Axisymmetric Contact Stresses About a Smooth Elastic Sphere in an Infinite Solid Stressed Uniformly at Infinity

1967 ◽  
Vol 34 (4) ◽  
pp. 960-966 ◽  
Author(s):  
H. B. Wilson ◽  
J. G. Goree
Keyword(s):  
Spherical Inclusion ◽  
Contact Stresses ◽  
Infinite Medium ◽  
Hertzian Contact ◽  
Normal Stresses ◽  
Elastic Parameters ◽  
Stress Components ◽  
Method Of Solution ◽  
Spherical Caps ◽  
Special Case

An evaluation is made of non-Hertzian contact stresses occurring during partial separation between a smooth elastic spherical inclusion and a surrounding infinite medium subjected to two independent axisymmetric stress components at infinity. Modifications of an analysis by another author for a special case involving a rigid inclusion and uniaxial tension applied at infinity are discussed, and an alternate method of solution is given. Extensive numerical results are presented for circumferential and normal stresses on the cavity corresponding to 12 different combinations of loading and elastic parameters which yield contact surfaces defined by either an equatorial spherical band or two polar spherical caps.

Subsurface and Surface Cracking Due to Hertzian Contact

1982 ◽  
Vol 104 (3) ◽  
pp. 347-351 ◽  
Author(s):  
L. M. Keer ◽  
M. D. Bryant ◽  
G. K. Haritos
Keyword(s):  
Crack Propagation ◽  
Half Space ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Vertical Crack ◽  
Subsurface Crack ◽  
Surface Cracking ◽  
Crack Geometry

Numerical results are presented for a cracked elastic half-space surface-loaded by Hertzian contact stresses. A horizontal subsurface crack and a surface breaking vertical crack are contained within the half-space. An attempt to correlate crack geometry to fracture is made and possible mechanisms for crack propagation are introduced.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

Behavior of a Horizontal Fluid Filled Crack Under Moving Hertzian Load

2005 ◽  
Author(s):  
X. Jin ◽  
L. M. Keer ◽  
E. L. Chez
Keyword(s):  
Half Plane ◽  
Continuous Distribution ◽  
Contact Stresses ◽  
Hertzian Contact ◽  
Subsurface Crack ◽  
Intensity Factors ◽  
Crack Volume ◽  
Rolling Body ◽  
Soft Inclusion ◽  
Edge Dislocations

Numerical analysis is presented for a fluid filled subsurface crack in an elastic half plane loaded by Hertzian contact stresses. The opening volume of the horizontal Griffith crack is fully occupied by an incompressible fluid. In the presence of friction, a moving Hertzian line contact load is applied at the surface of the half plane. The stress intensity factors at the tips of the fluid filled crack are analyzed on condition that the change of the opening crack volume vanishes due to the fluid incompressibility. The method used is that of replacing the crack by a continuous distribution of edge dislocations. As a cycle of rolling can be viewed as shifting the Hertzian contact stresses across the surface of the half plane, the results of this analysis may prove useful in the prediction of rolling fatigue of an elastic rolling body containing a soft inclusion.

Hertzian Contact-Stress Deformation Coefficients

1969 ◽  
Vol 36 (2) ◽  
pp. 296-303 ◽  
Author(s):  
Duane H. Cooper
Keyword(s):  
Contact Stress ◽  
Digital Computer ◽  
Approximate Calculation ◽  
Transcendental Equation ◽  
Contact Stresses ◽  
Elliptic Integrals ◽  
Hertzian Contact ◽  
Stress Deformation ◽  
Hertzian Contact Stress

Formulations are given for the coefficients λ, μ, ν defined by Hertz in terms of the solution of a transcendental equation involving elliptic integrals and used by him to describe the deformation of bodies subjected to contact stresses. Methods of approximate calculation are explained and errors in the tables prepared by Hertz are noted. For the purpose of providing a more extensive and more accurate tabulation, using an automatic digital computer, these coefficients are reformulated so that a large part of the variation is expressed by means of easily interpreted elementary formulas. The remainder of the variation is tabulated to 6 places for 100 values of the argument. Graphs of the coefficients are also provided.

