Large deformation of incompressible rubber cylinder under plane strain

The large deformation of incompressible rubber cylinder under inner pressure is analyzed by a kind of new rubber materials strain energy function. The theory formulation for the displacement and stress is presented. The penalty finite element formulation is established in order to analyze nonlinear rubber materials, and the results of finite element method agree well with theoretical ones. A new method for controlling the calculating stability and convergence rates is put forward. The selection of the appropriate penalty factor and its influence on calculated results are discussed.     

基于剪切变形的矩形梁剪力滞求解方法

Timoshenko梁通过假设截面的剪切刚度和附加平均剪切转角变形的方式来近似修正初等梁中未考虑剪切变形能的问题,这与梁剪应力沿梁高变化的实际不符。本文基于材料力学剪应力计算式和相应的剪切变形理论,从剪切变形与梁的位移关系入手,导出矩形梁考虑剪切变形时的纵向位移沿梁高方向的函数关系式,证明该位移可分解为纯弯曲引起的位移和剪力引起的剪力滞翘曲位移之和。应用剪力滞广义坐标与广义力的概念,基于能量变分原理得到等截面梁剪力滞控制微分方程组及其通解形式。对均布荷载作用下矩形简支梁的算例分析表明,本文算法与弹性力学精确解对比,两者的应力和挠度剪力滞系数求解结果非常接近,本文算法有足够的精度,且比弹性力学简单。     

箱形梁剪力滞和剪切效应引起的附加挠度分析

将箱形梁腹板剪切变形纳入初等梁挠曲变形,在全截面上引入剪力滞翘曲修正系数,重新定义了剪力滞翘曲位移模式。选取剪力滞效应引起的附加挠度为广义位移,计算外力势能时考虑剪力滞广义位移的影响,应用能量变分法建立了反映剪力滞和剪切效应的控制微分方程,并导出了均布荷载作用下简支箱梁和两跨连续箱梁剪力滞和剪切效应附加挠度的解析解。数值算例表明,本文方法计算的总挠度值与有限元数值解吻合良好,从而验证了本文方法的合理性。算例箱梁剪切附加挠度明显大于剪力滞附加挠度;简支箱梁跨中截面的剪切和剪力滞附加挠度分别占初等梁挠度的2.50%和1.97%,两跨连续箱梁距中支点9l/16截面分别占27.45%和16.87%。     

Simulating shear behavior of a sandy soil under different soil conditions

Understanding of soil shear behavior is very important in the field of agricultural machinery and soil dynamics. In this study, a discrete element model was developed using a simulation tool, Particle Flow Code in Three Dimensions (PFC^3D). The model simulates direct shear tests of soil and predicts soil shear behavior, in terms of shear forces and displacements. To determine and calibrate model parameters (stiffness of particles, strength and stiffness of bond between particles), laboratory direct shear tests were conducted to examine effects of soil moisture content and bulk density on shear behaviors of a sandy soil. Three soil moisture levels (0.02%, 13.0%, and 21.5%) and four bulk density levels (0.99, 1.28, 1.36, and 1.50 Mg/m³) were used in the tests. The test results showed that in general drier and denser soil conditions produced higher shear forces. Based on the test results, the bond strengths of the model particles were determined from soil cohesion and internal friction angle. The model particle stiffness was calibrated based on the yield forces from the tests. The calibrated particle stiffness varied from 1.0 × 10³ to 8.2 × 10³ N/m, depending on soil moisture and density levels. The bond stiffness calibrated was 1.0 × 10⁷ Pa/m for all soil conditions.     

Ti-6Al-4V在高应变率下的动态剪切特性及失效机理

采用基于霍普金森压杆的新型加载技术对Ti-6Al-4V材料的动态剪切特性及失效机理进行了测试研究。获得了Ti-6Al-4V材料在超过10⁴ s^-1应变率下的剪应力-剪应变曲线及失效参数。研究发现,材料的流动应力存在明显的应变率强化效应;随着应变率的增加,材料的失效应力逐渐增大,而失效应变逐渐减小。采用ABAQUS/Explicit对加载过程进行了数值模拟。结果显示,剪切区材料基本处于平面剪切状态,应力应变场分布较为均匀,计算得到的剪应力-剪应变曲线与实验结果吻合较好。经断口分析可知,随着应变率的升高,Ti-6Al-4V的失效机理存在由韧窝、拉伸韧窝至台阶及河流花样的演化过程,材料的失效模式主要表现为韧性断裂。

