Elastic interaction between force dipoles on a stretchable substrate

The objective of this paper is to study elastic interaction between force dipoles on the surface of a semi-infinite stretchable substrate. The substrate undergoes a uniform, finite pre-stretch, while the additional deformation induced by a force dipole is assumed infinitesimal. By adopting a neo-Hookean constitutive law, the surface Green function for the pre-stretched substrate is obtained. The result is then used to derive the energy of dipolar interaction on the surface. As an application, mutual interaction between two physisorbed molecules is discussed in detail. The dipole moment of a molecule is found from the elementary intermolecular potential, and its dependence on the pre-stretch is established explicitly. Numerical results indicate that pre-stretches can substantially alter the interaction, and thus provide a controllable way to guide the self-assembly of adsorbed molecules on the substrate surface.     

Static wetting on flexible substrates: a finite element formulation

In static wetting on an elastic substrate, force exerted by the liquid–vapour surface tension on a solid surface deforms the substrate, producing a capillary ridge along the contact line. This paper presents a finite element formulation for predicting elastic deformation, close to the static wetting line (with angle of contact=90o and σSV=σSL).The substrate deformation is modelled with the Mooney–Rivlin constitutive law for incompressible rubber‐like solids. At the contact line, a stress singularity is known to arise, due to the surface tension acting on a line of infinitesimal thickness. To relive the stress singularity, either (i) the surface tension is applied over a finite contact region (of macroscopic thickness), or (ii) the solid crease angle is fixed. These two options suggest that normal component of Neumann's triangle law of forces, for the three surface tensions, is not applicable for elastic substrates (as for rigid ones). The vertical displacement of the contact line is a strong function of liquid/vapour surface tension and shear modulus of the solid. Copyright 2004 John Wiley & Sons, Ltd.     

两种不同形状压头与单晶铜基体间接触力和摩擦力的纳观分析

在考虑单晶铜基体弹塑性形变和晶体各向异性情况下,基于原子尺度,采用混合势函数(EAM和Morse)和Verlet算法动态模拟了半球形和圆锥形两种不同形状压头与单晶铜基体的黏着接触和滑动摩擦过程,分析了接触力和摩擦力对单晶铜基体内失效原子变化情况.研究表明:当压头下压位移为0.9 nm时,由于半球形压头比圆锥形压头底部表面积大,导致半球形压头与基体之间的引力更大而更易产生黏着接触现象.在下压接触过程中,与半球形压头相接触的基体内出现位错原子长大成位错环,而与圆锥形压头相接触的基体未出现此位错环现象,但位错原子数均随压深的增加而增多;在滑动过程中,因半球形压头对基体的摩擦力和法向力比圆锥形压头对基体的摩擦力和法向力大,使得半球形压头比圆锥形压头正前方堆积的位错原子数多,但均随滑动距离的增加而增多.     

基于表面力模型的液滴冲击弹性基底SPH模拟

采用光滑粒子动力学SPH方法建立液滴冲击弹性基底的流固耦合数值模型,给出描述粘性流体和弹性固体运动的SPH离散方程和数值处理格式,引入人工耗散项来抑制标准SPH方法的数值震荡。为模拟液滴的表面张力效应,通过精确检测边界粒子,采用拉格朗日插值方法计算表面法向量和曲率,结合界面理论中的连续表面力CSF方法,建立了适用于自由表面液滴的表面力模型,方形液滴变形的模拟结果与拉普拉斯理论解吻合较好。随后,采用SPH流固耦合模型模拟1.0 mm直径水滴以不同速度(0.2 m/s～3.0 m/s)冲击两种薄板型基底,分析了基底弹性变形对液滴铺展、收缩以及回弹行为的影响。     

Spinodal surface instability of soft elastic thin films

When the thicknesses of thin films reduce to microns or even nanometers, surface energy and surface interaction often play a significant role in their deformation behavior and surface morphology. The spinodal surface instability induced by the van der Waals force in a soft elastic thin film perfectly bonded to a rigid substrate is investigated theoretically using the bifurcation theory of elastic structures. The analytical solution is derived for the critical condition of spinodal surface morphology instability by accounting for the competition of the van der Waals interaction energy, elastic strain energy and surface energy. Detailed examinations on the effect of surface energy, thickness and elastic properties of the film show that the characteristic wavelength of the deformation bifurcation mode depends on the film thickness via an exponential relation, with the power index in the range from 0.749 to 1.0. The theoretical solution has a good agreement with relevant experiment results.     