Solution of Non-Fourier Temperature Field in a Hollow Sphere under Harmonic Boundary Condition

2015 ◽  
Vol 772 ◽  
pp. 197-203 ◽  
Author(s):  
Amin Bahrami ◽  
Siamak Hosseinzadeh ◽  
Ramin Ghasemiasl ◽  
Morteza Radmanesh
Keyword(s):  
Heat Flux ◽  
Temperature Field ◽  
Hollow Sphere ◽  
Separation Of Variables ◽  
Time Dependent ◽  
Separation Of Variables Method ◽  
Method Of Solution ◽  
Duhamel Integral ◽  
Special Case ◽  
General Time

Analytical solution of the axisymmetric two-dimensional non-Fourier temperature field within a hollow sphere is investigated considering Cattaneo-Vernotte constitutive equation with general time-dependent heat flux. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The method of solution is the standard separation of variables method. Duhamel integral is used for applying the time-dependent boundary conditions. The presented solution is applied to special case of harmonic heat flux on outer surface.

scholarly journals WAVE SCATTERING BY PERMEABLE AND IMPERMEABLE BREAKWATER OF ARBITRARY SHAPE

1974 ◽  
Vol 1 (14) ◽  
pp. 110
Author(s):  
Takeshi Ijima ◽  
Chung Ren Chou ◽  
Yasu Yumura
Keyword(s):  
Arbitrary Shape ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Theoretical Method ◽  
Floating Body ◽  
Wave Forces ◽  
Method Of Calculation ◽  
Wave Channel ◽  
Method Of Solution ◽  
Special Case

This paper deals with a theoretical method of calculation of the fluid motion, when a sinusoidal plane wave incidents to a permeable breakwater of arbitrary shape at constant water depth and shows that the problem for impermeable breakwater is solved as a special case of this method. The method described here is the extension of the author's method of solution for two-dimensional permeable breakwater by the method of continuation of velocity potentials for two different fluid regions into three-dimensional problems by means of Green functions. Here, the analytical process of calculation is presented and as representative examples, wave height distributions and wave forces around an isolated elliptic- and rectangular breakwater are calculated and compared with experiments in wave channel. The principle of this method is also applied to the analysis of submerged and semi-immersed fixed cylinder and the motions of floating body of arbitrary.

scholarly journals Determination of Elastic Parameters due a Dynamic Hertzian Contact

2020 ◽  
Author(s):  
Juan Pablo Villacreses ◽  
Bernardo Caicedo ◽  
Silvia Caro ◽  
Fabricio Yepez ◽  
Joel Sebastián Puebla
Keyword(s):  
Hertzian Contact ◽  
Elastic Parameters

scholarly journals Stress Tensor and Gradient of Hydrostatic Pressure in the Contact Plane of Axisymmetric Bodies Under Normal and Tangential Loading

2020 ◽  
Author(s):  
Emanuel Willert ◽  
Fabian Forsbach ◽  
Valentin L. Popov
Keyword(s):  
Hydrostatic Pressure ◽  
Stress Tensor ◽  
Normal Component ◽  
Hertzian Contact ◽  
Von Mises Stress ◽  
Axially Symmetric ◽  
Principal Stresses ◽  
Contact Plane ◽  
Stress Components ◽  
Von Mises

The Hertzian contact theory, as well as most of the other classical theories of normal and tangential contact, provides displacements and the distribution of normal and tangential stress components directly in the contact surface. However, other components of the full stress tensor in the material may essentially influence the material behaviour in contact. Of particular interest are principal stresses and the equivalent von Mises stress, as well as the gradient of the hydrostatic pressure. For many engineering and biomechanical problems, it would be important to find these stress characteristics at least in the contact plane. In the present paper, we show that the complete stress state in the contact plane can be easily found for axially symmetric contacts under very general assumptions. We provide simple explicit equations for all stress components and the normal component of the gradient of hydrostatic pressure in the form of one-dimensional integrals.

scholarly journals Force Budget (Abstract)

1988 ◽  
Vol 11 ◽  
pp. 212-212
Author(s):  
I. M. Whillans ◽  
C. J. van der Veen
Keyword(s):  
Force Balance ◽  
Horizontal Gradient ◽  
Strain Rates ◽  
Normal Stresses ◽  
Lateral Shear ◽  
Vertical Column ◽  
Stress Components ◽  
Normal Resistance ◽  
Image Position ◽  
Deviatoric Stresses

An expression for force balance is derived for the general case of gradients in longitudinal and lateral normal stresses and lateral shear stress. In order to consider horizontal glacial mechanics in Newton’s style of actions and reactions, the full stresses are partitioned into lithostatic and resistive, Rij, components. The lithostatic stress is the weight of ice above, and the horizontal gradient in lithostatic force on a vertical column is the familiar driving stress, which accounts for the horizontal effect of body or action forces. The horizontal resistive-stress components describe the reactions to this horizontal action of gravity. Force balance iswith horizontal coordinates x1, x2 and vertical z. The upper and bottom elevations are h and b, and τdi and τbi are driving stress and basal drag respectively. This describes net reaction due to normal resistance, lateral shear resistance, and basal drag resistance, and finally the action or driving stress. This equation is exact. Resistive stresses are simply linked to deviatoric stresses, and hence to strain-rates, through the flow law.

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