基于能量等效原理的应变局部化分析:Ⅱ.有限元解法

以非局部塑性理论为基础,应用状态空间理论,通过局部和非局部两个状态空间的塑性能量耗散率等效原理,提出了一种求解应变局部化问题的新方法,以得到与网格无关的数值解.针对二维问题的屈服函数和流动法则导出了求解非局部内变量的一般方程,并提出了在有限元环境中求解应变局部化问题的应力更新算法.为了验证所提出的方法,对1个一维拉杆和3个二维平面应变加载试件进行了有限元分析.数值结果表明,塑性应变的分布和载荷-位移曲线都随着网格的变小而稳定地收敛,应变局部化区域的尺寸只与材料内尺度有关,而对有限元网格的大小不敏感.对于一维问题,当有限元网格尺寸减小时,数值解收敛于解析解.对于二维剪切带局部化问题,数值解随着网格尺寸的减小而稳定地向唯一解收敛.当网格尺寸减小时,剪切带的宽度和方向基本上没有变化.而且得到的塑性应变分布和网格变形是平滑的.这说明,所提方法可以克服经典连续介质力学模型导致的网格相关性问题,从而获得具有物理意义的客观解.此模型只需要单元之间的位移插值函数具有C~0连续性,因而容易在现有的有限元程序中实现而无需对程序作大的修改.     

基于有限体积法的三维局部冲刷数值模型研究及应用

局部冲刷的三维数值模拟可预测水力冲刷的破坏程度和破坏机制,进而提供更加合理的工程措施以减轻或避免局部冲刷造成的工程破坏。基于有限体积法和非结构化的计算网格构建了以水动力学模型、泥沙冲淤和河床变形方程为基础的三维局部冲刷数值模型。水动力学模型中的湍流模型为剪切应力SST k-ω输运模型,泥沙冲淤以底床切应力大小和分布为基础,水沙模型的耦合采用单向弱耦合方式。首先,通过ANSYS-FLUENT软件数值计算水动力学模型后,将水力特性数据单向传递至泥沙模块,并应用UDF函数二次开发实现泥沙模型的数值计算。利用动网格技术重构因河床地形更新引起的变形网格。与动床圆柱冲刷和丁坝局部冲刷的试验结果进行比较,验证了局部冲刷数值模型的可靠性。从平衡冲深时的冲刷深度和冲坑内水流特性等结果的对比可以看出,该数值模型成功地模拟出最终冲刷地形和形态,并能捕捉不同时刻的三维地形变化。根据数值模型的建立及应用结果分析主要得到以下结论,以切应力观点为基础开发该模型时,具有简易性和较强的可靠性;单元体泥沙通量的重构和床面坡度等因素均影响模型的精度;FLUENT软件提供的动网格技术能较好重构小变形网格,但是重构因地形变化引起的大变形网格时略显不足。     

非对称的非局部塑性理论

从非局部连续场论出发，假定形变与局部转动均属微小，当存在体力矩出现非对称应力场时，设对称应力的能量函数和非对称应力的能量函数可以独立计算。基于热力学原理和屈服面的概念，建立了一种新的非对称－非局部弹塑性力学理论。     

基于非局部塑性模型的应变局部化理论分析及数值模拟

通过求解一个第二类Fredholm方程,得到了基于非局部塑性软化模型的应变局部化问题理论解,结果表明,只有在当采用过非局部修正形式的非局部塑性软化模型才能得到应变局部化解,且得到的塑性应变分布和荷载响应依赖于所引入的特征长度及过非局部权参数。通过一维应变局部化有限元数值解,验证了非局部理论的引入能克服计算结果的网格敏感...     

弹塑性损伤模型在应变局部化分析中的应用

非局部本构理论是为了有效地模拟应变局部化现象而提出并被广泛采用的理论模型．将目前已有的模型归为两大类,一是面积加权平均的非局部非弹性模型;二是梯度依赖的非局部模型．经过对这两大类模型的比较研究,发现Aiflantis模型用于非均匀材料的局部化现象数值模拟时是一个较为理想的模型,但该模型还有需改进之处．     

微结构非局部效应的多重性模型及在微梁弯曲中的应用

基于Eringen非局部弹性理论,直接利用逐次逼近法推导了非局部应力场的精确表达,该精确的非局部应力可具体表示为一个无穷级数的形式. 然后以微梁的横向弯曲和纯弯曲变形为例,建立平衡方程并求解及分析了挠度受非局部效应的影响. 结果表明：根据所取非局部小尺度参数大小的不同,非局部微梁的弯曲挠度可低于也可以高于经典力学下的挠度,非局部效应的增大可提高亦可降低结构的抗弯刚度. 本文结果证明了Wang以及Lim等人分别提出的两种相反的非局部模型的各自正确性. 同时首次发现,弯曲挠度随着非局部效应的增大而上下波动且存在若干跳跃点,挠度是非局部小尺度参数的非单调函数,研究同时给出了一种确定材料非局部常数的建议途径.     

