伤势泛函,并由正交性法则,给出了塑性和损伤强化效应内变量的演化规律,同时,联立塑性屈服面和损伤加载面,给出了塑性流动和损伤演化内变量的演化法则。将损伤力学和塑性力学结合起来,建立了应变驱动的应力-应变增量本构关系,给出了本构数值积分的要点。以单轴加载-卸载往复试验识别和校准了本构材料常数,并对单轴单调试验、单轴加载-卸载往复试验、二轴受压、二轴拉压试验和三轴受压试验进行了预测,并与试验结果作了比较,结果表明,所建本构模型对准脆性材料的非线性材料性能有良好的预测能力。     

A thermodynamically-consistent microplane model for shape memory alloys

In microplane theory, it is assumed that a macroscopic stress tensor is projected to the microplane stresses. It is also assumed that 1D constitutive laws are defined for associated stress and strain components on all microplanes passing through a material point. The macroscopic strain tensor is obtained by strain integration on microplanes of all orientations at a point by using a homogenization process. Traditionally, microplane formulation has been based on the Volumetric–Deviatoric–Tangential split and macroscopic strain tensor was derived using the principle of complementary virtual work. It has been shown that this formulation could violate the second law of thermodynamics in some loading conditions. The present paper focuses on modeling of shape memory alloys using microplane formulation in a thermodynamically-consistent framework. To this end, a free energy potential is defined at the microplane level. Integrating this potential over all orientations provides the macroscopic free energy. Based on this free energy, a new formulation based on Volumetric–Deviatoric split is proposed. This formulation in a thermodynamic-consistent framework captures the behavior of shape memory alloys. Using experimental results for various loading conditions, the validity of the model has been verified.     

An orthotropic yield criterion in a 3-D general stress state

An anisotropic yield criterion with a general representation was suggested. The yield criterion was derived from the use of the invariants of the stress tensor, similar in constructing an isotropic yield criterion, but which contains a “three-yield-system hypothesis” specifying the state of anisotropy. When applied to rolled sheet metals, such as high strength steels and aluminum alloys, the criterion can be treated in an analytical form to facilitate analyses of engineering problems under a general triaxial stress state. For this specified form, anisotropic properties of the predicted yield surface were characterized by seven experimental results obtained from three standard uniaxial-tension tests and one equibiaxial-tension test. When the applied material becomes isotropic it is transformed back to the form of the von-Mises’s criterion. Since the convexity of the yield criterion was proven in its general type, the characterized criterion is valid as a plastic potential in the implementation of finite element programs. It was shown, in full agreement with experimental data, that the accuracy of predicted yield surface was similar to that of predicted by the polycrystal model. Considering the equibiaxial-tension data, in general, may be not available from material supplies, a formulated relation covered variables of the equibiaxial tension and uniaxial tension was proposed. The relation can be used to calculate the equibiaxial-tension yield stress from the experimental data in uniaxial tensions. Several calculated results showed very close to the experimental results.     

A new damage model for microcrack-weakened brittle solids

In the present paper, a micromechanically based damage model for microcrack-weakened solids is developed. The concept of the domain of microcrack growth (DMG) is defined and used to describe the damage state and the anisotropic properties of brittle materials. After choosing an appropriate fracture criterion of microcrack, we obtain the analytical expression of DMG under a monotonically increasing proportional plane stress. Under a complex loading path, the evolution equation of DMG and the overall effective compliance tensor of damaged materials are given. The project supported by National Natural Science Foundation of China     

Anisotropic damage–plasticity model for concrete

A material model for concrete is proposed here within the framework of a thermodynamically consistent elasto-plasticity–damage theory. Two anisotropic damage tensors and two damage criteria are adopted to describe the distinctive degradation of the mechanical properties of concrete under tensile and compressive loadings. The total stress tensor is decomposed into tensile and compressive components in order to accommodate the need for the above mentioned damage tensors. The plasticity yield criterion presented in this work accounts for the spectral decomposition of the stress tensor and allows multiple hardening rules to be used. This plastic yield criterion is used simultaneously with the damage criteria to simulate the physical behavior of concrete. Non-associative flow rule for the plastic strains is used to account for the dilatancy of concrete as a frictional material. The thermodynamic Helmholtz free energy concept is used to consistently derive dissipation potentials for damage and plasticity and to allow evolution laws for different hardening parameters. The evolution of the two damage tensors is accounted for through the use of fracture-energy-based continuum damage mechanics. An expression is derived for the damage–elasto-plastic tangent operator. The theoretical framework of the model is described here while the implementation of this model will be discussed in a subsequent paper.     

Numerical analysis and elastic–plastic deformation behavior of anisotropically damaged solids

The present paper is concerned with the numerical modelling of the large elastic–plastic deformation behavior and localization prediction of ductile metals which are sensitive to hydrostatic stress and anisotropically damaged. The model is based on a generalized macroscopic theory within the framework of nonlinear continuum damage mechanics. The formulation relies on a multiplicative decomposition of the metric transformation tensor into elastic and damaged-plastic parts. Furthermore, undamaged configurations are introduced which are related to the damaged configurations via associated metric transformations which allow for the interpretation as damage tensors. Strain rates are shown to be additively decomposed into elastic, plastic and damage strain rate tensors. Moreover, based on the standard dissipative material approach the constitutive framework is completed by different stress tensors, a yield criterion and a separate damage condition as well as corresponding potential functions. The evolution laws for plastic and damage strain rates are discussed in some detail. Estimates of the stress and strain histories are obtained via an explicit integration procedure which employs an inelastic (damage-plastic) predictor followed by an elastic corrector step. Numerical simulations of the elastic–plastic deformation behavior of damaged solids demonstrate the efficiency of the formulation. A variety of large strain elastic–plastic-damage problems including severe localization is presented, and the influence of different model parameters on the deformation and localization prediction of ductile metals is discussed.