计入横向剪切变形时层合板位移差分解法

在考虑横向剪切变形对层合板弹性解的影响时，本文提出一种数值计算方法。由边界条件给出边界结点位移的表达式，根据薄板的经典理论和一阶横向剪切变形理论导出位移增量所满足的平衡微分方程，引用经典理论计算的横向剪力修正了荷载列阵。致使在较粗的网格划分时、宽广的层合板长厚比范围内，仍能得到与解析解颇为一致的数值解。     

能量法分析纳晶材料裂纹的萌生

利用能量守恒定律分析了纳晶材料裂纹在三晶交处的萌生，分别推导了纳晶材料中的特定旋转变形能、晶界滑移能、晶界扩散能，并运用最大等效裂纹能量释放率准则来判断纳晶材料裂纹萌生。结果表明：特定旋转变形、晶界扩散均能松弛裂纹尖端的应力，阻碍裂纹的生长；而晶界滑移使得晶界位错在三晶交处堆积，造成三晶交处的应力集中，促使裂纹的生长；稳定状态下，外力做的功等于由特定旋转变形、晶界滑移、晶界扩散造成的能量耗散。     

考虑横向拉伸影响的FGM板的静态分析

在三阶剪切变形理论的基础上,添加关于厚度坐标z的幂函数项,并假设板结构的上下表面剪切力为0,提出了一种考虑横向拉伸影响的高阶剪切变形理论。并且研究了简支边界条件下受静态载荷作用的功能梯度材料矩形板的静态弯曲行为。基于虚功原理推导出了功能梯度矩形板的基本方程,利用Navier双三角级数法计算了功能梯度材料矩形板在静态载荷作用下沿厚度方向的位移及应力分布的数值结果。计算结果与三维精确解理论、其他高阶剪切变形理论得到的数值结果进行了比较。对比结果表明,改进的考虑横向拉伸影响的高阶剪切变形理论的正确性和优越性。     

弹塑性变形油藏中多相渗流的数值模拟

基于流固耦合力学理论,建立了弹性变形油藏中多相渗流的数学模型,该模型考虑了渗流与变形的耦合作用,以及注采交变载荷作下油藏多孔介质的弹性变形特征,给出了耦合数值模拟方法和算例。     

考虑全截面剪切变形的箱梁挠度简化计算方法

为进一步简化箱梁弯曲挠度计算方法，本文运用能量变分原理和铁摩辛柯梁理论推导了考虑全截面剪切变形的箱梁弯曲挠度计算公式，基于剪滞控制微分方程和现行公路桥规中翼缘有效宽度的折算办法，提出了全截面剪切变形的箱梁挠度简化计算方法。简支和连续箱梁算例分析表明：考虑全截面剪切影响的箱梁理论挠度、简化方法结果与ANSYS数值解吻合良好，且最大差值比基本在5%以内，验证了所提简化计算方法的正确性和适用性。     

弹性曲梁在机械和热载荷共同作用下的几何非线性模型及其数值解

基于Euler-Bernoulli梁的几何非线性理论,建立了弹性曲梁在任意分布机械载荷和热载荷共同作用下的几何非线性静平衡控制方程。该模型不仅计及了轴线伸长,同时也精确地考虑了梁的初始曲率对变形的影响以及轴向变形与弯曲变形之间的相互耦合效应。应用打靶法数值求解了半圆形曲梁在横向均匀升温作用下的非线性弯曲问题,数值比较了轴向伸长对曲梁变形的影响。     

阶跃载荷作用下弹塑性悬臂梁的变形机制与能量耗散

基于大挠度动力控制方程，应用有限差分离散求解，研究了阶跃载荷作用下弹塑性悬臂梁的动力行为。通过对动力响应早期内力、变形以及能量分布规律的分析，考察了悬臂梁的弹塑性响应模式和变形机制，并与已有的刚塑性分析进行了系统的比较。数值计算表明，阶跃载荷的不同幅值使得梁的响应模式存在较大差异，弹塑性分析肯定了刚塑性理论在处理中载情形的准确性，同时也指出了其在处理低载和高载情形时的缺陷。通过与小变形理论计算结果的比较，指出了考虑大变形效应的必要性，为今后的大变形刚塑性动力分析提出了建议。     

延性材料动态损伤演化模型研究

从微损伤系统的统计描述出发，应用Ｍｏｒｉ－Ｔａｎａｋａ理论的物理思想，考虑了微孔洞间的相互作用，建立了延性材料动态损伤的统计演化模型。结果能够描述材料在外载作用下的损伤弱化效应。还分析了材料变形中的两种不同的耗散机制，考虑了含损伤的本构关系。将上述模型用于几种材料的层裂过程数值模拟，并与实验结果作了初步比较。     