岩石变形局部化智能识别的DSCM-CNN方法

岩石变形局部化的识别对于岩石破坏机理、岩土工程灾害预测预警有着重要的意义。本文将数字散斑相关方法（digital speckle correlation methods,DSCM）与卷积神经网络（convolutional neural networks,CNN）相结合,提出了一种用于岩石变形局部化智能识别的DSCM-CNN模型。通过DSCM获取岩石试件在单轴压缩实验过程中的最大剪应变场云图,根据变形局部化带位置进行标注,完成数据集的构建;利用训练数据集对DSCM-CNN智能识别模型进行训练。通过红砂岩单轴压缩实验对该方法进行验证,结果表明：DSCM-CNN模型可以实现岩石变形局部化带位置的自动识别,子集准确率、精确度、召回率等指标分别达到94.19%,97.21%和96.41%,证明了岩石变形局部化智能识别的DSCM-CNN模型的可行性,为岩石变形局部化智能监测提供了一种新的思路。     

高分子材料平面应变拉伸变形局部化

将基于应变软化玻璃状高分子材料微观特征建立的ＢＰＡ８－链分子网络模型引入ＵｐｄａｔｉｎｇＬａｇｒａｎｇｅ有限元方法，建立了适于变形局部化分析的大变形弹塑性有限元驱动应力法．在此基础上，数值模拟了初始各向同性高分子材料平面应变拉伸变形局部化的传播过程．探讨了ＢＰＡ模型对具有加工硬化特性的结晶性高分子材料变形分析的适应性；分析了局部化传播过程中颈缩截面的非均匀应力三轴效应；最后，讨论了网格尺寸以及初始几何不均匀性对颈缩扩散以及应力三轴效应的影响     

基于一类非局部宏-微观损伤模型的裂纹模拟

结合近场动力学和统一相场理论的基本思想,最近提出了一类非局部宏-微观损伤模型,为固体裂纹扩展模拟提供了新途径.本文在此基础上改进了微观损伤准则,并给出损伤的■语言以刻画固体破坏过程中位移场的不连续程度.在改进模型中,首先根据两物质点(即物质点对)之间的变形量,基于相对临界伸长量的历史最大超越程度,给出表征物质键性能退化的微细观损伤.进而,对影响域内的物质键损伤进行空间局部加权平均,获得宏观拓扑损伤.通过引入能量退化函数,建立基于能量的损伤与宏观拓扑损伤之间的关系,由此将其嵌入连续损伤力学基本框架,形成了问题求解的基本方程.该模型是一类非局部化模型,可采用有限单元法进行离散求解,避免了经典局部损伤力学所面临的网格敏感性问题.文中,进一步将其应用于具有强非线性回弹特性的裂纹扩展模拟问题.实例分析表明,本文方法不仅可以把握裂纹扩展模式,而且能够定量刻画裂纹扩展过程中的载荷-变形关系.最后指出了需要进一步研究的问题.     

断裂力学及边界元法在有限体应变局部化问题中的应用

微裂纹模型是研究砂土变形中应变局部化问题的微观力学模型。本文在前文的基础上建立了有限平面的徽裂纹模型的基本方程。数值解析表明,微裂纹模型可再现应变局部化及应变软化现象。同时,本文简要地讨论了边界约束、尺寸效应及侧压对应变局部化的影响。     

Non-local continuum model and its numerical simulation for localization problem

A non-local continuum model for strain-softening simply taking plastic strain or damage variable as a non-local variable is derived by using the additive decomposition principle of finite deformation gradient. At the same time, variational equations, their finite element formulations and numerical convoluted integration algorithm of the model in current configuration usually called co-moving coordinate system are given. Stability and convergence of the model are proven by means of the weak convergence theorem of general function and the convoluted integration theory. Mathematical and physical properties of the characteristic size for material or structure are accounted for within the context of a statistical weighted or kernel function, and way is investigated. Numerical simulation shows that this model is suitable for to analyzing deformation localization problems. The project supported by the National Natural Science Foundation of China (No. 19632030).     