Two-dimensional model of vesicle adhesion on curved substrates

We develop a two dimensional model of a vesicle adhered on a curved substrate via long-range molecular interactions while subjected to a detachment force. The relationship between the force and displacement of the vesicle is investigated as a function of the substrate shape. It is shown that both the force– displacement relationship and the maximum force at pull-off are significantly dependent on the substrate shape. The results suggest that probes with different tip shapes may be designed for cell manipulation. For example, we demonstrate that a vesicle can be pulled off a flat surface using a probe with a curved tip.The project supported by the National Natural Science Foundation of China (10525210 and 10121202) and the 973 Program.     

Vision-based measurement of spatio-temporal deformation of excavated soil for the estimation of bucket resistive force

This paper reports a vision-based technique of measuring the spatio-temporal deformation of excavated soil for estimating the bucket resistive force. The proposed measurement technique uses two depth cameras to determine three-dimensional soil-surface displacement. The technique consists of the following two processes: the first is related to image correlation between the two cameras, and the second involves data filtering and smoothing for generating soil deformation as a continuously curved surface. The proposed technique delivers measurement accuracy to the nearest centimeter. Typical experimental results of the three-dimensional measurement of soil deformation using the proposed technique are presented in the paper. Further, this study updates an interaction model for the resistive-force estimation while a bucket excavates soil. The model introduces a correction variable that changes with the bucket wrist angle by exploiting the experimental measurement of soil deformation. The model estimates the resistive force with an error of less than one quarter of the maximum force. These updates also exhibit the effectiveness of the proposed technique.     

Delamination of an elastic film from an elastic–plastic substrate during adhesive contact loading and unloading

Adhesive contact between a rigid sphere and an elastic film on an elastic–perfectly plastic substrate was examined in the context of finite element simulation results. Surface adhesion was modeled by nonlinear springs obeying a force-displacement relationship governed by the Lennard–Jones potential. A bilinear cohesive zone law with prescribed cohesive strength and work of adhesion was used to simulate crack initiation and growth at the film/substrate interface. It is shown that the unloading response consists of five sequential stages: elastic recovery, interface damage (crack) initiation, damage evolution (delamination), film elastic bending, and abrupt surface separation (jump-out), with plastic deformation in the substrate occurring only during damage initiation. Substrate plasticity produces partial closure of the cohesive zone upon full unloading (jump-out), residual tensile stresses at the front of the crack tip, and irreversible downward bending of the elastic film. Finite element simulations illustrate the effects of minimum surface separation (i.e., maximum compressive surface force), work of adhesion and cohesive strength of the film/substrate interface, substrate yield strength, and initial crack size on the evolution of the surface force, residual deflection of the elastic film, film-substrate separation (debonding), crack-tip opening displacement, and contact instabilities (jump-in and jump-out) during a full load–unload cycle. The results of this study provide insight into the interdependence of contact instabilities and interfacial damage (cracking) encountered in layered media during adhesive contact loading and unloading.     

Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening

This study presents the ordinary state-based peridynamic constitutive relations for plastic deformation based on von Mises yield criteria with isotropic hardening. The peridynamic force density–stretch relations concerning elastic deformation are augmented with increments of force density and stretch for plastic deformation. The expressions for the yield function and the rule of incremental plastic stretch are derived in terms of the horizon, force density, shear modulus, and hardening parameter of the material. The yield surface is constructed based on the relationship between the effective stress and equivalent plastic stretch. The validity of peridynamic predictions is established by considering benchmark solutions concerning a plate under tension, a plate with a hole and a crack also under tension.     

Static and dynamic snap-through behaviour of an elastic spherical shell

The deformation and snap-through behaviour of athin-walled elastic spherical shell statically compressed on aflat surface or impacted against a flat surface are studied theoretically and numerically in order to estimate the influenceof the dynamic effects on the response.A table tennis ballis considered as an example of a thin-walled elastic shell.Itis shown that the increase of the impact velocity leads to avariation of the deformed shape thus resulting in larger deformation energy.The increase of the contact force is causedby both the increased contribution of the inertia forces andcontribution of the increased deformation energy.The contact force resulted from deformation/inertia ofthe ball and the shape of the deformed region are calculated by the proposed theoretical models and compared withthe results from both the finite element analysis and somepreviously obtained experimental data.Good agreement isdemonstrated.     

