对于正交异性材料屈服与流动的探讨

假定正交异性材料的屈服准则与各向同性材料的Huber-Mises准则同构,提出了无量纲应力屈服准则,进而推导了与之相关的塑性流动规则.用不同的简单应力状态下的应力-应变试验曲线,可以得到不同的广义等效应力-应变关系.     

Deformation Behavior Modeling of SMAs Under Cyclic Loading Based on Rational Interpolation北大核心CSCD

提出了一个有限弹塑性模型,用来模拟形状记忆合金(shape memory alloys,SMAs)在循环荷载下的变形行为.首先,通过分析上下屈服阶段形函数的特点,利用有理插值方法给出循环荷载下的应力-应变形函数显式表达,可以精确匹配任意形状的实验数据;其次,基于对数客观率,构建了有限弹塑性J2流模型,耦合了屈服中心的移动和屈服面的增大;再次,从单轴情况出发,推导得到了单个循环下的三个硬化函数显式表达,再引入局部因子和多轴扩展不变量,构造了光滑统一且多轴有效的硬化函数;最后,将模型得到的结果与经典实验结果比较,证明了新方法的有效性.该文创新点如下:第一,通过改进传统的背应力演化方程,使得新模型产生强烈的Bauschinger效应,从而使新方法具备模拟SMAs特殊变形行为的能力;第二,新的光滑统一硬化函数在单个循环下会自动退化,得到精确符合实验数据的结果;第三,利用本构方程推导得到有效塑性功演化规律,而有理插值得到的形函数中包含依赖有效塑性功的参数,给出这些参数方程以后使得模型具备了预测变形的能力.     

引用复变量伪应力函数来解幂硬化材料平面应力问题

本文引用复变量伪应力函数将幂硬化材料平面应力问题的协调方程化为双调和方程,从而使此类有强化材料的弹塑性平面应力问题能像线弹性力学平面问题那样采用复变函数法进行求解.本文推导出了幂硬化材料平面应力问题的应力、应变及位移分量的复变函数表达式,可推广应用于满足全量理论的一股弹塑性平面应力问题.作为算例,文中给出了含圆孔幂硬化材料无限大板单向受拉问题的解答,并和有关文献用摄动法获得的同一问题的渐近解进行了比较.     

考虑损伤效应的正交各向异性板的弹塑性后屈曲分析

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,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和损伤演化方程．基于经典非线性板理论,得到了考虑损伤效应的正交各向异性板的增量型非线性平衡方程,且采用有限差分法和迭代法进行求解．数值算例中,讨论了损伤演化、初始缺陷对正交各向异性板弹塑性后屈曲行为的影响．数值结果显示了弹塑性后屈曲与弹性后屈曲的不同,并且损伤和损伤演化对板的弹塑性后屈曲的影响不可忽略．     

功能梯度板中Griffith裂纹尖端应力场的三维解析研究

基于推广后的England-Spencer板理论,研究了横观各向同性功能梯度板中Griffith裂纹尖端的三维应力场.假定材料参数沿板厚方向可以任意连续变化,利用复变函数解法和保角变换技术分别给出了受无穷远处荷载作用和受均匀内压时裂纹尖端应力的三维解析解.当材料退化为各向同性均匀材料时,将该解答与经典二维解进行了比较,...     

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．     

横观各向同性弹性层点力解

本文根据弹性层状结构的传递矩阵法思想，由横观各向同性弹性力学基本方程，导出了含应力和位移两类变量的混合方程，利用Ｆｏｕｒｉｅｒ变换和文献［７］的位移函数通解，以及计算机代数软件，得到了横观各向同性层的点力解，这个点力解可直接退化到各同性情形的解．     

幂硬化不可压缩材料平面应变问题的解法

根据Илюшин微小弹塑性变形理论,本文导出了幂硬化不可压缩材料平面应变问题的基本方程. 另外,本文提出了这些基本方程的两种解法,即位移函数-应力法和应力函数-应变法.举了两个实例来说明这两个方法的应用.     

