Polygonization as low energy dislocation structure

Within continuum dislocation theory, one-dimensional energy functional of a bent beam, made of a single crystal, is derived. By relaxing the continuously differentiable minimizer of this energy functional, we construct a sequence of piecewise smooth deflections and piecewise constant plastic distortions reducing the energy and exhibiting polygonization. The number of polygons can be estimated by comparing the surface energy of small angle tilt boundaries with the contribution of the gradient terms from the weak minimizer in the bulk energy.     

On Landau theory and symmetric energy landscapes for phase transitions

The aim of this presentation is the development of a general approach for modelling the global complex energy landscapes of phase transitions. For the sake of clarity and brevity the exposition is restricted to martensitic phase transition (i.e., diffusionless phase transitions in crystalline solids). The methods, however, are more broadly applicable. Explicit energy functions are derived for the cubic-to-tetragonal phase transition, where data are fitted for InTl. Another example is given for the cubic-to-monoclinic transition in CuZnAl. The resulting energies are defined globally, in a piecewise manner. We use splines that are twice continuously differentiable to ensure sufficient smoothness. The modular (piecewise) technique advocated here allows for modelling elastic moduli, energy barriers and other characteristics independent of each other.     

Some axisymmetric problems for an elastic inhomogeneous thick-walled tube

An equilibrium differential equation for an axisymmetric problem is reduced to an integrable form under the assumption that the shear modulus is continuously differentiable and Poisson’s ratio is constant. A procedure of successive approximations is proposed for the case of a compressible material, and the Lamé problem is solved exactly for the case of an incompressible material. A piecewise continuous variation of the Lamé parameter as a function of radius is considered. Several examples of determining the stress-tensor components are given for various cases of inhomogeneity.     

Edge Contact Forces and Quasi-Balanced Power

We consider continuous media in which contact edge forces are present. Introducing thenotion of quasi-balanced contact force distribution, we are able to prove the conjectures by Noll andVirga [1] concerning the representation of contact edge forces. We generalize the Hamel--Nolltheorem on the Cauchy postulate. Then we adapt the celebrated tetrahedron construction of Cauchy in orderto obtain a representation theorem for stress states. In fact, we show that two stress tensors of order twoand three are necessary for such a representation. Moreover we find the relationship between the notionof interstitial working introduced by Dunn and Serrin [2] and the notion of contact edge force.     

晃荡液舱内水动冲击力的分段仿射模型

针对舱内晃荡液体与舱壁的相互作用,对舱内水动冲击力的等效力学模型进行了研究。基于混合系统理论,建立了强非线性液体晃荡的等效摆分段仿射模型,重点对矩形液舱的简化等效力学模型进行了分析。利用计算流体动力学软件Flow3D对矩形液舱内的强非线性液体晃荡进行了数值仿真。理论分析表明：分段仿射模型更符合刚性碰撞的假定,可以更有效地描述等效摆和舱壁碰撞时的速度跃变。仿真结果的对比表明：受到激励时,等效摆分段仿射模型所产生的力与Flow3D计算的结果比较接近,利用此模型可以恰当地描述强非线性液体晃荡。     

Types of Bifurcations of FitzHugh–Nagumo Maps

The FitzHugh–Nagumo-like systems are of fundamental importance to the understanding of the qualitative nature of nerve impulse propagation. Our work provides a numerical investigation of bifurcations associated with a family of piecewise differentiable canonical maps for a planar FitzHugh–Nagumo system. We describe the bifurcation structure of the maps with the variation of the parameters.     

混凝土框架结构内力测量传感器研制

研制了一种可用于混凝土结构试验中测量柱底截面轴向力、剪力和弯矩的内力测量传感器。该传感器主要由加载板、基座、4根竖向测力杆和2根水平测力杆组成。使用时,柱底截面的内力通过加载板传递给6根测力杆,根据6根测力杆的结果,通过力平衡方程可以计算实际加载的轴向力、剪力和弯矩的大小。对该传感器进行了4种工况下的标定试验。结果表明,传感器的测量误差满足框架结构内力测量精度要求。将该传感器应用到单层两跨的钢筋混凝土框架推覆试验中,获得了整个试验过程中构件的内力时程。     

基于力封闭的虚拟手稳定抓持力生成方法

为解决虚拟训练中抓持力反馈生成的问题,研究了满足软指点接触模型的力封闭条件。基于力封闭求解中的操作力和内力的摩擦锥条件,通过非线性规划方程求解内力平衡和内力满足摩擦锥条件,并获取最稳定抓持的标准;提出需求压力和可提供压力的概念,建立了稳定静力抓持模型,实验实现了抓持力的生成。本文方法为虚拟手交互中的力觉生成提供了一种新方法。     

Existence and Asymptotic Behavior of Solutions of the Cauchy Problem x (x′)γ = f(t,x, x′), x(0) = 0

We consider a singular Cauchy problem and prove the existence of continuously differentiable solutions with required asymptotic properties.     

