Indentation of the semi-infinite elastic solid by a concave rigid punch

1976 ◽  
Vol 6 (2) ◽  
pp. 149-159 ◽  
Author(s):  
J. R. Barber
Keyword(s):  
Elastic Solid ◽  
Rigid Punch

Computing the Stresses Induced Within Multi-Layered Elastic Media That Result From Sliding Contact With a Rigid Punch

2013 ◽  
Author(s):  
Stewart Chidlow ◽  
Mircea Teodorescu
Keyword(s):  
Contact Problem ◽  
Elastic Solid ◽  
Maximum Principal Stress ◽  
Functionally Graded ◽  
Material Failure ◽  
Rigid Punch ◽  
Vertical Displacements ◽  
The Fourier Transform ◽  
Graded Interlayer ◽  
Selection Of

This paper is concerned with the solution of the contact problem that results when a rigid punch is pressed into the surface of an inhomogeneously elastic solid comprising three distinct layers. The upper and lower layers of the solid are assumed to be homogeneous and are joined together by a functionally graded interlayer whose material properties progressively change from those of the coating to those of the substrate. By applying the Fourier transform to the governing boundary value problem (BVP), we may write the stresses and displacements within the solid in terms of indefinite integrals. In particular, the expressions for the horizontal and vertical displacements of the solid surface are used to formulate a coupled pair of integral equations which may be solved numerically to approximate the solution of the stamp problem. A selection of numerical results are then presented which illustrate the effects of friction on the contact problem and it is found that the presence of friction within the contact increases the magnitude of the maximum principal stress and changes its location. These observations indicate that material failure is much more likely to occur when friction is present within the contact as expected.

A Fast-Solving Semi-Analytical Solution Method for Contact Problems Involving Multi-Layered Inhomogeneously Elastic Solids

2012 ◽  
Author(s):  
Stewart Chidlow ◽  
Mircea Teodorescu
Keyword(s):  
Analytical Solution ◽  
Contact Pressure ◽  
Solution Method ◽  
Elastic Solid ◽  
Contact Problems ◽  
Accurate Estimation ◽  
Rigid Punch ◽  
Iterative Solver ◽  
Elastic Solids ◽  
Selection Of

This work is concerned with the derivation of an iterative solver which allows the accurate estimation of both the contact half-width and contact pressure when an inhomogeneouly elastic solid comprising a homogeneous coating and substrate joined by a graded layer is indented by a rigid punch. A selection of numerical results are then presented illustrating the accuracy of this model.

The elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch

1945 ◽  
Vol 41 (1) ◽  
pp. 16-26 ◽  
Author(s):  
J. W. Harding ◽  
I. N. Sneddon
Keyword(s):  
Arbitrary Shape ◽  
Plane Surface ◽  
Elastic Solid ◽  
Integral Transforms ◽  
Senior Author ◽  
Rigid Punch ◽  
Elastic Stresses ◽  
Distribution Of Stress ◽  
Special Case ◽  
General Method

During the course of some investigations on the distribution of stress in an elastic solid it was noticed by the senior author that a systematic application of the method of integral transforms to the problem of the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch reduced the problem essentially to one of solving a pair of integral equations belonging to a class which has been studied by Titchmarsh and by Busbridge (4,5). This procedure allows one to obtain the solution for an arbitrary shape of punch by a general method which leads automatically to the solution and avoids the troublesome procedure, adopted by Love (2) in the case of a conical punch, of being obliged to guess appropriate combinations of solutions which will satisfy the prescribed boundary conditions in any special case. Moreover, it can easily be seen that an attempt to apply Love's method to more complicated shapes of punch will lead to considerable analytical difficulties.

A Rigid Punch in Contact With a Nonhomogeneous Elastic Solid

1974 ◽  
Vol 41 (4) ◽  
pp. 1019-1024 ◽  
Author(s):  
M. K. Kassir ◽  
M. F. Chuaprasert
Keyword(s):  
Axisymmetric Problem ◽  
Integral Transform ◽  
Elastic Solid ◽  
Elastic Parameter ◽  
The Other ◽  
Graphical Form ◽  
Rigid Punch ◽  
Isotropic Solid ◽  
Physical Quantities ◽  
Quantities Of Interest

This paper treats the axisymmetric problem of a rigid punch in contact with a nonhomogeneous elastic isotropic solid whose modulus of rigidity is a continuous function of the depth while the other elastic parameter, Poisson’s ratio, is assumed to be constant. An integral transform solution is given which reduces the formulation of the problem to a Fredholm integral equation of the second kind which is amenable to numerical treatment. The physical quantities of interest are studied in detail and illustrative numerical results for several punch profiles are obtained and exhibited in tabulated and graphical form.

On Boussinesq's problem and penny-shaped cracks

1949 ◽  
Vol 45 (2) ◽  
pp. 251-257 ◽  
Author(s):  
A. E. Green
Keyword(s):  
Integral Equations ◽  
Bessel Functions ◽  
Plane Surface ◽  
Circular Crack ◽  
Elastic Solid ◽  
Rigid Punch ◽  
Systematic Application ◽  
Method Of Solution ◽  
Distribution Of Stress ◽  
Boussinesq’S Problem

Harding and Sneddon(3) and Sneddon(6) have shown that the systematic application of Hankel transforms to the problem of the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch, reduces the problem essentially to one of solving a pair of integral equations belonging to a class which has been studied by Titchmarsh(8) and Busbridge(1). The same method has also been applied by Sneddon(7) to the problem of the distribution of stress in the neighbourhood of a circular crack in an elastic solid. In both types of problem the results are expressed in quite simple forms independent of Bessel functions and this suggests that there should be an alternative method of solution. It is now possible to supply such a method with the help of a recent paper by Copson(2) on the problem of the electrified disk. In addition, some generalization of the stress systems considered by Harding and Sneddon can be made since they confined their analysis to stresses which were symmetrical about an axis.

The internal stability of an elastic solid

2000 ◽  
Vol 80 (12) ◽  
pp. 2827-2840 ◽  
Author(s):  
J. W. Morris Jr, C. R. K Renn
Keyword(s):  
Elastic Solid ◽  
Internal Stability

scholarly journals Thermal Stresses in Chemically Hardening Elastic Media With Application to the Molding Process

1974 ◽  
Vol 41 (3) ◽  
pp. 647-651 ◽  
Author(s):  
Myron Levitsky ◽  
Bernard W. Shaffer
Keyword(s):  
Residual Stress ◽  
Chemical Reaction ◽  
Thermal Stresses ◽  
Stress Component ◽  
Elastic Solid ◽  
Molding Process ◽  
Hardening Process ◽  
Exothermic Chemical Reaction ◽  
Component Parallel

A method has been formulated for the determination of thermal stresses in materials which harden in the presence of an exothermic chemical reaction. Hardening is described by the transformation of the material from an inviscid liquid-like state into an elastic solid, where intermediate states consist of a mixture of the two, in a ratio which is determined by the degree of chemical reaction. The method is illustrated in terms of an infinite slab cast between two rigid mold surfaces. It is found that the stress component normal to the slab surfaces vanishes in the residual state, so that removal of the slab from the mold leaves the remaining residual stress unchanged. On the other hand, the residual stress component parallel to the slab surfaces does not vanish. Its distribution is described as a function of the parameters of the hardening process.

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