     

Tangential discontinuities of parameters of a polar fluid under shear strain

Possible formation of tangential discontinuities of parameters of a deformable polar fluid is examined by the example of glycerin. It is experimentally established that glycerin under weak shear loads possesses the properties of a non-Newtonian elastoviscoplastic fluid, and formation of tangential discontinuities in viscosity is possible. In the discontinuity region, glycerin has the properties of a low-viscosity fluid, and the structure of the medium is reconstructed after unloading. A rheological equation of the examined fluid is derived, which allows one to analyze the behavior of the medium in different modes of its deformation, including the formation of a local region with reduced viscosity and a tensile stress field. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 41–49, May–June, 2005.     

The effect of shear deformation on the post-buckling behavior of imperfect nonlinear viscoelastic columns

Summary The post-buckling behavior of imperfect columns made of nonlinear viscoelastic materials is investigated, taking into account the effect of shear deformation. The material is modeled according to the Leaderman representation of nonlinear viscoelasticity. Solutions are developed, within the elastica and the shear deformation theories, in order to calculate the growth in time of the total deflection. The numerical results establish the importance of the shear and the nonlinear viscoelasticity effects, and of the h/ℓ ratio in the column post-buckling behavior. Accepted for publication 11 November 1996     

Ultrasonic characterization of point defects induced by cross slip under pure shear

Longitudinal wave velocity is used to characterize the point defects in crystalline solids. High purity Al single crystal was selected for both the finite element analysis and experimental work. Since the jog motions of dislocations caused by intersected slides such as cross slips induce point defects, the total amount of cross slips was calculated instead of calculating directly from the point defects. The effect of crystal orientations on total amount of cross slips under pure shear was also investigated via the finite element method. The result suggest that if the initial shear stress direction is located at the inner side of stereographic triangle, only single slip activities occurred at the beginning of plastic deformation and no effects due to point defects were present. However, as the shear stress direction rotates along the slip direction, point defects are induced by cross slips between primary and secondary slip systems due to work-hardening. This phenomenon was then examined by measuring longitudinal wave velocity changes propagating in Al single crystal subjected to the combination loads of equi-biaxial tension and compression (a pure shear state). Good qualitative agreement between the finite element result and measured data suggest that the longitudinal wave velocity can be used as an index to characterize point defects in crystalline materials.     

Numerical solution of singular integral equations in stress concentration problems under longitudinal shear loading

Summary The paper deals with numerical solutions of singular integral equations in stress concentration problems for longitudinal shear loading. The body force method is used to formulate the problem as a system of singular integral equations with Cauchy-type singularities, where unknown functions are densities of body forces distributed in the longitudinal direction of an infinite body. First, four kinds of fundamental density functions are introduced to satisfy completely the boundary conditions for an elliptical boundary in the range 0≤φ _k ≤2π. To explain the idea of the fundamental densities, four kinds of equivalent auxiliary body force densities are defined in the range 0≤φ _k ≤π/2, and necessary conditions that the densities must satisfy are described. Then, four kinds of fundamental density functions are explained as sample functions to satisfy the necessary conditions. Next, the unknown functions of the body force densities are approximated by a linear combination of the fundamental density functions and weight functions, which are unknown. Calculations are carried out for several arrangements of elliptical holes. It is found that the present method yields rapidly converging numerical results. The body force densities and stress distributions along the boundaries are shown in figures to demonstrate the accuracy of the present solutions. Received 26 May 1998; accepted for publication 27 November 1998     

On Anisotropic Elastic Materials for which Young''s Modulus E ( n ) is Independent of n or the Shear Modulus G ( n , m ) is Independent of n and m

It is shown that, among anisotropic elastic materials, only certain orthotropic and hexagonal materials can have Young modulus E(n) independent of the direction n or the shear modulus G(n,m) independent of n and m. Thus the direction surface for E(n) can be a sphere for certain orthotropic and hexagonal materials. The structure of the elastic compliance for these materials is presented, and condition for identifying if the material is orthotropic or hexagonal is given. We also study the case in which n of E(n) and n, m of G(n,m) are restricted to a plane. When E(n) is a constant on a plane so are G(n,m) and Poisson's ratio ν(n,m). The converse, however, does not necessarily hold. A plane on which E(n) is a constant can exist for all anisotropic elastic materials. In particular, existence of such a plane is assured for trigonal, hexagonal and cubic materials. In fact there are four such planes for a cubic material. For these materials, not only E(n) is a constant, two other Young's moduli, the three shear moduli and the six Poisson's ratio on the plane are also constant.     

