The Contact Stresses Between a Rigid Indenter and a Viscoelastic Half-Space

1966 ◽  
Vol 33 (4) ◽  
pp. 845-854 ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Contact Area ◽  
Contact Stresses ◽  
Spherical Indenter ◽  
Contact Radius ◽  
Rigid Sphere ◽  
Hertz Problem ◽  
Monotonically Increasing Function ◽  
Increasing Function

The Hertz problem for a rigid spherical indenter on a viscoelastic half-space was studied by Lee and Radok [1] in which the radius a(t) of the contact area is a monotonically increasing function of time t. Later, Hunter [2] studied the rebound of a rigid sphere on a viscoelastic half-space so that the contact radius a(t) increases monotonically to a maximum and then decreases to zero monotonically. The contact problem in which a(t) increases for the second time and decreases again does not seem to have been studied; nor has the contact problem in which a(t) is nonzero initially and decreases monotonically been studied. In this paper, a method is introduced so that the contact problem can be solved for arbitrary a(t). The rigid indenter is assumed to be smooth and axisymmetric but otherwise arbitrary. The viscoelastic solutions are expressed in terms of the associated elastic solutions. A means for measuring the viscoelastic Poisson’s ratio is suggested.

Axisymmetric contact with friction of a rigid sphere with an elastic half-space

2009 ◽  
Vol 465 (2108) ◽  
pp. 2565-2588 ◽  
Author(s):  
O. I. Zhupanska
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Integral Transform ◽  
Elastic Half Space ◽  
Rigid Sphere ◽  
Analytical Treatment ◽  
Normal Contact ◽  
Exact Analytical Solutions ◽  
Single Integral ◽  
Toroidal Coordinates

The problem of normal contact with friction of a rigid sphere with an elastic half-space is considered. An analytical treatment of the problem is presented, with the corresponding boundary-value problem formulated in the toroidal coordinates. A general solution in the form of Papkovich–Neuber functions and the Mehler–Fock integral transform is used to reduce the problem to a single integral equation with respect to the unknown contact pressure in the slip zone. An analysis of contact stresses is carried out, and exact analytical solutions are obtained in limiting cases, including a full stick contact problem and a contact problem for an incompressible half-space.

Contact Area Variation in Elastic Indentation Problems

2009 ◽  
Author(s):  
Roman Riznychuk
Keyword(s):  
Contact Problem ◽  
Pressure Distribution ◽  
Half Space ◽  
Analytical Solutions ◽  
Contact Area ◽  
Elastic Half Space ◽  
Exact Expression ◽  
Rigid Punch ◽  
Contact Pressure Distribution ◽  
Area Variation

Contact problem of the frictionless indentation of elastic half-space by smooth rigid punch of curved profile is investigated. An exact expression of the contact pressure distribution for a curved profile punch in terms of integral involving the pressure distribution for sequence of flat punches is derived. The method is illustrated and validated by comparison with some well-known analytical solutions.

scholarly journals Normal and Tangential Contact Between Anisotropic Materials With an Anisotropic Coating

2012 ◽  
Author(s):  
C. Bagault ◽  
D. Nélias ◽  
M.-C. Baietto
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Analytical Solutions ◽  
Analytical Methods ◽  
Rigid Sphere ◽  
Problem Solution ◽  
Numerical Techniques ◽  
Tangential Contact ◽  
Anisotropic Problems ◽  
Recent Developments

A contact model using semi analytical methods, relying on elementary analytical solutions, has been developed. It is based on numerical techniques adapted to contact mechanics, with strong potential for inelastic, inhomogeneous or anisotropic problems. Recent developments aim to quantify displacements and stresses of an anisotropic half space with an anisotropic coating which is in contact with a rigid sphere. The influence of symmetry axes on the contact problem solution will be more specifically analyzed.

scholarly journals To Solution of Contact Problem for Rectangular Plate on Elastic Half-Space

2020 ◽  
Vol 19 (3) ◽  
pp. 224-229
Author(s):  
S. V. Bosakov
Keyword(s):  
Contact Problem ◽  
Rectangular Plate ◽  
Half Space ◽  
Chebyshev Polynomials ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Rectangular Region ◽  
Double Row ◽  
Linear Algebraic Equations ◽  
Boussinesq Solution

