Properties of dynamic rupture and energy partition in a solid with a frictional interface

We study properties of dynamic ruptures and the partition of energy between radiation and dissipative mechanisms using two-dimensional in-plane calculations with the finite element method. The model consists of two identical isotropic elastic media separated by an interface governed by rate- and state-dependent friction. Rupture is initiated by gradually overstressing a localized nucleation zone. Different values of parameters controlling the velocity dependence of friction, the strength excess parameter and the length of the nucleation zone, lead to the following four rupture modes: supershear crack-like rupture, subshear crack-like rupture, subshear single pulse and supershear train of pulses. High initial shear stress and weak velocity dependence of friction favor crack-like ruptures, while the opposite conditions favor the pulse mode. The rupture mode can switch from a subshear single pulse to a supershear train of pulses when the width of the nucleation zone increases. The elastic strain energy released over the same propagation distance by the different rupture modes has the following order: supershear crack, subshear crack, supershear train of pulses and subshear single pulse. The same order applies also to the ratio of kinetic energy (radiation) to total change of elastic energy for the different rupture modes. Decreasing the dynamic coefficient of friction increases the fraction of stored energy that is converted to kinetic energy. General considerations and observations suggest that the subshear pulse and supershear crack are, respectively, the most and least common modes of earthquake ruptures.     

Nonlinear dynamics of an elastic rod with frictional impact

A model is presented for the impact with friction of a flexible body in translation and rotation. This model consists of a system of nonlinear differential equations which considers the multiple collisions as well as frictional effects at the contacting end, and allows one to predict the rigid and elastic body motion after the impact. The kinetic energy is derived by utilizing a generalized velocity field theory for elastic solids. The model uses a dry coefficient of friction and a nonlinear contact force. We introduce a finite number of vibrational modes to take into account the vibrational behavior of the body during impact. The vibrations, the multiple collisions, and the angle of incidence angle, are found to be important factors for the kinematics of frictional impact. Analytical and experimental results were compared to establish the accuracy of the model.     

强脉冲电磁力驱动的冲击载荷

冲击载荷在材料科学与工程领域具有一定的应用。随着研究的深入, 对冲击速度、冲击能量提出了更高的需求, 是落锤所无法达到的。强脉冲磁场可由脉冲大电流产生, 通过合适的装置可产生强脉冲电磁力, 进而可转换为冲击载荷。通过数值模拟, 给出了强脉冲磁场、电磁力及冲头运动过程的数值模拟结果。采用高速摄像对该压缩冲击装置的运动过程进行记录, 通过对影像数据处理获得了冲击速度及冲击能量, 验证了模拟结果。     

微液滴在PDMS软基体表面的动态摩擦行为研究

通过固液界面摩擦力测试装置研究了微液滴在PDMS软基体表面运动时的动态摩擦学行为,并对微液滴体积、滑动速度及软基体力学性能对固液界面动态摩擦行为的影响进行了分析. 结果表明:微液滴在软基体表面运动时表现出最大静摩擦力和动态摩擦力. 最大静摩擦力与微液滴黏度和速度梯度呈正比,动态摩擦力与微液滴体积、滑动速度和基体力学性能有关. 随着微液滴体积的增加,三相接触线长度增加,动态摩擦力增加;随着相对滑动速度增加,三相接触线长度及接触角滞后增加,动态摩擦力增加;随着软基体弹性模量降低,固液界面黏附力增加,固液界面运动能量耗散增加,动态摩擦力增加. 研究结果可为PDMS软基体表面微液滴的精确驱动和运动参数优化提供理论指导,也可进一步丰富固液界面摩擦理论.      

On longitudinal impact V

Summary Although during the last twenty years there has appeared an immense literature on plastic deformation caused by longitudinal tensile or compressive impact, it is difficult to find papers with direct bearing on such engineering applications as riveting where the hammer and the anvil, between which the rivet is compressed, are so light that elastic pulses in hammer and anvil must be considered besides elastic and plastic pulses in the rivet. In this article such cases are treated by means of a graphical method developed from those given by Clark and Duwez and especially De Juhasz. It is shown how the amount, extension and efficiency of plastic straining are influenced by the energy, velocity, weight and form of the hammer, as well as by the form of the anvil, for different rivet lengths. For example, maximum efficiency in producing a prescribed plastic strain at the top of the rivet can be obtained by suitable choice of hammer diameter and velocity. The treatment is limited to rivets with stress-strain curves consisting of two straight lines. Some experiments on aluminium rivets with approximately this type of curve are reported, and the results agree reasonably well with the corresponding theoretical analysis.     

