Transient analysis of sliding contact of layered elastic/plastic solids with rough surfaces

 Based on the boundary element method (BEM) and a variational principle, a numerical model is developed to analyze the time – transient sliding contact of two layered elastic/plastic solids. Two cases are considered: one is the loading/sliding/unloading of a rough surface on a smooth surface, and the other is of two rough surfaces. Contact statistics, contact pressure profile and stress distribution are predicted at each time step with updated surface roughness. The results are used to study the effect of surface roughness, physical properties of the layer and the substrate, and lubricant film thickness on friction, stiction, and wear. Discussion on the integration of this contact model into advanced tribological models, e.g., wear model, is also presented. Received: 28 June 2002/Accepted: 23 October 2002 Currently at: Seagate Technology, Pittsburgh, PA Paper presented at the 13th Annual Symposium on Information Storage and Processing Systems, Santa Clara, CA, USA, 17–18 June, 2002     

范德华力作用下粗糙表面静态粘附的研究

通过在硅微接触表面上涂覆低表面能的憎水性OTS膜以除去接触面间的表面张力,把两表面均接地以除去接触面间的静电力,研究了仅有范德华力作用时硅微结构接触表面的粘附.根据实际粗糙表面凸峰自相似的高度分布,计算了发生粘附后,微观接触表面产生弹性和塑性变形的两种情况下的范德华粘附能,分析了表面形貌对其影响.     

An on-chip micro-friction tester for tribology research of silicon based MEMS devices

An on-chip micro-tribotester has been developed to investigate the friction and wear properties on side contacting surfaces of single crystal silicon that is most widely used in usual microelectromechanical systems actuators. The device is fabricated with standard bulk silicon process and bonding technology based on parameters that have been theoretically calculated to get the stiffness and friction forces. In this device, two comb shuttles are used. One comb shuttle is used to contact the friction surfaces under a certain normal load. The other comb shuttle moves back and forth to provide relative motion between the two friction surfaces. The tested two surfaces are the top surface of an anchor with rounded end and the lateral surface of a beam that has been connected to the two comb shuttles. Tribology experiments on the etched silicon surfaces that are side contacted have been carried out. Friction coefficients testing results suggest that dynamic friction coefficient is about 0.31–0.33 and the obtained static friction coefficient increases with the decrease of normal force. Wear experiment indicates that oxidation happens between the rubbing surfaces during the course of the testing. Wear debris is collected as agglomerates because of the function of adhesion force and water vapor and the agglomerates that are collected on top and lateral surfaces are of different shapes.     

Roughness optimization for biomimetic superhydrophobic surfaces

For non-wetting liquids the contact angle with a rough surface is greater than with a flat surface and may approach 180°, as reported for leaves of water-repellent plants, such as lotus. Roughness affects the contact angle due to the increased area of solid–liquid interface and due to the effect of sharp edges of rough surfaces. High roughness may lead to composite solid–liquid–air interface, which may be either stable or unstable. A comprehensive analytical model is proposed to provide a relationship between local roughness and contact angle, which is used to develop roughness distribution and to create biomimetic superhydrophobic surfaces. Various roughness distributions are considered, including periodic and surfaces with rectangular, hemispherically topped cylindrical, conical and pyramidal asperities and the random Gaussian height distribution. Verification of the model is conducted using experimental data for the contact angle of water droplet on a lotus leaf surface. For two solid bodies in contact, for wetting liquids, wetting leads to the meniscus force, which affects friction. Dependence of the meniscus force on roughness, previously ignored, is considered in the paper and it is found that with increasing roughness meniscus force can grow due to scale effect.

Topology optimization based on finite strain plasticity

In this paper infinitesimal elasto-plastic based topology optimization is extended to finite strains. The employed model is based on rate-independent isotropic hardening plasticity and to separate the elastic deformation from the plastic deformation, use is made of the multiplicative split of the deformation gradient. The mechanical balance laws are solved using an implicit total Lagrangian formulation. The optimization problem is solved using the method of moving asymptotes and the sensitivity required to form convex separable approximations is derived using a path-dependent adjoint strategy. The optimization problem is regularized using a PDE-type filter. A simple boundary value problem where the plastic work is maximized is used to demonstrate the capability of the presented model. The numerical examples reveal that finite strain plasticity successfully can be combined with topology optimization.     