微重力环境下硅基纳米器件碰撞滑动接触问题研究

随着纳米技术的发展,微机电系统被广泛应用于微纳卫星、皮卫星以及各种高精密仪器. 单晶硅广泛应用于微机电系统,考虑微重力环境空间机构无规则碰撞的运动特性,建立刚性金刚石压头与弹性硅基体之间碰撞滑动接触的分子动力学模型,对比研究压头不同振动频率和振幅对平均摩擦力的影响. 结果表明:压头振动频率低于基体固有频率时,平均摩擦力无明显变化,而高于固有频率时,平均摩擦力随振动频率增大呈现先减小后不变的趋势;振幅的增大导致压头和基体的碰撞更加剧烈,剧烈的碰撞导致基体表面更多原子晶格结构破坏,失效原子数增多,降低了平均摩擦力;在基体表面引入纹理,发现纹理表面能够有效降低平均摩擦力.      

非公度接触石墨烯层间摩擦对压入深度的依赖性

近年来, 以石墨烯为代表的层状二维纳米材料的摩擦力学行为受到广泛关注, 许多新的纳尺度摩擦现象、规律及机理被陆续报道, 推动纳米摩擦学取得了重要进展. 然而, 由于纳米级摩擦十分复杂, 在建立摩擦力与影响因素之间的直接关联方面依然进展非常缓慢. 本文利用分子动力学模拟方法, 研究了衬底支撑石墨烯基底与石墨烯滑片之间的摩擦行为, 着力考察了非公度接触情况下的摩擦规律. 结果表明, 石墨烯滑片和基底之间的摩擦力与压入深度直接相关, 说明压入深度可作为纳尺度摩擦力的重要度量指标. 特别地, 法向载荷和衬底刚度对石墨烯摩擦的影响,都可通过压入深度归一化处理. 该结果对理解二维材料表面弹性影响的摩擦规律具有重要的理论意义.     

Nanoindentation modeling of a nanodot-patterned surface on a deformable substrate

A numerical model was developed to simulate the nanoindentation of a Ni nanodot-patterned surface (NDPS) on a deformable Si substrate. Each contacting nanodot on the Si substrate was treated individually in this model and the interaction among the nanodots was considered through the elastic deformation of the Si substrate. The load–deformation relationship for the single-asperity contact between the indenter tip and a nanodot was determined using finite element analysis. A nanoindentation experiment on a Ni NDPS was performed to test the developed model. The simulation and experimental results were found to be in good agreement. The experimentally verified model was used to explore the effects of substrate deformation and surface roughness caused by the Ni nanodots on the nanoindentation behavior. It was found that the effect of the substrate and the effect of roughness must be considered. A detailed study of the substrate deformation shows that the interaction among nanodots, through the substrate, can contribute a considerable portion of the total deformation under a nanodot. The yield strength of the nanodot was found to have a significant effect on the contact deformation, while the elastic modulus was found to have little effect.     

非公度接触石墨烯层间摩擦对压入深度的依赖性

近年来, 以石墨烯为代表的层状二维纳米材料的摩擦力学行为受到广泛关注, 许多新的纳尺度摩擦现象、规律及机理被陆续报道, 推动纳米摩擦学取得了重要进展. 然而, 由于纳米级摩擦十分复杂, 在建立摩擦力与影响因素之间的直接关联方面依然进展非常缓慢. 本文利用分子动力学模拟方法, 研究了衬底支撑石墨烯基底与石墨烯滑片之间的摩擦行为, 着力考察了非公度接触情况下的摩擦规律. 结果表明, 石墨烯滑片和基底之间的摩擦力与压入深度直接相关, 说明压入深度可作为纳尺度摩擦力的重要度量指标. 特别地, 法向载荷和衬底刚度对石墨烯摩擦的影响,都可通过压入深度归一化处理. 该结果对理解二维材料表面弹性影响的摩擦规律具有重要的理论意义.     