A NEW SPATIAL THIN-WALLED BEAM ELEMENT INCLUDING TRANSVERSE AND TORSIONAL SHEAR DEFORMATION

基于Timoshenko梁及Benscoter薄壁杆件理论,建立了考虑剪切变形、弯扭耦合以及翘曲剪应力影响的空间任意开闭口薄壁截面梁单元. 通过引入单元内部结点,对弯曲转角和翘曲角采用三节点Lagrange独立插值的方法,考虑了剪切变形和翘曲剪应力的影响并避免了横向剪切锁死问题;借助载荷作用下薄壁梁的截面运动分析,在位移和应变方程中考虑了弯扭耦合的影响. 通过数值算例将该单元的计算结果与理论解以及商用有限元软件和其他文献中的数值解进行对比和验证,结果对比表明该薄壁梁单元具有良好的精度和收敛性.     

考虑剪切变形的矩形截面薄壁杆件畸变分析

在以往不考虑剪切变形的畸变分析理论基础上，假设翘曲位移及切向位移的分布函数，考虑剪切变形的影响，利用最小势能原理建立单位均布畸变荷载作用下的畸变角微分方程。采用一般解法对该畸变角微分方程进行求解，并推导求解的初参数法。随之，通过实例验证了本文理论的正确性，结果表明考虑剪切变形的影响大大提高了考虑畸变效应的计算精度。     

A finite deformation analysis of polycrystal by considering the influence of grain boundary

By combining grain boundary (GB) and its influence zone, a micromechanic model for polycrystal is established for considering the influence of GB. By using the crystal plasticity theory and the finite element method for finite deformation, numerical simulation is carried out by the model. Calculated results display the microscopic characteristic of deformation fields of grains and are in qualitative agreement with experimental results.The project is supported by National Natural Science Foundation of China.     

Numerical investigation of grain boundary effects on elevated-temperature deformation and fracture

A three-dimensional (3D) polycrystal intergranular model that accounts for grain boundary deformation and intergranular weakening at elevated temperatures is presented. The effects of grain boundaries on the accumulated slip deformation of grain interiors and lattice rotation have been investigated through a comparison between results from a model including grain boundary region (GBM) and a model representing only the grain interiors not the grain boundary region directly (NGBM). It is found that the presence of grain boundaries seems to suppress the grain interior slip deformation, and this suppressive role is reduced with increased relative thickness of the grain boundaries. In addition, grain boundaries promote the lattice rotation of individual grains in shear bands but suppress that of individual grains within non-shear bands. Mutual rotation of grains in both shear and non-shear bands is caused by the introduction of grain boundary regions. Rate-dependence of high-temperature plasticity could be more accurately captured by the GBM than by the NGBM. By considering creep damage of grain boundary, when the damage variable reaches a critical value, the corresponding grain boundary element is eliminated to describe dynamic intergranular fracture processes. The volume-averaged stress–strain curve by a model considering grain boundary damage (DGBM) showed better agreement with experimental results than that by a model not considering grain boundary damage (GBM).     

A crack on the grain boundary — An analysis based on crystal plasticity theory

The influence of the mismatch of the lattice orientation on the deformation and stress fields of a crack located on the grain boundary is studied by means of the finite-element analysis taking account of finite deformatio and finite lattice rotation. The plane strain calculations for an fcc crystal subjected to mode I loading are performed on the basis of the crystalline plasticity described by a planar three-slip model. For the crack-tip shapes and the dominant deformation modes on slip systems, results of all the cases analysed here are in qualitative agreement with the earlier analytical and numerical solutions. Our results indicate that the lattice orientation difference may greatly influence the shear stress along the grain boundary which is related to grain-boundary sliding, while the normal stress along the grain boundary, which may induce cleavage fracture, is virtually insensitive to it. The influence of the lattice orientations on the crack-tip fields is also investigated under small-scale-yielding conditions and the comparison with the results of finite deformation is made.     

磁电弹复合材料和刚性导电导磁圆柱压头的二维微动接触分析

本文求解平面应变状态下磁电弹复合材料半平面和刚性导电导磁圆柱压头的二维微动接触问题。假设压头具有良好的导电导磁性，且表面电势和磁势是常数。微动接触依赖载荷的加载历史，所以首先求解单独的法向加载问题，然后在法向加载问题的基础上求解循环变化的切向加载问题。整个接触区可以分为内部的中心粘着区和两个外部的滑移区，其中滑移区满足Coulomb摩擦法则。利用Fourier积分变换，磁电弹半平面的微动接触问题将简化为耦合的Cauchy奇异积分方程组，然后数值离散为线性代数方程组，利用迭代法求解未知的粘着/滑移区尺寸、电荷分布、磁感应强度、法向接触压力和切向接触力。数值算例给出了摩擦系数、总电荷和总磁感应强度对各加载阶段的表面接触应力、电位移和磁感应强度的影响。     