Until the present time there is no exact solution to the contact problem for a rectangular plate on an elastic base with distribution properties. Practical analogues of this design are slab foundations widely used in construction. A lot of scientists have solved this problem in various ways. The methods of finite differences, B. N. Zhemochkin and power series do not distinguish a specific feature in contact stresses at the edges of the plate. The author of the paper has obtained an expansion of the Boussinesq solution for determining displacements of the elastic half-space surface in the form of a double series according to the Chebyshev polynomials of the first kind in a rectangular region. For the first time, such a representation for the symmetric part of the Boussinesq solution was obtained by V. I. Seimov and it has been applied to study symmetric vibrations of a rectangular stamp, taking into account inertial properties of the half-space. Using this expansion, the author gives a solution to the problem for a rectangular plate lying on an elastic half-space under the action of an arbitrarily applied concentrated force. In this case, the required displacements are specified in the form of a double row in the Chebyshev polynomials of the first kind. Contact stresses are also specified in the form of a double row according to the Chebyshev polynomials of the first kind with weight. In the integral equation of the contact problem integration over a rectangular region is performed while taking into account the orthogonality of the Chebyshev polynomials. In the resulting expression the coefficients are equal for the same products of the Chebyshev polynomials. The result is an infinite system of linear algebraic equations, which is solved by the amplification method. Thus the sought coefficients are found in the expansion for contact stresses.

Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space

2005 ◽  
Vol 127 (2) ◽  
pp. 325-330 ◽  
Author(s):  
J. Yang ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Contact Pressure ◽  
Contact Area ◽  
Real Contact Area ◽  
Rigid Sphere ◽  
Small Surface ◽  
Real Contact ◽  
Homogeneous Half Space ◽  
The Mean

The impact of a rigid sphere moving at constant velocity on elastic homogeneous half-space was analyzed by the finite element method. Frictionless dynamic contact was modeled with special contact elements at the half-space surface. A dimensionless parameter, β, was introduced to study the effect of wave propagation on the deformation behavior. For small surface interference (β⩽1), the front of the faster propagating dilatational waves extends up to the contact edge, the real contact area is equal to the truncated area, and the contact pressure distribution is uniform. However, for large surface interference (β>1), the dilatation wave front extends beyond the contact edge, the real contact area is less than the truncated area, and the contact pressure exhibits a Hertzian-like distribution. The mean contact pressure increases abruptly at the instant of initial contact, remains constant for β⩽1, and increases gradually for β>1. Based on finite element results for the subsurface stress, strain, and velocity fields, a simple theoretical model that yields approximate closed-form relationships for the mean contact pressure and kinetic and strain energies of the half-space was derived for small surface interference (β⩽1), and its validity was confirmed by favorable comparisons with finite element results.

The Dynamic Problem of Torsion by a Rigid Shaft of a Nonhomogeneous Half-Space

2019 ◽  
Vol 968 ◽  
pp. 396-403
Author(s):  
Viktoriia Denysenko ◽  
Iryna Kovalova ◽  
Dina Lazarieva
Keyword(s):  
Approximate Solution ◽  
Contact Problem ◽  
Half Space ◽  
Contact Area ◽  
Dynamic Problem ◽  
Polynomial Method ◽  
Integral Transformations ◽  
Subsequent Application ◽  
Axisymmetric Contact Problem ◽  
Angle Of Rotation

An axisymmetric contact problem concerning the torsion of a circular shaft of an orthotropic-nonhomogeneous half-space is considered. By means of the technique of integral transformations of Laplace and Hankel, with the subsequent application of the orthogonal polynomial method, an approximate solution in the transformant space is constructed. Also was performed reverse transformation. Calculated formulas for the angle of rotation of the shaft and the tangential stress acting on the contact area are obtained. Numerical calculations for certain types of heterogeneity have been performed. Comparison of the obtained results with the previously known results is made.

scholarly journals CHARACTERISTICS OF CONTACT OF A ROUGH SURFACE WITH A LOW-MODULUS HALF-SPACE

2017 ◽  
Author(s):  
P. Ogar ◽  
S. Belokobylsky ◽  
D. Gorokhov ◽  
V. Elsukov
Keyword(s):  
Contact Problem ◽  
Pressure Distribution ◽  
Rough Surface ◽  
Half Space ◽  
Geometric Parameter ◽  
Contact Area ◽  
Beta Function ◽  
Uniform Loading ◽  
Roughness Model ◽  
Low Modulus

Initially, the contact of a single spherical asperity is considered with taking into account the influence of the remaining contacting asperities. It is assumed that the influence of the remaining contacting asperities is equal to the action of the uniform loading qc outside the asperity contour. This made possible to solve the contact problem as an axisymmetric one. An equation for the pressure distribution at the contact area is obtained. To determine the contact characteristics, a discrete roughness model is used, the surface bearing curve of which is described by a regularized beta function. The relative contact area and the gap density in the joint are determined depending on the dimensionless force elastic-geometric parameter fq. When determining the gap density in the joint, the displacements of the rough surface and half-space are taken into account. It is shown that the contact characteristics do not depend on the values of the regularized beta function parameters p and q.

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