scholarly journals Frictional half-plane contact problems subject to alternating normal and shear loads and tension in the steady state

2019 ◽  
Vol 168 ◽  
pp. 166-171 ◽  
Author(s):  
H. Andresen ◽  
D.A. Hills ◽  
J.R. Barber ◽  
J. Vázquez
Keyword(s):  
Steady State ◽  
Half Plane ◽  
Contact Problems ◽  
Plane Contact ◽  
Shear Loads

Flamant solution of a half-plane with surface flexural resistibility and its applications to nanocontact mechanics

2019 ◽  
Vol 25 (3) ◽  
pp. 664-681 ◽  
Author(s):  
Xiaobao Li ◽  
Lijian Jiang ◽  
Changwen Mi
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Contact Problems ◽  
Plane Boundary ◽  
Material Surface ◽  
Surface Model ◽  
Surface Traction ◽  
Bending Rigidity ◽  
Plane Contact ◽  
Plane Contact Problem

This article presents a semianalytical solution to a half-plane contact problem subjected to an arbitrarily distributed surface traction. The half-plane boundary is treated as a material surface of the Steigmann–Ogden type. Under the assumption of plane strain condition, the problem is formulated by coupling the methods of an Airy stress function and Fourier integral transforms. Stresses and displacements in the form of semi-infinite integrals are derived. A non-classical Flamant solution that is able to simultaneously account for the surface tension, membrane stiffness, and bending rigidity of the half-plane boundary is derived through limit analysis on the half-plane contact problem owing to a uniform surface traction. The fundamental Flamant solution is further integrated for tackling two half-plane contact problems owing to classical contact pressures corresponding to a rigid cylindrical roller and a rigid flat-ended punch. The resultant semi-infinite integrals are integrated by the joint use of the Gauss–Legendre numerical quadrature and the Euler transformation algorithm. Extensive parametric studies are conducted for comparing and contrasting the effects of Gurtin–Murdoch and Steigmann–Ogden surface mechanical models. The major observations and conclusions are two-fold. First, the introduction of either surface mechanical model results in size-dependent elastic fields. Second, the incorporation of the curvature-dependent nature of the half-plane boundary leads to bounded stresses and displacements in the fundamental Flamant solution. This is in contrast to the otherwise singular classical and Gurtin–Murdoch solutions. For all four case studies, the Steigmann–Ogden surface model also results in much smoother displacement and stress variations, indicating the significance of surface bending rigidity in nanoscale contact problems.

Asymptotic Solutions for Contact Problems: The Effect of an Internal Discontinuity in Surface Profile

2006 ◽  
Vol 220 (4) ◽  
pp. 387-391 ◽  
Author(s):  
C M Churchman ◽  
A Sackfield ◽  
D A Hills
Keyword(s):  
Contact Problem ◽  
Contact Pressure ◽  
Half Plane ◽  
Surface Profile ◽  
Contact Problems ◽  
Asymptotic Solutions ◽  
Plane Contact ◽  
Plane Contact Problem ◽  
Full Solution

The contact pressure adjacent to the apex of a tilted punch is studied and used to form a refined, two-term asymptote for the contact pressure at a point of discontinuous gradient interior to a half-plane contact problem. The asymptote is compared with the full solution for an example problem, the wheel with a flat.

scholarly journals Half-plane contacts subject to remote tension

2021 ◽  
pp. 030932472098844
Author(s):  
Nils Cwiekala ◽  
David A Hills
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Asymptotic Form ◽  
Fretting Fatigue ◽  
The State ◽  
Partial Slip ◽  
Practical Relevance ◽  
Plane Contact ◽  
State Of Stress ◽  
Plane Contact Problem

The state of stress present in an elastic half-plane contact problem, where one or both bodies is subject to remote tension has been investigated, both for conditions of full stick and partial slip. The state of stress present near the contact edges is studied for different loading scenarios in an asymptotic form. This is of practical relevance to the study of contacts experiencing fretting fatigue, and enables the environment in which cracks nucleate to be specified.

Thermal Distortion of an Anisotropic Elastic Half-Plane and its Application in Contact Problems Including Frictional Heating

2005 ◽  
Vol 128 (1) ◽  
pp. 32-39 ◽  
Author(s):  
Yuan Lin ◽  
Timothy C. Ovaert
Keyword(s):  
Heat Flux ◽  
Half Plane ◽  
Frictional Heating ◽  
Contact Problems ◽  
Local Heat ◽  
Extended Version ◽  
Parabolic Profile ◽  
Local Heat Flux ◽  
Anisotropic Elastic ◽  
Thermoelastic Contact Problem

The thermal surface distortion of an anisotropic elastic half-plane is studied using the extended version of Stroh’s formalism. In general, the curvature of the surface depends both on the local heat flux into the half-plane and the local temperature variation along the surface. However, if the material is orthotropic, the curvature of the surface depends only on the local heat flux into the half-plane. As a direct application, the two-dimensional thermoelastic contact problem of an indenter sliding against an orthotropic half-plane is considered. Two cases, where the indenter has either a flat or a parabolic profile, are studied in detail. Comparisons with other available results in the literature show that the present method is correct and accurate.

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