单晶有限变形的热力耦合计算模型

以弹性变形梯度作为基本变量,结合热力学理论构造了单晶有限变形的热、力耦合计算模型。该模型考虑了温度、变温速率以及塑性耗散等条件对单晶有限变形的影响,相对于传统的以弹性变形梯度为基本变量的晶体塑性模型,算法能够体现温度效应的影响。采用隐式的积分方法对建立的控制方程进行计算以保证求解过程的稳定。以1100Al单晶为例计算了不同升温、降温速率,以及不同应变率影响下的材料应力-应变的响应。结果表明,模型能较好地反映变温过程中,单晶各向异性性质的演化以及应力、应变之间关系的变化。     

A new integration algorithm for finite deformation of thermo-elasto-viscoplastic single crystals

An algorithm for integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key feature of this new approach is that it can describe the finite deformation of crystals under thermal conditions. The obtained plastic deformation gradient contains not only plastic defor- mation but also thermal effects. The governing equation for the plastic deformation gradient is obtained based on ther- mal multiplicative decomposition of the total deformation gradient. An implicit method is used to integrate this evo- lution equation to ensure stability. Single crystal 1 100 aluminum is investigated to demonstrate practical applications of the model. The effects of anisotropic properties, time step, strain rate and temperature are calculated using this integration model.     

气泡在液体中运动过程的数值模拟

本文用数值方法预测气泡在液体中的百定常运动。运用位标函数进行界面的隐含跟踪并且与有限体积法相结合构成一种可行的计算方法。本文方法允许在界面处存在很大的物性差，而且较容易将表面张力引入控制方程。我们对气液两相流中单个气泡的运动进行了计算，得到了与实验结果符合很好的数值结果。     

Static and dynamic behaviour of nonlocal elastic bar using integral strain-based and peridynamic models

The static and dynamic behaviour of a nonlocal bar of finite length is studied in this paper. The nonlocal integral models considered in this paper are strain-based and relative displacement-based nonlocal models; the latter one is also labelled as a peridynamic model. For infinite media, and for sufficiently smooth displacement fields, both integral nonlocal models can be equivalent, assuming some kernel correspondence rules. For infinite media (or finite media with extended reflection rules), it is also shown that Eringen's differential model can be reformulated into a consistent strain-based integral nonlocal model with exponential kernel, or into a relative displacement-based integral nonlocal model with a modified exponential kernel. A finite bar in uniform tension is considered as a paradigmatic static case. The strain-based nonlocal behaviour of this bar in tension is analyzed for different kernels available in the literature. It is shown that the kernel has to fulfil some normalization and end compatibility conditions in order to preserve the uniform strain field associated with this homogeneous stress state. Such a kernel can be built by combining a local and a nonlocal strain measure with compatible boundary conditions, or by extending the domain outside its finite size while preserving some kinematic compatibility conditions. The same results are shown for the nonlocal peridynamic bar where a homogeneous strain field is also analytically obtained in the elastic bar for consistent compatible kinematic boundary conditions at the vicinity of the end conditions. The results are extended to the vibration of a fixed–fixed finite bar where the natural frequencies are calculated for both the strain-based and the peridynamic models.     

The Payne effect in finite viscoelasticity: constitutive modelling based on fractional derivatives and intrinsic time scales

As we know from experimental testing, the stiffness behaviour of carbon black-filled elastomers under dynamic deformations is weakly dependent on the frequency of deformation but strongly dependent on the amplitude. Increasing strain amplitudes lead to a decrease in the dynamic stiffness, which is known as the Payne effect. In this essay, we develop a constitutive approach of finite viscoelasticity to represent the Payne effect in the context of continuum mechanics. The starting point for the constitutive model resulting from this development is the theory of finite linear viscoelasticity for incompressible materials, where the free energy is assumed to be a linear functional of the relative Piola strain tensor. Motivated by the weak frequency dependence of the dynamic stiffness of reinforced rubber, the memory kernel of the free energy functional is of the Mittag Leffler type. We demonstrate that the model is compatible with the Second Law of Thermodynamics and equal to a fractional differential equation between the overstress of the Second Piola Kirchhoff type and the Piola strain tensor. In order to represent the dependence of the dynamic stiffness on the amplitude of strain, we replace the physical time by an intrinsic time variable. The temporal evolution of the intrinsic time is driven by an internal variable, which is a measure for the current state of the material's microstructure. The material constants of the model are estimated using a stochastic identification algorithm of the Monte Carlo type. We demonstrate that the constitutive approach pursued here represents the combined frequency and amplitude dependence of filler-reinforced rubber. In comparison with the micromechanical Kraus model developed for sinusoidal strains, the theory set out in this essay allows the representation of the stress response under arbitrary loading histories.     