裂纹在冲击载荷作用下起裂的临界载荷面

采用有限元方法研究裂纹在I型短脉冲载荷作用下应力强度因子随时间的变化 ,用应力强度因子的初始上升时间Tr 对时间坐标无量纲化 ,对应力强度因子初始上升段进行曲线拟合 ,得到了上升段的曲线表达式。运用简单弹性梁理论和Lagrangian运动方程 ,获得载荷与时间对裂纹作用的关系式 ,结合有限元的结果 ,得到了上升时间Tr 的计算表达式 ,并进一步推出了裂纹在冲击载荷作用下起裂的临界载荷面。     

Similarity solutions for granular avalanches of finite mass with variable bed friction

This paper continues a series of studies on the plane flow of a pile of cohesionless granular material down a rough inclined plane. Internal and basal friction laws are assumed to obey the Mohr-Coulomb yield criterion but in contrast to previous investigations the angle of friction at the bottom of the pile is considered to depend on the position or on the velocity or on both. Similarity, i.e. shape preserving solutions are constructed. The depth of the pile and the profile of the total minus the centre of mass velocity are determined analytically, but the total length and the position of the centre of mass are calculated numerically. If the basal friction angle is constant, the centre of mass moves with constant acceleration and the length of the pile extends monotonically. These motions change, when the angle of friction varies along the pile — the length of the pile may extend, contract or remain stationary and the centre of mass motion may decelerate or even reach steady state. Eight special cases are exhibited which demonstrate the influence of the friction law on the speed and spread of the pile.     

高孔隙率闭孔泡沫铝的低应变率压缩行为

通过落锤冲击实验研究高孔隙率闭孔泡沫铝的动态压缩性能及抗低速冲击特性, 同时通过高速摄影仪观察试件的动态压缩行为, 并记录落锤冲击速度的衰减过程. 结果表明, 高孔隙率闭孔泡沫铝的抗冲击缓冲效果明显, 且在低速冲击条件下其变形特征与准静态变形类似. 采用有限元方法分析了落锤和泡沫中应力的分布特点以及表面摩擦系数对应力分布的影响. 由于摩擦力阻碍了接触面处泡沫的横向位移, 致使其压缩外形呈``鼓形'; 在低速冲击时, 应力在泡沫铝试件内部的传播周期远小于冲击的缓冲时间, 应力波现象并不明显, 应力的变化与准静态压缩时相似. 在考虑接触面上摩擦力的基础上, 通过第2类Lagrange方程建立了落锤-泡沫材料的碰撞解析模型, 将预测的落锤冲击速度的衰减过程分别与实验和有限元结果进行比较, 取得了较为一致的结论, 并进一步讨论了不同冲击速度和材料参数对冲击过程的影响.      

Tension of a cylindrical membrane partially stretched over a rigid cylinder

We study a contact problem with friction for a hyperelastic long thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder and an axial force is applied to another end. We assume the deformation of the tube is finite and axisymmetric. The tube is modeled by a semi-infinity cylindrical membrane. The axial force tends to a constant value at large distances from the inclusion. The membrane is made of an incompressible, homogeneous, isotropic elastic material. A contact between the membrane and the rigid cylinder is with a dry friction. The membrane will not slide off the cylinder only by friction and at a sufficient contact area. The friction is described by Coulomb’s law. We study a minimum length of the membrane which is in contact with the rigid cylinder and is needed to hold the membrane on the rigid cylinder. We obtain an explicit solution for the Bartenev–Khazanovich (Varga) strain–energy function and numerical results for the Mooney–Rivlin and Fung models.     

Experimental investigation and dimensionless analysis of forming of rectangular plates subjected to hydrodynamic loading

This paper describes an experimental setup consisting of a drop hammer and a shock tube filled with a liquid, where a shock wave is formed, and results of experiments performed with fully clamped rectangular plates subjected to an impact load of the water shock wave. The results are presented in terms of the central deflection of the plates as a function of the kinetic energy of the drop hammer. The singular value decomposition method is used in conjunction with dimensionless numbers to obtain analytical dependences of the central deflection of the plates on the impact load parameters.     