用张量导数法求横观各向同性弹性材料的弹性张量的一般形式

用对张量函数求导的方法导出了横观各向同性材料和各向同性材料的弹性张量的一般形式与应力-应变关系式.从推导过程可更清楚地看出为什么横观各向同性材料和各向同性材料分别有五个和两个独立的弹性常数,即材料有几个独立的弹性常数是由其应变能函数的形式所决定的.     

梯度材料平板弯拉耦合力学的精确化支配方程

基于非均匀材料弹性力学理论,采用算子谱分解和算子代数方法,对梯度材料平板结构弯曲与拉伸问题进行了研究.首次给出了指数梯度材料平板弯曲与拉伸的力学方程.研究结果表明:与各向同性平板结构弯曲和拉伸问题不同,在功能梯度平板中描述弯曲应力状态与描述拉伸应力状态的广义位移函数以及剪切函数都是耦合的.没有采用工程假设,推导得到的梯度材料平板结构力学方程是精确化的.通过分析可以认识和理解,分别对应于弯曲状态与拉伸状态的应力场耦合机理以及力学响应的构成等.给出的方程及其分析过程可望能够用于类平板形式热防护材料结构的应力分析与强度设计,推进热防护材料结构的轻型化.     

A phenomenological method of calculating the residual stresses and plastic deformations in a hollow surface-hardened cylindrical sample

A phenomenological method is proposed for calculating the residual stress and plastic deformation fields in a hollow surface-hardened cylindrical sample. Versions of the hardening are considered that lead to isotropy and anisotropy in the plastic deformations in the surface layer. A hardening anisotropy parameter is introduced that relates the axial and circumferential components of the residual plastic deformation tensor. The experimentally determined axial and/or circumferential components of the residual plastic stress tensor are used as the initial information. The tensor fields of the residual stresses and deformations are constructed assuming the hypothesis of surface hardening anisotropy and the absence of secondary plastic compression deformations and that the tangential components of the residual stress tensor and the plastic incompressibility of the material are small. A technique is developed for identifying the parameters of the proposed method. The adequacy is checked using experimental data for test pieces of type 45 and 12X18H10T steels hardened by hydro-shot blasting treatment and of type 45 steel hardened by treatment with a roller. Good agreement is observed between the calculated and experimental results. It is noted that the anisotropic hardening procedure leads to a substantial difference between the circumferential and axial components of the residual stresses in the hardened layer, unlike the case of isotropic hardening where they are practically identical.     

Construction of the Equivalent Plastic Strain Increment

Strain hardening plastic deformation of a material possessing a yield locus (f(σ_ij)) which may be written as a homogeneous function of the stress components (σ_ij), and which obeys the classical associated flow rule for metals (e.g. Bishop and Hill, 1951) is considered. The material may be anisotropic and may display plastic dilatation. A method is given for constructing the equivalent plastic strain increment in such a way that the increment of plastic work is always equal to the product of the equivalent plastic strain increment and the equivalent yield stress. Construction of the equivalent plastic strain at a corner in the yield locus is given. The method given here is implied in classical treatments of hardening (e.g. Hill, 1950) but seems not to have been given explicitly heretofore.     

高速扩展平面应力裂纹尖端的各向异性塑性场

在裂纹尖端的应力分量都只是θ的函数的条件下,利用定常运动方程,Hill各向异性屈服条件及应力应变关系,我们得到高速扩展平面应力裂纹尖端的各向异性塑性场的一般解.将这个一般解用于四种各向异性特殊情形,我们就导出这四种特殊情形的一般解.最后,本文给出X=Y=Z情形的高速扩展平面应力Ⅰ型裂纹尖端的各向异性塑性场.     