层合板六参量几何非线性高阶剪切理论

提出了层合板六参量的高阶剪切变形理论的位移场假定,以考虑在大变形条件下层合板法向变形和厚度的变化。同时对ｖｏｎ Ｋａｒｍａｎ应变位移简化假设进行补充修改,考虑某些有限变形条件下被忽略小量的影响,建立了对应于该文六参量模型和更加适凳大变形分析的层合板几何非线性关系,平衡方程和边界条件。利用该文模型分析了橡胶复合材料简支板的大变形弯曲行为,并对比Ｒｅｄｄｙ五参量几何非线性简单高阶剪切变形层合理论解和弹     

A finite strain kinematic hardening constitutive model based on Hencky strain: General framework, solution algorithm and application to shape memory alloys

The logarithmic or Hencky strain measure is a favored measure of strain due to its remarkable properties in large deformation problems. Compared with other strain measures, e.g., the commonly used Green-Lagrange measure, logarithmic strain is a more physical measure of strain. In this paper, we present a Hencky-based phenomenological finite strain kinematic hardening, non-associated constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The derivation is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, and on the use of the isotropic property of the Helmholtz strain energy function. We also use the fact that the corotational rate of the Eulerian Hencky strain associated with the so-called logarithmic spin is equal to the strain rate tensor (symmetric part of the velocity gradient tensor). Satisfying the second law of thermodynamics in the Clausius-Duhem inequality form, we derive a thermodynamically-consistent constitutive model in a Lagrangian form. In comparison with the available finite strain models in which the unsymmetric Mandel stress appears in the equations, the proposed constitutive model includes only symmetric variables. Introducing a logarithmic mapping, we also present an appropriate form of the proposed constitutive equations in the time-discrete frame. We then apply the developed constitutive model to shape memory alloys and propose a well-defined, non-singular definition for model variables. In addition, we present a nucleation-completion condition in constructing the solution algorithm. We finally solve several boundary value problems to demonstrate the proposed model features as well as the numerical counterpart capabilities.     

The reptation model with segmental stretch

The Doi-Edwards model with segmental stretch and a non-linear finitely extensible spring law is described and examined in simple flow situations where analytic results are derivable; namely oscillatory flow and steady state flow at high deformation rates. The model is shown to be consistent with the Bueche-Ferry hypothesis in fast large strain unidirectional flows but to violate this rule in small strain reversing flows. The discrepancy is identified with a preaveraging approximation used to describe the relative tube-chain velocity. Experimentally verifiable scaling rule for the birefringence as a universal function of a planar flow-type parameter and deformation rate are identified. Sensitivity to the extensional flow character, absent in the original tube model, manifests itself with the introduction of segmental stretch. Although the model generates a non-separable memory function kernel the deformation dependence of the memory function is quantitatively shown to have negligible impact on the predicted theological properties relative to the original Doi-Edwards model. With this simplification, relatively uncomplicated approximations to the segmental stretch model can be deduced.     

A coupled temperature and strain rate dependent yield function for dynamic deformations of bcc metals

A coupled temperature and strain rate microstructure physically based yield function is proposed in this work. It is incorporated along with the Clausius–Duhem inequality and an appropriate free energy definition in a general thermodynamic framework for deriving a three-dimensional kinematical model for thermo-viscoplastic deformations of body centered cubic (bcc) metals. The evolution equations are expressed in terms of the material time derivatives of the elastic strain, accumulated plastic strain (isotropic hardening), and the back stress conjugate tensor (kinematic hardening). The viscoplastic multipliers are obtained using both the Consistency and Perzyna viscoplasticity models. The athermal yield function is employed instead of the static yield function in the case of the Perzyna viscoplasticity model. It is found that the static strain rate value, at which the material shows rate-independent behavior, varies with the material deformation temperature. Computational aspects of the proposed model are addressed through the finite element implementation with an implicit stress integration algorithm. Finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program ABAQUS/Explicit [ABAQUS, 2003. User Manual, Version 6.3. Habbitt, Karlsson and Sorensen Inc., Providence, RI] via the user material subroutine coded as VUMAT. Numerical implementation for a simple compression problem meshed with one element is used to validate the proposed model implementation with applications to tantalum, niobium, and vanadium at low and high strain rates and temperatures. The analysis of a tensile shear banding is also investigated to show the effectiveness and the performance of the proposed framework in describing the strain localizations at high velocity impact. Results show mesh independency as a result of the viscoplastic regularization used in the proposed formulation.