Elasto-Plastic Normal Contact of Three-Dimensional Fractal Surfaces Using Halfspace Theory

2004 ◽  
Vol 126 (1) ◽  
pp. 28-33 ◽  
Author(s):  
K. Willner
Keyword(s):  
Fractal Dimension ◽  
Three Dimensional ◽  
Contact Problems ◽  
Plastic Range ◽  
Elastic Halfspace ◽  
Normal Contact ◽  
Simple Modification ◽  
Surface Parameters ◽  
Fractal Surfaces ◽  
Approximative Solution

The elasto-plastic normal contact of fractal surfaces is investigated. To study the influence of several surface parameters like fractal dimension and resolution, the surfaces are numerically generated using a special form of the structure function which is motivated by measurements of real rough surfaces. The contact simulation uses an iterative elastic halfspace solution based on a variational principle. A simple modification allows also the approximative solution of elasto-plastic contact problems. The influence of different surface parameters is studied with respect to the load-area relationship and the load-gap relationship. The simulations show that for realistic surface parameters the deformation is always in the plastic range.

Influence of Surface Parameters on the Elastoplastic Contact Behavior of Fractal-Regular Surfaces

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
K. Willner
Keyword(s):  
Three Dimensional ◽  
Atomic Scale ◽  
Normal Contact ◽  
Surface Parameters ◽  
Fractal Surfaces ◽  
Minor Influence ◽  
Dimensionless Ratio ◽  
Transition Length ◽  
Geometric Surface ◽  
Height Data

In a recent paper (2004, “Elasto-Plastic Normal Contact of Three-Dimensional Fractal Surfaces Using Halfspace Theory,” J. Tribol., 126, pp. 28–33) the author developed a halfspace model for the elasto-plastic normal contact of rough surfaces. This model is now used to study the influence of intrinsic surface parameters on constitutive contact laws, such as load-gap relation and load-area relation, for a specific type of surface topography known as fractal-regular surfaces. Numerical investigations show that the fractal dimension has only minor influence on the load-gap relationship, which is mostly determined by the dimensionless ratio between the transition length and the rms values of the height data. Due to the fractal nature of the surfaces at the small wavelength limit, initial deformation will always be in the plastic range. The load-area relation becomes then completely independent of the geometric surface parameters and is determined by material properties alone, at least if the predicted plastic deformation occurs at a length scale larger than the atomic scale.

A General Three-Dimensional Numerical Technique for Determining the Contact Area of an Arbitrary Punch on an Elastic Half-Space

2016 ◽  
Vol 08 (01) ◽  
pp. 1650005 ◽  
Author(s):  
Jing Jin Shen ◽  
Feng Yu Xu ◽  
Guo Ping Jiang
Keyword(s):  
Numerical Method ◽  
Contact Area ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Contact Problems ◽  
Linear Interpolation ◽  
Contact Boundary ◽  
Reciprocal Theorem ◽  
Normal Contact ◽  
Indentation Force

The paper presents a numerical method for determining the contact area in three-dimensional elastostatic normal contact without friction. The method makes use of the theorem developed by Barber, the contact area is that over which the total indentation force achieves its maximum value. By approximating the punch by linear interpolation, the analytical expression for the indentation force is derived by virtue of the reciprocal theorem. The physical meaning of the parameter which determines the contact boundary is discussed, and its feasible range corresponding to the contact area is found. Then, the numerical algorithm for determining the parameter is developed and applied to solve several normal contact problems. The results show that the proposed numerical method possesses a good property on accuracy and convergency.

scholarly journals Roughness-Induced Adhesive Hysteresis in Self-Affine Fractal Surfaces

Lubricants ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 7
Author(s):  
Guido Violano ◽  
Luciano Afferrante
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Applied Load ◽  
Roughness Parameters ◽  
Normal Contact ◽  
Fractal Surfaces ◽  
Elastic Bodies ◽  
Roughness Amplitude ◽  
Loading And Unloading ◽  
Hysteretic Loss

