冲击载荷下钨合金圆台试件绝热剪切变形局部化的数值模拟

采用有限元计算编码ABAQUS模拟了钨合金圆台试件在冲击载荷下的变形和剪切局部化行为.计算采用二维轴对称应变条件下的绝热模型.钨合金的本构方程采用热粘塑性形式的Johnson-Cook模型.为了得到不同尺度的变形信息,计算中用了两种网格;先用粗糙网格分析试件变形局部化的概貌;接着,用细密网格(在变形局部化区域,网格尺寸达到10μm)分析绝热剪切带的形成和发展.有限元模拟得到的绝热剪切带位置和方向与实验一致.计算结果表明,绝热剪切带的形成和发展与试件的应力状态密切相关.     

冲击载荷下钨合金圆台试件绝热剪切变形局部化的数值模

采用有限元计算编码ABAQUS模拟了钨合金圆台试件在冲击载荷下的变形和剪切局部化行为。计算采用二维轴对称应变条件下的绝热模型。钨合金的本构方程采用热粘塑性形式的Johnson Cook模型。为了得到不同尺度的变形信息 ,计算中用了两种网格 ;先用粗糙网格分析试件变形局部化的概貌 ;接着 ,用细密网格 (在变形局部化区域 ,网格尺寸达到 10 m)分析绝热剪切带的形成和发展。有限元模拟得到的绝热剪切带位置和方向与实验一致。计算结果表明 ,绝热剪切带的形成和发展与试件的应力状态密切相关。     

基于偶应力理论剪切带问题的弹塑性有限元分析

对于软化材料的剪切带问题，传统弹塑性有限元分析遇到了困难，进入弹塑 性阶段，计算结果对网格划分敏感，出现所谓的有限元网格依赖性问题，随着网格的细分， 计算常常因不收敛导致失效. 用有限元软件ABAQUS计算了3个例题，证实了传统弹塑性 有限元分析软化材料剪切带问题的局限性，同时证实对于无剪切带的厚壁筒问题不会出现上 述问题. 进一步引入细观非局部化理论，对非局部理论含有的细观参数\ell 进行了深入讨论，并采用可通过C0 -1分片检验的18参偶应力三角形单元， 重新计算了3个例题，结果避免了上述问题，说明 细观偶应力有限元尤其适用于分析剪切带问题.     

平面Cosserat模型有限元分析的4和8节点单元与分片试验研究

经典连续体理论不包括物质内部尺度，当考虑应变软化问题时，有限元结果对网格具有很强的依赖性。与经典连续介质力学理论不同，Cosserat连续体模型在传统平动自由度的基础上添加了一独立的旋转自由度，在本构模型中引入了内尺度参数。本文研究了基于Cosserat理论的平面4和8节点等参元以及8（4）节点线、角位移混合插值等参单元，给出Cosserat单元分片试验的实施过程。最后将单元运用到小孔应力集中问题的分析当中，通过计算结果与理论解的比较，表明了4和8节点以及8（4）节点等参元的适用性，为问题的非线性分析打下基础。     

高速切削过程中诱发绝热剪切带形成的热塑性剪切波

提出了高速切削过程中诱发绝热剪切带形成的热塑性剪切波的传播机理,针对锯齿形切屑中热望性区域内的塑性梯度变形特征、动量和能量耗散情况,建立了与切削条件相关的热塑性剪切波的传播模型及剪切带宽度模型.在此基础上,通过淬硬45钢的切削实验并结合改进的Johnson-Cook本构模型分析了热塑性剪切波的传播规律,并将剪切带宽度模型与已提出的DB模型、WR模型和DM模型做了对比,结果表明,由热塑性剪切波传播理论推导的剪切带宽度模型与实验结果较其他模型吻合较好.     

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.     

基于应变梯度中厚板单元的石墨烯振动研究

基于应变梯度理论建立了单层石墨烯等效明德林(Mindlin) 板动力学方程,推导了四边简支明德林中厚板自由振动固有频率的解析解. 提出了一种考虑应变梯度的4 节点36 自由度明德林板单元,利用虚功原理建立了单层石墨烯的等效非局部板有限元模型. 通过对石墨烯振动问题的研究,验证了应变梯度有限元计算结果的收敛性. 运用该有限元法研究了尺寸、振动模态阶数以及非局部参数对石墨烯振动特性的影响. 研究表明,这种单元能够较好地适用于研究考虑复杂边界条件石墨烯的尺度效应问题. 基于应变梯度理论的明德林板所获得石墨烯的固有频率小于基于经典明德林板理论得到的结果. 尺寸较小、模态阶数较高的石墨烯振动尺度效应更加明显. 无论采用应变梯度理论还是经典弹性本构关系,考虑一阶剪切变形的明德林板模型预测的固有频率低于基尔霍夫(Kirchho) 板所预测的固有频率.     