Modeling large strain anisotropic elasto-plasticity with logarithmic strain and stress measures

In this paper we present a model and a fully implicit algorithm for large strain anisotropic elasto-plasticity with mixed hardening in which the elastic anisotropy is taken into account. The formulation is developed using hyperelasticity in terms of logarithmic strains, the multiplicative decomposition of the deformation gradient into an elastic and a plastic part, and the exponential mapping. The novelty in the computational procedure is that it retains the conceptual simplicity of the large strain isotropic elasto-plastic algorithms based on the same ingredients. The plastic correction is performed using a standard small strain procedure in which the stresses are interpreted as generalized Kirchhoff stresses and the strains as logarithmic strains, and the large strain kinematics is reduced to a geometric pre- and post-processor. The procedure is independent of the specified yield function and type of hardening used, and for isotropic elasticity, the algorithm of Eterovi? and Bathe is automatically recovered as a special case. The results of some illustrative finite element solutions are given in order to demonstrate the capabilities of the algorithm.     

Profile-based roughness discrimination with pen-type texture sensor

Tactile discriminations of surface roughness using artificial sensors have been challenging. The modeling methods and parameters that have been using to describe the mechanical properties of rough surface are insufficient for haptic roughness. This paper proposes a method to characterize surface roughness based on the profiles of the surface. A compact handheld pen-type texture sensor with a right probe is developed for the measurement of surface profiles. Based on the contact force and the motion of the senor, profiles in the paths of scanning are estimated. The height variations of a profile are converted to a series of tactile stimuli to represent the contact stimulations in haptic explorations. The mean and the standard deviation of the amplitudes of stimuli are identified as haptic features that indicate the required tangential force to slide on the rough surface and how rough the surface is, respectively. Experiments show that the roughness on four kinds of sandpapers can be clearly distinguished by the proposed discrimination method.     

Calculations of radar backscattering coefficient of vegetation-covered soils

A model for simulating the measured radar backscattering coefficient of vegetation-covered soil surfaces is presented in this study. The model consists of two parts: the first is a soil surface model to describe the backscattered radar pulses from a rough soil surface, and the second part takes into account the effect of vegetation cover. The soil surface is characterized by two parameters, the surface height standard deviation σ and the horizontal correlation length l. The effect of vegetation canopy scattering is incorporated into the model by making the radar pulse subject to two-way attenuation and volume scattering when it passes through the vegetation layer. These processes are characterized by the two parameters, the canopy optical thickness τ and the volume scattering factor η. The model results agree well with the measured angular distributions of the radar backscattering coefficient for HH polarization at the 1.6 GHz and 4.75 GHz frequencies over grass-covered fields. These observations were made from an aircraft platform during six flights over a grass watershed in Oklahoma. It was found that the coherent scattering from soil surfaces is very important at angles near nadir, while the vegetation volume scattering is dominant at larger incident angles (> 30°). The results show that least-squares fits to scatterometer data can provide reliable estimates of the surface roughness parameters, particularly the surface height standard deviation σ. The range of values for σ for the six flights is consistent with a 2 or 3 dB uncertainty in the magnitude of the radar response.     

Dynamic analysis of viscoelastoplastic anisotropic shells

This paper is concerned with an application of the finite elementmethod to the viscoelastoplastic response of an anisotropic shell under dynamic loads. The generalized Maxwell model is incorporated into the von Mises' anisotropic yield function. This permits a derivation of the incremental stress as functions of elastic, viscous, and plastic strains. This relationship is then inserted into the incremental equation of motion for direct numerical integration. Anisotropic parameters and plastic tangent stiffness matrices are updated at each incremental time step. Numerical results are presented for a spherical cap subjected to uniformly distributed transverse dynamic loads of infinite duration.     

Metamodelling of wheel–rail normal contact in railway crossings with elasto-plastic material behaviour

A metamodel considering material plasticity is presented for computationally efficient prediction of wheel–rail normal contact in railway switches and crossings (S&C). The metamodel is inspired by the contact theory of Hertz, and for a given material, it computes the size of the contact patch and the maximum contact pressure as a function of the normal force and the local curvatures of the bodies in contact. The model is calibrated based on finite element (FE) simulations with an elasto-plastic material model and is demonstrated for rail steel grade R350HT. The error of simplifying the contact geometry is discussed and quantified. For a moderate difference in contact curvature between wheel and rail, the metamodel is able to accurately predict the size of the contact patch and the maximum contact pressure. The accuracy is worse when there is a small difference in contact curvature, where the influence of variation in curvature within the contact patch becomes more significant. However, it is shown that such conditions lead to contact stresses that contribute less to accumulated plastic deformation. The metamodel allows for a vast reduction of computational effort compared to the original FE model as it is given in analytical form.