MEASUREMENT OF ADHESION FORCES IN AIR WITH THE VIBRATION METHOD

The vibration method represents a practical method for the measurement of adhesion forces and adhesion force distributions. This method causes sinusoidally altemating stresses and yields detachment and contact forces between particles and substrate of the same order of magnitude. Alternating contact forces of the vibration method can cause an adhesion force intensification through flattening of asperities. The measuring principle of the vibration method and the analysis of experimental results are described in the article. Normal adhesion forces (pull-off forces) are measured using the vibration method and the colloidal probe technique. The results of both methods show good agreement for small particle sizes. The influence of the detachment force direction is shown by comparing tangential and normal adhesion forces measured using particle reentrainment in a turbulent air flow and the vibration method, respectively. The surface roughness of the substrate and the relative humidity are shown to significantly influence the measured adhesion forces. For the calculation of the adhesion forces, an approach by Rabinovich was combined with approximations of plastic micro asperity flattening. The Rabinovich approach accounts for roughness effects on the van der Waals force by incorporating the rms roughness of the interacting surfaces. rms-values of the particles and substrates were measured with atomic force microscopy at different scanning areas.     

A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows

Accurate momentum coupling model is vital to simulation of dispersed multiphase flows. The overall force exerted on a particle is divided into four physically meaningful contributions, i.e., quasi-steady, stress-gradient, added-mass, and viscous-unsteady (history) forces. Time scale analysis on the turbulent multiphase flow and the viscous-unsteady kernel shows that the integral representation of the viscous-unsteady force is required except for a narrow range of particle size around the Kolmogorov length scale when particle-to-fluid density ratio is large. Conventionally, the particle-to-fluid density ratio is used to evaluate the relative importance of the unsteady forces (stress-gradient, added-mass, and history forces) in the momentum coupling. However, it is shown from our analysis that when particle-to-fluid density ratio is large, the importance of the unsteady forces depends on the particle-to-fluid length scale ratio and not on the density ratio. Provided the particle size is comparable to the smallest fluid length scale (i.e., Kolmogorov length scale for turbulence or shock thickness for shock-particle interaction) or larger, unsteady forces are important in evaluating the particle motion. Furthermore, the particle mass loading is often used to estimate the importance of the back effect of particles on the fluid. An improved estimate of backward coupling for each force contribution is established through a scaling argument. The back effects of stress-gradient and added-mass forces depend on particle volume fraction. For large particle-to-fluid density ratio, the importance of the quasi-steady force in backward coupling depends on the particle mass fraction; while that of the viscous-unsteady force is related to both particle mass and volume fractions.     

作用在裂隙中的渗透力分析

裂隙岩体中流体对岩体的作用力, 是研究岩体稳定性的重要问题。本文认为流体作用于裂隙壁面上的力包括两部分, 即垂直于裂隙壁面的流体静水压力 (导致裂隙垂向变形)和平行于裂隙壁面的拖曳力 (导致裂隙切向变形), 此拖曳力为面力。文中以单裂隙水流的立方定律为基础, 运用流体力学的动量方程, 推导出了单一平直光滑无充填裂隙、有充填的裂隙及水流和充填物一起运动情况下, 裂隙壁面承受的切向拖曳力公式。该公式对于分析流体对裂隙岩体变形性能及强度的影响具有重要价值。     

Validation of fluid–particle interaction force relationships in binary-solid suspensions

In this work several relationships governing solid–fluid dynamic interaction forces were validated against experimental data for a single particle settling in a suspension of other smaller particles. It was observed that force relationships based on Lattice-Boltzmann simulations did not perform as well as other interaction types tested. Nonetheless, it is apparent that, in the case of a suspension of different particle types, it is important that the correct choice is made as to how the contribution to the overall fluid–particle interaction force is split between buoyancy and drag. Experimental evidence clearly suggests that the “generalized” Archimedes’ principle (where the foreign particle is considered to displace the whole suspension and not just the fluid) provides the best result.     

Contact force and mechanical loss of multistage cable under tension and bending

A theoretical model for calculating the stress and strain states of cabling structures with different loadings has been developed in this paper. We solve the problem for the first-and second-stage cable with tensile or bending strain. The contact and friction forces between the strands are presented by two-dimensional contact model. Several theo-retical models have been proposed to verify the results when the triplet subjected to the tensile strain, including contact force, contact stresses, and mechanical loss. It is found that loadings will affect the friction force and the mechanical loss of the triplet. The results show that the contact force and mechanical loss are dependent on the twist pitch. A shorter twist pitch can lead to higher contact force, while the trend of mechanical loss with twist pitch is compli-cated. The mechanical loss may be reduced by adjusting the twist pitch reasonably. The present model provides a simple analysis method to investigate the mechanical behaviors in multistage-structures under different loads.     