可变网格的有限单元分析在边坡稳定计算中的应用

本文在非线性有限单元法的基础上，引进八节点的狭长单元来描述边坡中的滑动面，同时对于有限元单元网格可调节点坐标进行变更形成新的网格，于是利用原有基本网格架，通过多次有限元分析求出边坡中可能滑动面的稳定系数曲线Ｋ＝ｆ（α），并进而确定最危险的滑动面，在此基础上开展一系列稳定分析工作。     

封面故事

<正>图片为Trefftz基本解有限元法分析轴对称热传导问题的应用实例。带孔圆环内壁恒温外壁绝热,其几何参数如图Ⅰ所示。分析中采用8节点8源点Trefftz基本解环单元(图Ⅱa)进行网格划分,ABAQUS温度云图如图Ⅱb所示。同时,图Ⅲ给出了Trefftz有限元与ABAQUS的等温线对比,     

数据驱动梯度结构材料弹塑性本构

梯度结构材料因其优异的力学性能被广泛应用于工程结构中。本文整合塑性理论和人工神经网络技术,发展了一种构建梯度结构材料弹塑性本构模型的新方法。该方法基于梯度结构材料不同位置的微结构,构建不同代表性体积单元,进而生成应力应变数据,应用生成的数据训练人工神经网络,建立基于神经网络的材料本构模型。应用该方法,本文开展了针对实际工程结构件的计算,算例结果表明,该方法可快速计算梯度功能复合材料在循环载荷反向载荷状态下的宏观响应,且较为准确。该方法为模拟含复杂梯度结构材料的结构件弹塑性力学响应提供了新的工具。     

On large-strain finite element solutions of higher-order gradient crystal plasticity

A finite-strain higher-order gradient crystal plasticity model accounting for the backstress effect originating from the existence of geometrically necessary dislocations (GNDs) is applied to plane strain finite element analysis. Different element types are tested to seek out an element formulation that is reliable and useful for solving problems involving severe plastic deformation. In the present finite element formulation, the GND density rates are chosen to be additional nodal degrees of freedom. Different orders of shape functions are employed for the interpolation of displacement rates and GND density rates. Their effects on solutions are examined in detail by considering three boundary value problems: a simple shear of a constrained layer (a film), a compression problem with loading surfaces impenetrable to dislocations, and a tension problem involving shear band formation. In all the cases, the formulation in which eight-node elements with reduced integration and four-node elements with full integration are used respectively for displacement rates and the GND density rates gives reasonable solutions. In addition to the discussion on the choice of finite elements, detailed behavior in gradient-dependent solids, such as the accumulation of GND density and the distribution of backstress on each slip system, is investigated by utilizing the reliable computational results obtained.     

Strain gradient crystal plasticity effects on flow localization

In metal grains one of the most important failure mechanisms involves shear band localization. As the band width is small, the deformations are affected by material length scales. To study localization in single grains a rate-dependent crystal plasticity formulation for finite strains is presented for metals described by the reformulated Fleck–Hutchinson strain gradient plasticity theory. The theory is implemented numerically within a finite element framework using slip rate increments and displacement increments as state variables. The formulation reduces to the classical crystal plasticity theory in the absence of strain gradients. The model is used to study the effect of an internal material length scale on the localization of plastic flow in shear bands in a single crystal under plane strain tension. It is shown that the mesh sensitivity is removed when using the nonlocal material model considered. Furthermore, it is illustrated how different hardening functions affect the formation of shear bands.     

Effects of texture on shear band formation in plane strain tension/compression and bending

In this study, effects of typical texture components observed in rolled aluminum alloy sheets on shear band formation in plane strain tension/compression and bending are systematically studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic–viscoplastic continuum slip constitutive relation. First, a simple model analysis in which the shear band is assumed to occur in a weaker thin slice of material is performed. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. Second, the shear band development in plane strain tension/compression is analyzed by the finite element method. Predictability of the finite element analysis is compared to that of the simple model analysis. Third, shear band developments in plane strain pure bending of a sheet specimen with the typical textures are studied. Regions near the surfaces in a bent sheet specimen are approximately subjected to plane strain tension or compression. From this viewpoint, the bendability of a sheet specimen may be evaluated, using the knowledge regarding shear band formation in plane strain tension/compression. To confirm this and to encompass overall deformation of a bent sheet specimen, including shear bands, finite element analyses of plane strain pure bending are carried out, and the predicted shear band formation in bent specimens is compared to that in the tension/compression problem. Finally, the present results are compared to previous related studies, and the efficiency of the present method for materials design in future is discussed.     