Cylindrical membrane partially stretched on a rigid cylinder

We consider the equilibrium problem of a hyperelastic thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder. We assume that the deformation of the tube is finite and axisymmetric. The tube is modeled by a cylindrical membrane. The membrane is composed of an incompressible, homogeneous, isotropic elastic material. We use Bartenev–Khazanovich (Varga) strain energy function. A contact between the membrane and the rigid cylinder is with a dry friction. The membrane will not slide off the cylinder only by a friction and at a sufficient contact area. The friction is described by Coulomb's law. We study a minimum length of the membrane which is in contact with the rigid cylinder and is needed to the equilibrium of the membrane.     

环空流道液流失速水击特性及其成因的研究

环空流道与圆管的结构差异,使得其失速水击特性及其成因亦有不同。为了对其进行分析研究,利用PIV对套管环空和圆管流水击流场进行拍摄,并通过Tecplot显示流场,提取轴向速度和径向速度、等速度线等参数加以分析;同时采用高精度智能动态压力传感器采集了套管环空内、外壁及内管内壁压力,对环空中水击特性进行了进一步研究。结论是:水击发生时环空断面外壁面水击压力大于内壁面水击压力;同初速情况下环空液流水击压力大于圆管流水击压力;环空中水击压力衰减速度快于圆管中;涡流是水击压力衰减以及速度变化的主要因素;水击压力振荡变化主要是压力涡流引起的断面能量的相互转化形成的。     

聚乙烯泡沫单填充纸瓦楞管的轴向跌落冲击缓冲吸能特性

利用聚乙烯闭孔泡沫单填充纸瓦楞管开展轴向跌落冲击试验,对比分析了结构参数和冲击参数对其缓冲吸能特性参数（比吸能、行程利用率、压缩力效率、比总体效率）的影响。结果表明,X向单填充管的动态缓冲吸能特性优于Y向单填充管,而静态缓冲吸能特性差于Y向单填充管。正四边形单填充管的动态缓冲吸能特性优于正五、六边形单填充管,X向正四边形单填充管的比吸能相较于正五、六边形管分别提高了114.4%和182.3%。对于跌落冲击压缩,单填充管的比吸能、行程利用率、比总体效率随着管长比的增大而减小,管长比为1.4的X向单填充管的比吸能相较于管长比为2.2和3.0的单填充管分别增加了45.8%和117.9%,而压缩力效率随着管长比的增大而增大。随着跌落冲击质量或冲击能量的增加,比吸能、行程利用率、压缩力效率和比总体效率皆呈增大趋势,冲击质量对X向单填充管的影响较大,而冲击速度则对Y向单填充管的影响较大。     

On longitudinal impact I

Summary Central longitudinal impact of slender bodies has a number of important technical applications. Theoretical treatment of these cases has, however, often been unduly scarce or crude, probably because available methods suitable for engineering applications have not been sufficiently well known. This is the first one of a series of papers intended to fill this gap by presenting theoretical solutions for a number of cases of various types, including hammers and bars of various fundamental forms, impact with elastic and plastic deformation and restraint by solid friction, and by suggesting some applications. This paper reviews known analytical, graphical and numerical methods for one-dimensional treatment of longitudinal impact and introduces a slightly modified version of the graphodynamical method which will be used in the following. Stress pulse measurements made with wire strain gauges on a bar impacted by cylindrical hammers of various diameters and materials are presented and found to agree reasonably well with corresponding theoretical pulse forms. Formulae and diagrams are given for the influence of the ratio of areas and material constants of hammer and bar on force, stress, energy transmission and other important quantities of the type of impact mentioned.     

Multiple impacts with friction in rigid multibody systems

An impact model for two-dimensional contact situations is developed which contains the main physical effects of a compliance element in the normal direction and a series of a compliance and Coulomb friction elements in the tangential direction. For systems with multiple impacts a unilateral formulation based on Poisson's hypothesis is used to describe the impulses which are transferred in the normal direction. The event of an impact is divided into two phases. The phase of compression ends with vanishing approaching velocity if normal impulses are transferred and is equivalent to a completely inelastic collision. The phase of expansion allows the bodies to separate under the action of the normal impulses whenever they are large enough. The absolute values of the tangential impulses are bounded by the magnitudes of the normal impulses, due to the Coulomb friction relationship on the impulse level. One part of the transferred tangential impulse during compression is assumed to be partly reversible which may be regarded as an application of Poisson's law. The remaining part is completely irreversible and considered friction. This formulation contains the special case of completely elastic tangential impacts as well as the situation when only Coulomb friction acts. It is proven that the presented impact model is always dissipative or energy preserving. The evaluation of the problem is done by solving one set of complementarity conditions during compression and a nearly identical set of equations during expansion. The theory is applied to some basic examples which demonstrate the difference between Newton's and Poisson's hypotheses.     