基于应变能法的单搭接螺栓剪切模型

为了简化复杂结构在冲击数值分析中的大量螺栓连接,可用等效的载荷位移模型代替复杂的螺栓连接关系,本文中针对单搭接螺栓连接在剪切载荷下建立了连接本构关系。首先通过对有预紧力的单搭接螺栓进行实验和精细有限元模拟,揭示了螺栓剪切载荷位移曲线的特征并针对不同特征阶段进行了相应的物理机理分析。在此基础上对于载荷位移曲线的界面黏结、部分滑移、整体滑移阶段提出了连接本构模型的基本形式和各阶段的参数估算方法。在部分滑移阶段考虑了4个方面的刚度贡献,其中部件对螺栓的支撑刚度是三维非轴对称变形问题,理论求解非常困难,本文中通过应力分布研究,采用应变能法解决了螺栓的支撑刚度的估算问题。提出的单搭接螺栓剪切模型物理含义明确,参数估算简单,准确度高。     

Orientation behavior of AB and ABC block copolymers under large amplitude oscillatory shear flow

Flow alignment in a large amplitude oscillatory shear field (LAOS) of a lamellar AB and a lamellar ABC block copolymer (A,B are lamellae, C forms cylinders in B-lamellae) has been studied. 2D-small angle X-ray scattering (2D-SAXS) and scanning electron microscopy were used for morphological characterization, and flow birefringence and Fourier-Transform rheology were used to monitor the orientation. The diblock copolymer shows the known frequency-dependent orientation behavior, i.e., a perpendicular or a parallel orientation of the lamellae, while under all conditions for the ABC block copolymer only a perpendicular orientation after a long induction period was found. Due to the introduced third block C the AB lamellar structure with a high viscosity contrast between the A and B domains cannot adapt a parallel orientation of sliding phases. Dynamic mechanical analysis indicates shear induced improvement of the microphase separation of the short C block.     

TC4在动态载荷下的剪切行为研究

使用分离式霍布金森压杆(SHPB)对2种TC4(Ti-6Al-4V)试样(单边剪切试样与双边剪切试样)在应变率10⁴ s^-1下进行动态剪切加载,利用SIM D8高速照相系统捕捉了绝热剪切带扩展的整个历程,得到了TC4在拍照时刻的应力应变曲线;使用金相显微镜和SEM扫描电镜对TC4绝热剪切带的微观形貌进行观察,发现绝热剪切带宽度为5~12 μm,断口从韧窝断裂演变为解理断裂,可观测到韧窝状与河流花样断口形貌,但是并未看到相变的发生;对2种试样就产生绝热剪切带的形式与敏感性进行了分析,实验表明双边试样更易产生绝热剪切带;通过高速照相系统的标定换算,得到TC4绝热剪切带产生的临界剪切应变在78%~88%之间。在SHPB动态加载条件下,TC4绝热剪切带的扩展速度在460~1 250 m/s之间,且应变率越高,剪切带扩展越快,扩展平均速度与名义应变率近似呈线性关系;另外,在同一加载速率下,剪切带并不是匀速扩展,其扩展速度随载荷的增加而不断增加。

     

Elastic stress distributions for hyperbolic and parabolic notches in round shafts under torsion and uniform antiplane shear loadings

Closed-form solutions are developed for the stress fields induced by circumferential hyperbolic and parabolic notches in axisymmetric shafts under torsion and uniform antiplane shear loading. The boundary value problem is formulated by using complex potential functions and two different coordinate systems, providing two classes of solutions. It is also demonstrated that some solutions of linear elastic fracture and notch mechanics reported in the literature can be derived as special cases of the general solutions proposed herein.Finally the analytical frame is used to link the Mode III notch stress intensity factor to the maximum shear stress at the notch tip, as well as to give closed-form expressions for the strain energy averaged over a finite size volume surrounding the notch root.     