岩质边坡稳定性及预应力锚固分析现状

本文首先对目前常用的各类边坡稳定性分析方法的主要特点进行了评述,包括定性方法类的历史分析法、工程地质类比法、图解法、专家系统法,定量分析方法类的确定性模型法,如极限平衡法,应力应变分析法;非确定性模型法,如可靠性分析法、灰色系统理论法及模糊综合评判法等;及两类方法结合而成的随机有限元法。其次,对预应力锚固边坡的设计及稳定性分析作了阐述。     

Meshfree analysis of softening elastoplastic solids using variational multiscale method

A meshfree multiscale method is presented for efficient analysis of elastoplastic solids. In the analysis of softening elastoplastic solids, standard finite element methods or meshfree methods typically yield mesh-dependent results. The reason for this well-known effect is the loss of ellipticity of the boundary value problem. In this work, the scale decomposition is carried out based on a variational form of the problem. A coarse scale is designed to represent global behavior and a fine scale to represent local behavior. A fine scale region is detected from the local failure analysis of an acoustic tensor to indicate a region where deformation changes abruptly. Each scale variable is approximated using a meshfree method. Meshfree approximation is well-suited for adaptivity. As a method of increasing the resolution, a partition of unity based extrinsic enrichment is used. In particular, fine scale approximations are designed to appropriately represent local behavior by using a localization angle. Moreover, the regularization effect through the convexification of non-convex potential is embedded to represent fine scale behavior. Each scale problem is solved iteratively. The proposed method is applied to shear band problems. In the results of analysis about pure shear and compression problems, straight shear bands can be captured and mesh-insensitive results are obtained. Curved shear bands can also be captured without mesh dependency in the analysis of indentation problem.     

基于多元线性回归分析的土坡有限元失稳判据定量研究

塑性区连通程度是有限单元法判别土坡是否达到极限状态的重要依据,鉴于此判据目前尚未取得统一,本文着重对均质土坡失稳判据进行了定量研究。在主要考虑对土坡稳定性影响较大的三大参数(黏聚力c、内摩擦角φ、坡比λ)的前提下,通过经典条分法选取了多组处于极限平衡状态的土坡参数组合,对这些参数组合进行有限元程序计算,求得极限平衡状态下土坡剪切带等效塑性应变中值连通率,再采用多元线性统计回归方法,得出塑性区中值连通率与土坡参数的关系公式y=0.020702c+0.024417φ-0.67898λ+0.46799,从而为土坡有限元稳定性分析提供了定量失稳判据,并且使得有限单元法与经典条分法计算成果具有一定的可比性。算例分析表明,利用本文判据公式得到的安全系数与Bishop法计算成果相吻合,从而验证了失稳判据公式的正确性。     

Finite element implementation and numerical issues of strain gradient plasticity with application to metal matrix composites

A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories.     

JRC-JCS模型抗剪强度估算的平均斜率法

结构面对工程岩体的稳定性有着决定性的影响,结构面的抗剪强度参数是分析岩体稳定的关键的参数。本文回顾了结构面抗剪强度估算的JRC-JCS模型及其估算方法,提出了可快速估算结构面抗剪强度参数的平均斜率法,并通过对比分析阐明平均斜率法的优越性。     

双剪统一弹塑性有限差分方法研究

基于拉格朗日有限差分方法,建立了双剪统一弹塑性有限差分计算格式,并利用VC++语言编写动态链接库文件将双剪统一弹塑性模型导入拉格朗日有限差分程序FLAC(Fast Lagrangian Analysis of Continua)中进行计算分析。双剪统一弹塑性有限差分方法可以模拟复杂应力状态下结构的渐进破坏,无需形成刚度矩阵,对于材料非线性问题无需进行迭代计算,因此在理论和工程应用中都有积极的意义。本文利用双剪统一弹塑性有限差分方法对拉压强度不等材料的厚壁圆筒受内压、中心带孔板条受拉压、条形基础下的地基极限分析及边坡问题进行了数值分析并与滑移线场等解析方法计算结果进行对比,结果均吻合较好。