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.

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.

Rolling Contact With Friction and Non-Hertzian Pressure Distribution

1989 ◽  
Vol 56 (4) ◽  
pp. 814-820 ◽  
Author(s):  
C. Liu ◽  
B. Paul
Keyword(s):  
Pressure Distribution ◽  
Numerical Technique ◽  
Contact Region ◽  
Three Dimensional ◽  
Contact Problems ◽  
Rolling Contact ◽  
Sliding Contact ◽  
Hertzian Contact ◽  
Limiting Case ◽  
Large Spin

A numerical technique has been developed to deal with three-dimensional rolling contact problems with an arbitrary contact region under an arbitrary pressure. Results of this technique are checked against existing solutions for cases of Hertzian contact. A solution for a case of non-Hertzian contact is also presented. This numerical technique works satisfactorily for cases with small spin creepage. For cases of large spin creepage, we utilize a recent work (by the authors) for the limiting case of fully developed sliding contact.

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.

scholarly journals Penetration factor of the surfaces in fast algorithm of solution of contact problems for wheel and rail.

2015 ◽  
Vol 2015 (1) ◽  
pp. 46-51
Author(s):  
Владимир Сакало ◽  
Vladimir Sakalo ◽  
Алексей Сакало ◽  
Aleksey Sakalo
Keyword(s):  
Contact Area ◽  
Fast Algorithm ◽  
Contact Problems ◽  
Normal Contact ◽  
Contact Patch ◽  
Penetration Factor ◽  
Rolling Surface

Values of penetration factor of wheel and rail surfaces that is used on application of fast algorithm for solution of normal contact problems are defined. Three cases had been considered: contact area has not strongly expressed spatial character; contact patch is situated nearby middle of rail rolling surface, radii of curvature of wheel and rail profiles have close values; contact patch is situated on fillet sections of the profiles.

An Extension of Hertz’s Theory in Contact Mechanics

2006 ◽  
Vol 74 (2) ◽  
pp. 373-374 ◽  
Author(s):  
Guanghui Fu
Keyword(s):  
Contact Area ◽  
General Procedure ◽  
Contact Problems ◽  
The Body ◽  
Polynomial Functions ◽  
Contact Pressure Distribution ◽  
Total Load ◽  
Normal Contact ◽  
Elastic Bodies ◽  
Hertz's Solution

Hertz’s theory, developed in 1881, remains the foundation for the analysis of most contact problems. In this paper, we consider the axisymmetric normal contact of two elastic bodies, and the body profiles are described by polynomial functions of integer and noninteger positive powers. It is an extension of Hertz’s solution, which concerns the contact of two elastic spheres. A general procedure on how to solve this kind of problem is presented. As an example, we consider the contact between a cone and a sphere. The relations among the radius of the contact area, the depth of the indentation, the total load, and the contact pressure distribution are derived.

Development and Experimental Validation of a Point Contact Model for Dynamical Problems With Friction

2001 ◽  
Author(s):  
Walter Sextro
Keyword(s):  
Pressure Distribution ◽  
Relative Motion ◽  
Contact Area ◽  
Point Contact ◽  
Contact Problems ◽  
Normal Pressure ◽  
Tangential Direction ◽  
Contact Model ◽  
Impact Oscillator ◽  
Normal Contact

Abstract The contact forces are dependent on many parameters, such as contact stiffnesses, surface profiles, material parameters, temperature distribution, relative motion and normal pressure distribution. These parameters can change within the contact area and from here, it is impossible to derive a general force law. The only possibility to overcome this problem is to discretize the contact areas, since in general the relative motion and the contact parameters are not constantly distributed within the contact surface. This leads to a point contact model, which has to include all main physical effects as described above, which are important, when simulating dynamical contact problems with friction. The friction model includes the main parameters such as the roughness of the contact surfaces, the nonlinear friction law, the contact stiffnesses in normal and tangential direction. The decreasing characteristic of the friction coefficient with respect to the relative velocity has to be modeled in a sufficient way. With respect to the dissipation of energy, the hysteretic behavior is studied with respect to the normal and tangential direction. Separation of the contact is included. This point contact model is be applied to real dynamical contact problems. In the first example, a simple impact oscillator with an elastic contact is used to check the overall modeling with respect to the elastic normal contact. Then, a self excited friction oscillator is investigated with respect to the tangential contact. Here, the modeling of surface waviness leads to high periodic solutions, which is also observed within the experiments. In both examples, the comparison of measurements and calculated phase plots is good. Furthermore, the influence of wear on to the surface profile, contact area and normal pressure distribution is investigated. From here, it follows, that friction leads to time dependent systems.

Elastic Plastic Finite Element Analysis of Bolted Joint During Tightening Process

2003 ◽  
Vol 125 (4) ◽  
pp. 823-830 ◽  
Author(s):  
Toshimichi Fukuoka ◽  
Tomohiro Takaki
Keyword(s):  
Numerical Method ◽  
Degrees Of Freedom ◽  
Plastic Region ◽  
Three Dimensional ◽  
Contact Problems ◽  
Torque Control ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Computation Efficiency ◽  
Bolt Stress

Mechanical behavior of bolted joints during the tightening process with torque control is analyzed by FEM as elastic plastic contact problems. Three-dimensional analysis was conducted employing two-dimensional model with each node having three degrees of freedom that attains high computation efficiency. Such important factors as development of plastic zones, variations of load distributions along engaged threads, the relationships between axial bolt stress and nut rotation angle were analyzed in order to provide an effective guideline when tightening critical structures with high bolt preloads. It was also shown that the proposed numerical method can be applied to evaluate the tightening process by “plastic region tightening” used extensively in recent years. The validity of the numerical method is demonstrated by comparing the calculated bolt elongation with that obtained from experiment.

Unilateral Contact Problems with Friction for Hemitropic Elastic Solids

2009 ◽  
Vol 16 (4) ◽  
pp. 629-650
Author(s):  
Avtandil Gachechiladze ◽  
Roland Gachechiladze ◽  
David Natroshvili
Keyword(s):  
Original Problem ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Contact Problems ◽  
Unilateral Contact ◽  
Contact Boundary ◽  
Elastic Solids ◽  
Necessary And Sufficient ◽  
Unilateral Contact Problems

Abstract We study three-dimensional unilateral contact problems with friction for hemitropic elastic solids. We give their mathematical formulation in the form of spatial variational inequalities and show the equivalence to the corresponding minimization problem. Based on our variational inequality approach, we prove existence and uniqueness theorems. We prove also that solutions continuously depend on the data of the original problem and on the friction coefficient. Our investigation includes the special particular case of only traction-contact boundary conditions without prescribing displacement and microrotation vectors along some part of the boundary of a hemitropic elastic body. Then the problems are not unconditionally solvable and we derive the necessary and sufficient conditions of their solvability.

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.

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