Periodic and asymptotically periodic solutions of systems of differential-difference equations of neutral type

We establish sufficient conditions for the existence of a continuously differentiable T -periodic solution of a system of differential-difference equations of neutral type and study some properties of this solution.     

Influence of atomic force microscope (AFM) probe shape on adhesion force measured in humidity environment

In micro-manipulation, the adhesion force has very important influence on behaviors of micro-objects. Here, a theoretical study on the effects of humidity on the adhesion force is presented between atomic force microscope （AFM） tips and substrate. The analysis shows that the precise tip geometry plays a critical role on humidity depen- dence of the adhesion force, which is the dominant factor in manipulating micro-objects in AFM experiments. For a blunt （paraboloid） tip, the adhesion force versus humidity curves tends to the apparent contrast （peak-to-valley corrugation） with a broad range. This paper demonstrates that the abrupt change of the adhesion force has high correla- tion with probe curvatures, which is mediated by coordinates of solid-liquid-vapor contact lines （triple point） on the probe profiles. The study provides insights for further under- standing nanoscale adhesion forces and the way to choose probe shapes in manipulating micro-objects in AFM experiments.     

Acoustic radiation force of a solid elastic sphere immersed in a cylindrical cavity filled with ideal fluid

An expression for the acoustic radiation force function on a solid elastic spherical particle placed in an infinite rigid cylindrical cavity filled with an ideal fluid is deduced when the incident wave is a plane progressive wave propagated along the cylindrical axis. The acoustic radiation force of the spherical particle with different materials was computed to validate the theory. The simulation results demonstrate that the acoustic radiation force changes demonstrably because of the influence of the reflective acoustic wave from the cylindrical cavity. The sharp resonance peaks, which result from the resonance of the fluid-filled cylindrical cavity, appear at the same positions in the acoustic radiation force curve for the spherical particle with different radii and materials. Relative radius, which is the ratio of the sphere radius and the cylindrical cavity radius, has more influence on acoustic radiation force. Moreover, the negative radiation forces, which are opposite to the progressive directions of the plane wave, are observed at certain frequencies.     

Modeling and simulation of a novel vertical actuator based on electrowetting on dielectric

A novel vertical actuator based on electrowetting on dielectric （EWOD） was designed, analyzed and simulated. Modeling results indicated that the vertical driving force of the actuator obeyed a second order polynomial of applied voltage, which was verified by Covent_ware 2006. As a resuit, the vertical driving force of the EWOD actuator with a 1.1 nL droplet and a 1.75 μm thick polymer was about 0.5 μN under an applied voltage 100V which was comparable to that of the electrostatic actuators. Moreover, the noise from plane forces we analyzed and simulated was very low. Therefore, we made a conclusion that the EWOD actuator can be used in MEMS transducer.     

An improved three-dimensional model for interface pressure calculations in free-surface flows

A three-dimensional method for the calculation of interface pressure in the computational modeling of free surfaces and interfaces is developed. The methodology is based on the calculation of the pressure force at the interfacial cell faces and is mainly designed for volume of fluid (VOF) interface capturing approach. The pressure forces at the interfacial cell faces are calculated according to the pressure imposed by each fluid on the portion of the cell face that is occupied by that fluid. Special formulations for the pressure in the interfacial cells are derived for different orientations of an interface. The present method, referred to as pressure calculation based on the interface location (PCIL), is applied to both static and dynamic cases. First, a three-dimensional motionless drop of liquid in an initially stagnant fluid with no gravity force is simulated as the static case and then two different small air bubbles in water are simulated as dynamic cases. A two-fluid, piecewise linear interface calculation VOF method is used for numerical simulation of the interfacial flow. For the static case, both the continuum surface force (CSF) and the continuum surface stress (CSS) methods are used for surface tension calculations. A wide range of Ohnesorge numbers and density and viscosity ratios of the two fluids are tested. It is shown that the presence of spurious currents (artificial velocities present in case of considerable capillary forces) is mainly due to the inaccurate calculation of pressure forces in the interfacial computational cells. The PCIL model reduces the spurious currents up to more than two orders of magnitude for the cases tested.

Also for the dynamic bubble rise case, it is shown that using the numerical solver employed here, without PCIL, the magnitude of spurious currents is so high that it is not possible to simulate this type of surface tension dominated flows, while using PCIL, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.