ADHESIVE CONTACT PROBLEM OF AXISYMMETRIC MINIATURE CIRCULAR PLATES WITH CENTRAL RIGID BUMP

Considering the adhesive effect and geometric nonlinearity, the adhesive contactbetween an elastic substrate and a clamped miniature circular plate with two different centralrigid bumps under the action of uniform transverse pressure and in-plane tensile force in theradial direction was analyzed. And an analytical solution is presented by using the perturbationmethod. The relation of surface adhesive energies with critical load to detach the contacted surfacesis obtained. In the numerical results, the effects of adhesive energy, in-plane tensile force, rigidbump size and contact radius on the critical load are discussed, and the relation of critical contactradius with the gap between the central rigid bump and the substrate for different adhesive energiesis investigated.     

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在重轨万能轧制过程中,首先建立了简化的三维理论模型. 然后分别给出了轨腰、轨头及轨 底的运动学许可速度场以及相应的应变速度场和剪应变速度强度,并求出了相应变形区的塑 性变形功率、速度间断面上消耗的功率以及由于摩擦产生的摩擦功率. 最后根据上限原理分 别求解了水平辊和两个立辊的轧制力上限解. 通过比较可知,二辊轧制理论公式误差很大因 此不能用于万能轧制过程,而上限法求得的轧制力近似解大于轧制现场数据但最大误差不超 过13\%, 因此根据上限原理进行轧制工艺参数设定及优化是比较可靠的.     

Experimental study on wheel-soil interaction mechanics using in-wheel sensor and particle image velocimetry part II. Analysis and modeling of shear stress of lightweight wheeled vehicle

Wheeled vehicle mobility on loose sand is highly subject to shear deformation of sand around the wheel because the shear stress generates traction force of the wheel. The main contribution of this paper is to improve a shear stress model for a lightweight wheeled vehicle on dry sand. This work exploits two experimental approaches, an in-wheel sensor and a particle image velocimetry that precisely measure the shear stress and shear deformation generated at the interaction boundary. Further, the paper improves a shear stress model. The model proposed in this paper considers a force chain generated inside the granular media, boundary friction between the wheel surface and sand, and velocity dependency of the friction. The proposed model is experimentally validated, and its usefulness is confirmed through numerical simulation of the wheel traction force. The simulation result confirmed that the proposed model calculated the traction force with an accuracy about 70%, whereas the conventional one overestimated the force, and its accuracy was 13% at the best.     

Scaling theory of adsorption-induced stresses in polymer brushes grafted onto compliant structures

The lateral forces exerted on a substrate by a layer of end-grafted polymer molecules are calculated on the basis of simple scaling arguments. The results are cast in terms of an equilibrium surface stress and an elastic constant, which describes the rate of change of the surface stress upon deformation of the substrate. This allows for straightforward integration of the present results into a continuum framework describing the response of a compliant structure, which facilitates device design and analysis. The results are illustrated with calculations for end-grafted poly(styrene) and poly(ethylene oxide), and the implications for building micromechanical devices based on adsorption-induced deformation are discussed.     

Green’s function-based multiscale modeling of defects in a semi-infinite silicon substrate

We have developed a Green’s function (GF) based multiscale modeling of defects in a semi-infinite silicon substrate. The problem—including lattice defects and substrate surface, i.e., an extended defect, at different length scales—is first formulated within the theory of lattice statics. It is then reduced and solved by using a scale-bridging technique based on the Dyson’s equation that relates a defect GF to a reference GF and on the asymptotic relationship of the reference lattice-statics GF (LSGF) to the continuum GF (CGF) of the semi-infinite substrate. The reference LSGF is obtained approximately by solving the boundary-value problem of a super-cell of lattice subject to a unit point force and under a boundary condition given by the reference CGF. The Tersoff potential of silicon, germanium and their compounds is used to derive the lattice-level force system and force constants and further to derive the continuum-level elastic constants (of the bulk silicon, needed in the reference CGF). We have applied the method to solve for the lattice distortion of a single vacancy and a single germanium substitution. We have further calculated the relaxation energy in these cases and used it to examine the interaction of the point defects with the (traction-free) substrate surface and the interaction of a single vacancy with a relatively large germanium cluster in the presence of the substrate surface. In the first case, the point defects are found to be attracted to the substrate surface. In the second case, the single vacancy is attracted to the germanium cluster as well as to the substrate surface.