An interfacial energy incorporated couple stress crystal plasticity and the finite element simulation of grain subdivision

A couple stress crystal plasticity formulation that incorporates interfacial couple stress energy was proposed in terms of the virtual work-rate principle for finite element method. By applying the assumed constitutive models of couple stress at the grain boundary as well as the grain interior, finite element simulations were conducted for various crystal models, with different grain subdivision models to examine how plastic deformation work is affected by grain subdivision from the interfacial couple stress energy effect.Finite element simulation results showed that the amount of predicted plastic deformation work depends on grain subdivision, and that the amount of work can be minimized for a particular grain subdivision. We inferred from the simulation results that actual grain subdivision might correspond to the minimum amount of plastic deformation work and, if this correlation is validated, actual grain subdivision might be predicted based on the interfacial energy incorporated couple stress crystal plasticity.     

用晶体弹塑性有限单元法研究双晶金属拉伸变形

本文从单晶体应力-应变关系的精确实验结果和多晶体滑移特性出发,建立相应的计算模型,并采用微观力学和晶体弹塑性有限单元法,研究双晶金属试样的拉伸变形,得到其应力-应变曲线,晶体内滑移变形和应力分布规律,以及晶界影响区对它们的影响。     

A two-dimensional finite element method for simulating the constitutive response and microstructure of polycrystals during high temperature plastic deformation

We describe a finite element method designed to model the mechanisms that cause superplastic deformation. Our computations account for grain boundary sliding, grain boundary diffusion, grain boundary migration, and surface diffusion, as well as thermally activated dislocation creep within the grains themselves. Front tracking and adaptive mesh generation are used to follow changes in the grain structure. The method is used to solve representative boundary value problems to illustrate its capabilities.     

A variational multiscale constitutive model for nanocrystalline materials

This paper presents a variational multi-scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior phase and a grain boundary effected zone (GBAZ). A rate-independent isotropic porous plasticity model is employed to describe the GBAZ, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the grain interior. The constitutive models of both phases are formulated in a small strain framework and extended to finite deformation by use of logarithmic and exponential mappings. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylor-type homogenization where a log-normal grain size distribution is assumed. It is shown that the proposed model is able to capture the inverse Hall-Petch effect, i.e., loss of strength with grain size refinement. Finally, the predictive capability of the model is validated against experimental results on nanocrystalline copper and nickel.     

AN ANALYSIS OF THE EFFECTS OF SYMMETRICAL TILT GRAIN BOUNDARIES ON THE PLASTIC DEFORMATION

A numerical investigation on the simple polycrystals containing threesymmetrical tilt grain boundaries(GBs)is carried out within the framework of crystalplasticity which precisely considers the finite deformation and finite lattice rotation aswell as elastic anisotropy.The calculated results show that the slip geometry and theredistribution of stresses arising from the anisotropy and boundary constraint play animportant role in the plastic deformation in the simple polycrystals.The stress levelalong GB is sensitive to the load level and misorientation,and the stresses along GB aredistributed nonuniformly.The GB may exhibit a softening or strengthening feature,which depends on the misorientation angle.The localized deformation bands usuallydevelop accompanying the GB plastic deformation,the impingement of the localizedband on the GB may result in another localized deformation band.The yield stresseswith different misorientation angles are favorably compared with the experimentalresults.     

Assessment of plastic heterogeneity in grain interaction models using crystal plasticity finite element method

Micromechanical models aimed at simulating deformation textures and resulting plastic anisotropy need to incorporate local plastic strain heterogeneities arising from grain interactions for better predictions. The ALAMEL model [Van Houtte, P., Li, S., Seefeldt, M., Delannay, L. 2005. Deformation texture prediction: from the Taylor model to the advanced Lamel model. Int. J. Plasticity 21, 589–624], is one of the models in which the heterogeneous nature of plastic deformation in metals is introduced by accounting for the influence of a grain boundary on the cooperative deformation of adjacent grains. This is achieved by assuming that neighbouring grains undergo heterogeneous shear rates parallel to the grain boundary. The present article focuses on understanding the plastic deformation fields near the grain boundaries and the influence of grain interaction on intra-grain deformations. Crystal Plasticity Finite Element Method (CPFEM) is employed on a periodic unit cell consisting of four grains discretised into a large number of elements. A refined study of the local variation of strain rates, both along and perpendicular to the grain boundaries permits an assessment of the assumptions made in the ALAMEL model. It is shown that the ALAMEL model imbibes the nature of plastic deformation at the grain boundaries very well. However, near triple junctions, the influence of a third grain induces severe oscillations of the stress tensor, reflecting a singularity. According to CPFEM, such singularity can lead to grain subdivision by the formation of new boundaries originating at the triple junction.