It is known that in the presence of surface roughness, adhesion can lead to distinct paths of loading and unloading for the area–load and penetration–load relationships, thus causing hysteretic loss. Here, we investigate the effects that the surface roughness parameters have on such adhesive hysteresis loss. We focus on the frictionless normal contact between soft elastic bodies and, for this reason, we model adhesion according to Johnson, Kendall, and Roberts (JKR) theory. Hysteretic energy loss is found to increase linearly with the true area of contact, while the detachment force is negligibly influenced by the maximum applied load reached at the end of the loading phase. Moreover, for the micrometric roughness amplitude hrms considered in the present work, adhesion hysteresis is found to be affected by the shorter wavelengths of roughness. Specifically, hysteresis losses decrease with increasing fractal dimension and cut-off frequency of the roughness spectrum. However, we stress that a different behavior could occur in other ranges of roughness amplitude.

scholarly journals Characterization of 2D and 3D Rough Fractal Surfaces from Backscattered Radar Data

2017 ◽  
Vol 23 (3) ◽  
pp. 53-58
Author(s):  
Apostolos Kotopoulis ◽  
Georgios Pouraimis ◽  
Evangelos Kallitsis ◽  
Panayiotis Frangos
Keyword(s):  
Fractal Dimension ◽  
Three Dimensional ◽  
Radar Data ◽  
Wave Number ◽  
Backscattering Coefficient ◽  
Surface Fractal Dimension ◽  
Fractal Surfaces ◽  
Surface Fractal ◽  
Number Frequency ◽  
2D And 3D

AbstractThe scattering of electromagnetic (EM) waves, emitted by a monostatic radar, from two - dimensional (2D) rough fractal surfaces is examined by using the Kirchhoff approximation. We examine the way that the level of roughness of the fractal surface affects the backscattered EM wave captured by a radar as a function of frequency (therefore, a ‘spectral method’) and whether the roughness of the surface can be estimated from these radar measurements. The backscattering coefficient is calculated for a number of radar frequencies and for different values of the surface fractal dimension. It is found that the values of the slopes between the main lobe and the first sidelobes of the backscattering coefficient as a function of the wave number (frequency) of the incident EM waves increase with the surface fractal dimension. Therefore, we conclude that the magnitude of the above slopes provides a reliable method for the classification of the rough fractal surfaces. Furthermore, concerning three - dimensional (3D) fractal surfaces, investigations similar to the above are already performed by the authors and will be presented during the Conference. The above are also investigated in the presence of electronic noise in the radar receiver (effect of SNR values in the above proposed technique).

Linear Complementary Formulations Involving Frictional Contact for Elasto-Plastic Deformable Bodies

1997 ◽  
Vol 64 (1) ◽  
pp. 80-89 ◽  
Author(s):  
Maocheng Li ◽  
Desong Sha ◽  
K. K. Tamma
Keyword(s):  
Frictional Contact ◽  
Three Dimensional ◽  
Nonlinear Behavior ◽  
Small Deformation ◽  
Contact Problems ◽  
Tangential Direction ◽  
Normal Direction ◽  
Contact Forces ◽  
Contact Boundary ◽  
Normal Contact

In the present study, an incremental variational inequality is described for frictional contact problems with material non linear behavior assumed to be elasto-plastic for the contacting bodies. On the contacting boundaries, the constraint conditions include noninterpenetration along the normal direction of the contact boundary and Coulomb friction law in the sliding direction. After numerical discretization using the finite element method, an effective linear complementary formulation is then established with two unknown variables and two complementary variables for each contact nodal pair. The proposed developments permit a reduced number of unknown variables which are chosen as the gap function for the normal direction and the norm of the incremental sliding displacements for the tangential direction; and the complementary variables are taken as the normal contact forces and slack variables in the tangential directions. The resulting linear complementary equations are then solved employing an explicit Conjugate Gradient Based Projection (CGBP) method in conjunction with a generalized Newton-Raphson iteration procedure to account for the material nonlinear behavior. The methodology is valid for three-dimensional frictional contact representations; however, for purposes of illustration of the proposed approaches, attention is confined to applications involving two-dimensional static elasto-plastic problems under small deformation. Numerical examples are presented which clearly show that the developments satisfy the problem physics and contact conditions with features to include high accuracy and reduced computational costs.