Stress-dependent Failure Surface of Granular Materials

Numerical computations of geotechnical problems will become increasingly important because of the growing complexity of geotechnical applications. Therefore, a well-founded prediction of stability statements requires appropriate models, which are able to realistically depict the stress-strain behaviour of non-cohesive-frictional granular materials. On several stress paths, drained triaxial compression experiments on compact dense sand specimen exhibited that the size of the failure surface is not independent from the hydrostatic pressure. The failure surface and, thus, the maximal shear stresses at a specific confining pressure σ₃^exp can be increased by a compression preload at a level higher than σ₃^exp. This means that granular materials own several failure surfaces in dependence of the hydrostatic pressure. Consequently, the failure criteria based on the assumption of a compression stress-path-independent single-failure surface cannot recover the newly detected plastic yielding behaviour of granular materials. An improved approach for modelling the plastic hardening and softening behaviour coupled with the new yield properties at the limit state will be presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of property anisotropy of a rock mass on its stressed state and length of the plastic region of an excavated seam

The solution of the mixed problem of the theory of elasticity for a half plane modeling the stress-strain state of an anisotropic rock mass during the excavation of a seam is constructed. The results of numerical investigation of the length of the neardrift plastic zone of the seam being excavated as a function of the anisotropy of its plastic properties are given. Diagrams showing the stress distribution in the mass are presented.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 38–43, 1987.     

Anisotropic multiplicative elastoplasticity for the prediction of earings in sheet forming

In this work, the simulation of earings in cup drawing by means of a recently developed anisotropic combined hardening material model is discussed. The model represents a multiplicative formulation of anisotropic elastoplasticity in the finite strain regime with nonlinear kinematic and isotropic hardening. Plastic anisotropy is described by the use of second-order structure tensors as additional arguments in the representation of the yield function and the plastic flow rule. The evolution equations are integrated by a form of the exponential map that preserves the plastic volume and the symmetry of the internal variables. Finite element simulations of cylindrical cup drawing processes are performed by means of ABAQUS/Standard where the discussed material model has been implemented into a user-defined reduced integration solid-shell element. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The limit equilibrium of an anisotropic medium under the general plasticity condition

A theory of the limit equilibrium of an anisotropic medium under the general plasticity condition in the plane strain state is developed. The proposed yield criterion (the limit equilibrium condition) is obtained by combining the von Mises–Hill yield criterion of an ideally plastic anisotropic material and Prandtl's limit equilibrium condition for a medium under the general plasticity law. It is shown that the problem is statically determinate, i.e., if the boundary conditions are specified in stresses, the stress state in plastic region can only be obtained using equilibrium equations. It is established that the equations describing the stress state are hyperbolic and have two families of characteristic curves that intersect at variable angles. In deriving the equations describing the velocity field, the material is assumed to be rigid plastic, and the associated law of flow is applied. It is shown that the equations for the velocities are also hyperbolic, and their characteristic curves are identical with those of the equations for stresses. However, the directions of the principal values of the stress and strain rate tensors are different due to the anisotropy of the material. The characteristic directions differ from the isotropic case in that the normal and tangential components of the stress tensor do not satisfy the limit conditions. It is established that the equations obtained allow of partial solutions, and in this case, at least one family of characteristic curves consists of straight lines. The conditions along the lines of discontinuity of the velocity are investigated, and it is shown that, as in the isotropic case, these are characteristic curves of the system of governing equations. In the anisotropic formulation, the well-known Rankine problem of the limit state of a ponderable layer is solved. From an analysis of the velocity field it is shown that plastic flow of the entire layer is possible only for a slope angle equal to the angle of internal friction. For slope angles less than the angle of internal friction, the solutions obtained are solutions of problems of the pressure of the medium on the retaining walls. The change in this pressure as a function of the parameters of anisotropy is investigated, and turns out to be significant.     

关于平面应变和反平面应变复合型裂纹尖端的理想塑性应力场

文献[1]在裂纹尖端的理想塑性应力分量都只是θ的函数的条件下,利用平衡方程、应力应变率关系、相容方程和屈服条件导出了平面应变和反平面应变复合型裂纹尖端的理想塑性应力场的一般解析表达式。但文献[1]对应力应变率关系式中的比例因子λ(r,θ)作了很多限制,即假定λ与θ无关,并假定λ=c或cr-1。本文取消了对λ的这些限制。而文献[1]所研究的λ=crn(n=0或-1)的情形,只是本文的一个特殊情况。