     

Flat Dry Elastomer Adhesives as Attachment Materials for Climbing Robots

In this paper, flat elastomers are proposed as an attachment material for climbing robots on less than a few micrometer-scale rough surfaces due to their energy-efficient, quiet, and residue-free characteristics. The proper elastomer is chosen by the use of the current adhesion, friction, and peeling elastomer-contact-mechanics models. Then, adhesion and friction properties of the chosen dry flat-elastomer thick films (Vytaflex-10) are characterized on acrylic and smooth and rough glass surfaces for variations in preloads, speeds, contact times, and elastomer thicknesses. A climbing robot with four-bar-based legged-body kinematics is designed and fabricated as simple and lightweight as possible to demonstrate the feasibility of the elastomers as attachment materials on relatively smooth surfaces. The robot utilizes a passive alignment system to make the footpads parallel to the surface on light contact, a peeling mechanism to minimize the detachment vibration, and a passive tail to minimize the pitch-back moment. Experimental results showed that the robot can climb stably on vertical, smooth surfaces in any direction and can walk inverted for a limited amount of time.      

Surface radiance correction for shape from shading

It is well known that many surfaces exhibit reflectance that is not well modelled by Lambert's law. This is the case not only for surfaces that are rough or shiny, but also those that are matte and composed of materials that are particle suspensions. As a result, standard Lambertian shape from shading methods cannot be applied directly to the analysis of rough and shiny surfaces. In order to overcome this difficulty, in this paper, we consider how to reconstruct the Lambertian component for rough and shiny surfaces when the object is illuminated in the viewing direction (retroreflection). To do this we make use of the diffuse reflectance models described by Oren and Nayar, and by Wolff. Our experiments with synthetic and real-world data reveal the effectiveness of the correction method, leading to improved surface normal and height recovery.     

A MEMS Device for Studying the Friction Behavior of Micromachined Sidewall Surfaces

A microelectromechanical system device fabricated by deep reactive ion etching for friction characterization was developed with single-crystal silicon in this paper. Two orthogonally placed electrostatic comb-drive actuators were adopted to apply the normal load and generate the tangential motion. A sensing plate for sliding contact and a driving plate with two bumps designed for the Hertzian contact are included in the testing device. With an image processing technique developed, experimental displacement data were extracted from the captured video frames. A quasi-static stick–slip model was developed to predict the transitions between static and kinetic friction at the contacting sidewall surfaces. Both static and kinetic friction coefficients can be determined by using this model, and these measured results are shown to be insensitive to errors in the calculation of the electrostatic forces. The measured displacements of the driving and sensing plates are in good agreement with the trend predicted by the model. Based on the Hertz theory, the contact silicon interface has been found to be in an elastic regime at the scale of the designed bumps. With the aid of the quasi-static stick–slip model, a saturation phenomenon of the kinetic friction at the sidewall surfaces was observed while the normal load was increased. $hfill$[2007-0302]      

非高斯随机粗糙表面计算机仿真的研究

在摩擦学、光学等工程领域中,对于表面粗糙度的研究,总是以生成的随机粗糙表面为研究对象,且大多数研究都是建立在高斯随机表面的基础上,而实际的工程表面大多是非高斯随机表面.为此提出了一种基于快速傅里叶变换(FFT)、Johnson转换系统和自相关函数等理论仿真生成非高斯随机粗糙表面的方法,它可以生成具有给定偏斜度和峰度的随机粗糙表面.为了说明该方法的可行性和正确性,给出了不同偏斜度、峰度和自相关长度下的计算机仿真结果.结果表明:在一定的条件下用该方法仿真生成的非高斯随机粗糙表面,其输入的随机表面的统计参数与输出的统计参数吻合较好.     

Elasto-plastic buckling of curved webs

This paper presents an investigation on elastic buckling strength of curved girder webs subjected to uniform shears or bending stresses at the edges.An elastic 20 degrees of freedom finite element model was used to formulate the eigenvalue problem and a Gauss-Seidel iterative procedure was employed to yield the lowest critical edge loads.In case of pure bending, the investigation is extended into the plastic range. The deformation theory of plasticity in conjunction with a new formulation of the secant modulus is used to derive the elasto-plastic buckling equations. The same Gauss-Seidel iterative procedure was used to find the critical load for each assumed stress level. Further iterations with incremental stress were done to match the elasto-plastic buckling stresses. The material is assumed to be elastic-perfectly plastic and incompressible.In order to aid design professions, the dimensions of the web panel studied are within the practical ranges of curved plate girders. Four boundary conditions that represent various constrain conditions from flanges to stiffeners of plate girder designs, were considered.The results are presented in graphical forms. Interaction curves relating to various dimensionless parameters are constructed. Comparisons and convergence studies were made with existing available data. It is found that boundary conditions and aspect ratio influence the buckling stresses greatly. However, curvature effect is relatively insignificant over the range of practical application.     