The influence of fractal dimension in the microcontact of three-dimensional elastic-plastic fractal surfaces

2018 ◽  
Vol 104 (1-4) ◽  
pp. 17-25 ◽  
Author(s):  
Qijing Lin ◽  
Qingzhi Meng ◽  
Chenying Wang ◽  
Qidong Zhang ◽  
Man Zhao ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Three Dimensional ◽  
Elastic Plastic ◽  
Fractal Surfaces

scholarly journals A Review of the Method of Dimensionality Reduction in Contact Mechanics: Applications for Structural Damping, Wear and Adhesion

2015 ◽  
Author(s):  
V.L. Popov ◽  
M. Heß ◽  
M. Popov
Keyword(s):  
Dimensionality Reduction ◽  
Three Dimensional ◽  
Contact Problems ◽  
Adhesive Contact ◽  
Tangential Direction ◽  
Fretting Wear ◽  
Normal Contact ◽  
Method Of Dimensionality Reduction ◽  
Frictional Damping ◽  
Arbitrary Axis

In the method of dimensionality reduction (MDR), contacts of three-dimensional bodies are mapped to the contact problem with a one-dimensional elastic or viscoelastic foundation. This is valid for the normal contact, the tangential contact and the normal contact of viscoelastic bodies. For the above classes of contact problems, several examples are considered and discussed in detail. This includes: (a) Fretting wear for arbitrary histories of loading (for simultaneous oscillations both in normal and horizontal directions); (b) Frictional damping under the influence of oscillations in normal and tangential direction as well as normal and torsional loading; (c) Adhesion of bodies of arbitrary axis-symmetric shape with extension to the adhesive contact of elastomers.

Tire Modeling by Finite Elements

1992 ◽  
Vol 20 (1) ◽  
pp. 33-56 ◽  
Author(s):  
L. O. Faria ◽  
J. T. Oden ◽  
B. Yavari ◽  
W. W. Tworzydlo ◽  
J. M. Bass ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Rolling Contact ◽  
Test Problems ◽  
State Behavior ◽  
Normal Contact ◽  
New Developments ◽  
Applied Torque ◽  
Dimensional Finite Element ◽  
Tire Modeling ◽  
Three Dimensional Finite Element

Abstract Recent advances in the development of a general three-dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure-volume. Several new test problems and examples of tire analysis are presented.

A Nonlinear Rail Vehicle Dynamics Computer Program SAMS/Rail: Part 1—Theory and Formulations

2009 ◽  
Author(s):  
Khaled E. Zaazaa ◽  
Brian Whitten ◽  
Brian Marquis ◽  
Erik Curtis ◽  
Magdy El-Sibaie ◽  
...  
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Contact Element ◽  
Contact Forces ◽  
Simulation Code ◽  
Vehicle Performance ◽  
Normal Contact ◽  
Advantages And Disadvantages ◽  
High Speed Trains

Accurate prediction of railroad vehicle performance requires detailed formulations of wheel-rail contact models. In the past, most dynamic simulation tools used an offline wheel-rail contact element based on look-up tables that are used by the main simulation solver. Nowadays, the use of an online nonlinear three-dimensional wheel-rail contact element is necessary in order to accurately predict the dynamic performance of high speed trains. Recently, the Federal Railroad Administration, Office of Research and Development has sponsored a project to develop a general multibody simulation code that uses an online nonlinear three-dimensional wheel-rail contact element to predict the contact forces between wheel and rail. In this paper, several nonlinear wheel-rail contact formulations are presented, each using the online three-dimensional approach. The methods presented are divided into two contact approaches. In the first Constraint Approach, the wheel is assumed to remain in contact with the rail. In this approach, the normal contact forces are determined by using the technique of Lagrange multipliers. In the second Elastic Approach, wheel/rail separation and penetration are allowed, and the normal contact forces are determined by using Hertz’s Theory. The advantages and disadvantages of each method are presented in this paper. In addition, this paper discusses future developments and improvements for the multibody system code. Some of these improvements are currently being implemented by the University of Illinois at Chicago (UIC). In the accompanying “Part 2” and “Part 3” to this paper, numerical examples are presented in order to demonstrate the results obtained from this research.

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