Mechanical behaviour of the upper layers of a sandy loam soil under shear loading

The mechanical behaviour of the upper layers of a sandy loam soil was studied under standard triaxial compression and direct shear box tests. Variations of soil material properties were investigated at four different initial dry bulk densities of 1410, 1520, 1610 and 1670 kg/m³. Soil deformation and volume change under the triaxial compression loading were also studied at these bulk densities. Results from the two tests showed increases in the soil mechanical properties with the initial dry bulk density. The internal friction angle values measured with the triaxial compression apparatus exceeded those measured with the direct shear box. In contrast, the soil cohesion values measured with the direct shear box exceeded those measured with the triaxial compression apparatus. Under the triaxial compression test, the loose soil samples underwent contraction and volume reduction, whereas the dense samples swelled and failure cracks appeared clearly at various planes. The soil contraction for the former case characterizes the occurrence of soil compaction, whereas the cracks propagation and volume increase in the latter case characterizes the breaking up and loosening of soil during tillage operations. For the loose and moderately compacted states, the engineering Poisson's ratio increased with the axial strain until loading was completed. It also increased at the compacted and very compacted states until reaching given loading stages, after which its value started to decrease. This shifting in the engineering Poisson's ratio during loading may provide another identification of the moment of soil failure occurrence, in addition to that of the maximum shear stress.     

Investigation of bed shear stresses subject to external turbulence

The fluctuating bed shear stress has largely been investigated only for uniform channel flows and boundary layers. In practical engineering, the flow conditions are often modified due to the presence of various hydraulic structures. To what extent the modification affects the known characteristics of the bed shear stress is not clear. This study presents experimental results of the bed shear stress fluctuations, which are obviously subjected to external turbulence generated by superimposing artificial structures in the open channel flows. The statistical analysis of the measurements shows that the probability density function of the bed shear stress can be described by the lognormal function. Some associated relations concerning higher-order moments, skewness and kurtosis, which are derived from the lognormal function, are further compared with the experimental data. Physical implication of the skewed probability density distribution is finally discussed.     

Transient behavior of Boger fluids under extended shear flow in a cone-and-plate rheometer

Three different dilute solutions of high molecular weight polymers in viscous, binary solvents were used in experiments performed in a cone-and-plate rheometer. The solutions all fall into the class of fluids referred to as Boger fluids and were previously used in studies of viscoelastic Taylor-Couette instabilities. Under prolonged shearing in the cone-and-plate geometry, these fluids all exhibited a decrease of the first normal stress growth function N₁⁺(t) from an initial plateau value to a second, lower plateau value. This behavior has been previously observed, but is here reported for widely used polyisobutylene-based Boger fluids for the first time. As in earlier studies (Magda JJ, Lee C-S, Muller SJ, Larson RG (1993) Macromolecules 26:1696–1706; MacDonald M, Muller SJ (1997) J Rheol Acta 36:97–109), the time at which this decrease occurs (the decay time) is much longer than the polymer molecules relaxation time. Here, we focus on three issues: 1) the time-temperature superposition of the first normal stress growth function N₁⁺(t), including the decay time and the value of the second plateau, 2) the sample recovery time required to reproduce the initial plateau value of N₁⁺ and the decay time, and 3) the relationship between the time scales for this decay of normal stresses and the onset of viscous heating induced instabilities in the Taylor-Couette geometry. Our results suggest that shear-induced conformational changes, possibly coupled to viscous heating of the sample, may be responsible for the decrease in the first normal stress growth function during prolonged shearing.     

钢板剪力墙结构的耗能能力

在钢板剪力墙结构(简称SPSW)基于能量的性态抗震设计中,需要合理计算有不同滞回特征构件的滞回耗能.为反映剪力墙板滞回曲线的捏缩特征,本文提出了过程捏缩系数及平均捏缩系数,给出了剪力墙板滞回耗能的计算方法.采用数值方法细致分析1榀梁柱刚接的单层、单跨钢板剪力墙结构的滞回性能及耗能能力,并设计了12榀梁柱铰接的单层、单跨SPSW试件,考察了跨高比及高厚比两个参数对剪力墙板滞回性能的影响,总结了捏缩系数的变化规律,提出了简化计算公式.