An elasto-plastic damage model cast in a co-rotational kinematic framework for large deformation analysis of laminated composite shells

This paper presents an elasto-plastic damage model that is based on irreversible thermodynamics and internal state variable formalism for the analysis of multi-layered composites. The model is based on a damage surface that is defined in terms of an internal damage variable of energy, along with a set of rate-independent elasto-plastic constitutive equations defined in an effective stress–strain space. Employing the operator splitting methodology, a three-step predictor/multi-corrector algorithm is developed that includes an elastic predictor, a plastic corrector, and a damage corrector. The constitutive model is cast in a co-rotational kinematic framework for damage analysis in laminated plates and shells undergoing large deflections. Numerical examples are presented to demonstrate the accuracy and range of applicability of the proposed model.     

Combining vibrational linear-by-part dynamics and kinetic-based decoupling of the dynamics for multiple smooth impacts with redundancy

This article proposes a simple linear-by-part approach for perfectly elastic 3D multiple-point impacts in multibody systems with perfect constraints and no friction, applicable both to nonredundant and redundant cases (where the normal velocities of the contact points are not independent). The approach is based on a vibrational dynamical model, and uses the so called “independent contact space.” Two different time and space scales are used. At the macroscale, the impact interval is negligible, and the overall system configuration is assumed to be constant. Consequently, the inertia and Jacobian matrices appearing in the formulation are also constant. The dynamics at the contact points is simulated through stiff springs undergoing very small deformations and generating system vibrations at the microscale. The total impact interval is split into phases, each corresponding to a constant set of compressed springs responsible for an elastic potential energy. For each phase, a reduced inertia matrix associated with a set of contact points, and a reduced stiffness matrix obtained from the potential energy (associated with all contact points undergoing compression) are introduced. From these matrices, a modal analysis is performed yielding an all-analytical solution within each phase. The main difference between the redundant and nonredundant cases concerns the inertia and stiffness matrices for modal analysis. While in the former case, both are related to the total set of contact points (total contact space), in the latter one they are related to two subsets: a subset of independent points for the inertia matrix (independent contact space), and the total set for the stiffness matrix. A second difference concerns the calculation of the normal impulses generated at each contact point. For the nonredundant case, they can be directly obtained from the total incremental normal velocities of the contact points through the inertia and stiffness matrices. For the redundant one, they can be obtained by adding up their incremental values at each impact phase. This requires an updating of a new effective stiffness matrix depending on the contact points undergoing compression at each phase. Four planar application cases are presented involving a single body and a multibody system colliding with a smooth ground.     

The Matchstick Model for Anisotropic Friction Cones

Inspired by frictional behaviour that is observed when sliding matchsticks against one another at different angles, we propose a phenomenological anisotropic friction model for structured surfaces. Our model interpolates isotropic and anisotropic elliptical Coulomb friction parameters for a pair of surfaces with perpendicular and parallel structure directions (e.g. the wood grain direction). We view our model as a special case of an abstract friction model that produces a cone based on state information, specifically the relationship between structure directions. We show how our model can be integrated into LCP and NCP-based simulators using different solvers with both explicit and fully implicit time-integration. The focus of our work is on symmetric friction cones, and we therefore demonstrate a variety of simulation scenarios where the friction structure directions play an important part in the resulting motions. Consequently, authoring of friction using our model is intuitive and we demonstrate that our model is compatible with standard authoring practices, such as texture mapping.     

A gap element for three-dimensional elasto-plastic contact problems

A simple yet efficient contact algorithm with gap elements is developed to solve three-dimensional elasto-plastic contact problems without friction. A special gap element is presented, together with a stress invariance principle, to model the contact process. The solution is achieved through an iterative procedure which adjusts the modulus of the gap elements. The elasto-plastic solid element with variable nodes and nonconforming modes is employed for the effective and economic three-dimensional finite element analysis. The validity and performance of the proposed contact algorithm with gap elements are demonstrated through various numerical tests.