On longitudinal impact IV

Summary A survey is given of common pile-driving formulae, and special attention is paid to the so-called dynamic formulae whose characteristic features are compiled in a table and a diagram. The well-known situation that these formulae are fairly reliable for drop-hammers (heavy rams) but quite unreliable for double-acting compressed air hammers (light rams) is analyzed and illustrated by means of an example from the literature. An alternative method of computing the dynamic resistance of the ground by means of the measured set and the data of the hammer is presented, and evidence is given that it can be expected to apply equally well to light rams as to heavy ones. It is based on the graphodynamical method of treating longitudinal impact according to the complete pulse solution of the one-dimensional wave equation which was presented and developed in the previous articles of this series. One important parameter of this computing method is the elastic property of the ground. Suggestions are given for the experimental determination of this parameter. Contrary to common opinion this theory leads to the conclusion that high efficiency may well be obtained with light rams (compressed air hammers). In order to give best results, ram, capblock, helmet etc. should be constructed according to the demands of the pulse theory, and if this is done, a reduction of pile stresses can sometimes be obtained. Examples show that the assumptions of current dynamic formulae are better valid for heavy rams (short piles) than for light rams (long piles). Suggestions are given for further theoretical and experimental development of the new method.     

复合地基承载特性的弹塑性分析

对桩及承台采用线弹性有限元模型,对承台下桩周土采用弹塑性有限元模型,对群桩以外的土体采用线弹性无限元模型,在桩土接触面上设置接触面单元,利用三维弹塑性有限元对桩%D土%D承台相互作用进行了分析。得出了如下结论 :承台下桩顶反力总体表现出角桩最大,边桩次之,中桩最小的分布规律,随着作用在承台上的荷载增大,桩顶反力趋于均匀分布,承台下桩侧摩阻力是由桩端向桩顶逐渐发展的,承台对桩上部侧摩擦阻力存在“削弱作用”。为了验证本文方法的可行性,对承台下有九桩的情况进行了静载试验,将试验结果与本文计算结果进行了比较。     

Asymptotic modeling of the impact of a spherical indenter on an elastic half-space

The impact of a rigid sphere on a homogeneous, isotropic elastic half-space in the absence of friction and adhesion is considered. The influence of the superseismic stage immediately following the moment of first contact upon the impact process is investigated in the frame of the Hertzian impact theory. The first order asymptotic approximation for the contact force in a three-dimensional dynamic contact problem with the slowly moving contact zone boundary is obtained and the corresponding asymptotic model of impact is developed. The motion of the indenter as it indents and rebounds from the elastic medium is analytically described. Explicit formulas are derived for the peak indentation depth, contact time, and rebound velocity as functions of the initial impact velocity, indenter mass, and characteristics of the elastic half-space.     

预折纹管在低速冲击载荷作用下的能量吸收

为了降低结构的初始载荷、增加有效塑性变形面积,进而提高其吸能效率,研究一种以新型的预折纹管,在普通管的管壁上引入特别设计的折角。基于有限元软件ABAQUS/EXPLICIT的数值分析验证了预折纹在低速冲击载荷作用下可以引导预期的大变形模式,预折纹管的这种大变形模式相较于普通方管的对称变形模式有更低峰值载荷和更高的平均载荷。通过低速落锤实验获得了与有限元模拟结果相似的载荷-位移曲线和变形模式,验证了数值结果的可信性和预折纹方管的高效吸能特点。     

堆载下单桩负摩阻力工作性状非线性数值分析

利用三维非线性数值方法对一算例在堆载作用下桩侧负摩阻力进行了计算分析。计算结果揭示了摩擦型、端承型桩负摩阻力工作性状的异同; 分析了堆载速度、桩顶荷载对负摩阻力的影响: 堆载越快,负摩阻力越小; 在无桩顶荷载作用下,由负摩阻力引起的下拉荷载最大,可视为常规方法设计的上限值; 桩顶荷载与堆载施工顺序对负摩阻力的影响也很大,先施加桩顶荷载,后进行堆载所产生的负摩阻力最大,反之最小。