scholarly journals On a Contact Problem of an Elastic Half-Plane with a Circular Hole : 2nd Report, The Case of Frictionless Contact

1964 ◽  
Vol 30 (218) ◽  
pp. 1212-1219 ◽  
Author(s):  
Osamu TAMATE
Keyword(s):  
Contact Problem ◽  
Circular Hole ◽  
Half Plane ◽  
Frictionless Contact

Two-Dimensional Frictionless Contact of a Coated Half-Plane Based on Couple Stress Theory

2018 ◽  
Vol 10 (05) ◽  
pp. 1850049 ◽  
Author(s):  
Hongxiaia Song ◽  
Liaoliang Ke ◽  
Yuesheng Wang ◽  
Jie Yang ◽  
Han Jiang
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Strong Dependence ◽  
Stress Theory ◽  
Frictionless Contact ◽  
Size Dependent ◽  
Contact Width ◽  
Material Length

Based on the couple stress theory, the size-dependent frictionless contact problem between a rigid punch and a homogeneous coated half-plane is investigated in this paper. This theory describes the size effect that emerges from the material microstructures by introducing the characteristic material length. With the aid of the Fourier transform method, the size-dependent contact problem of the rigid flat, cylindrical, parabolic and wedge punches is reduced to a Cauchy singular integral equation of the first kind. Subsequently, it is transformed into algebraic ones and solved numerically by using Gauss–Chebyshev integration formulas. Numerical results for the normal and in-plane contact stresses, contact width and indentation depth are given. The effect of the length scale parameters on the contact stress and indentation is predicted by the couple stress elasticity, which shows a strong dependence on the characteristic material length.

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.

Frictionless Contact on Elastic Half Plane with Influence of Surface and Couple Stresses

2020 ◽  
Vol 897 ◽  
pp. 73-77
Author(s):  
Toan Minh Le ◽  
Tinh Quoc Bui ◽  
Jintara Lawongkerd ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Contact Pressure ◽  
Half Plane ◽  
Numerical Study ◽  
Surface Elasticity ◽  
Fundamental Solutions ◽  
Internal Length ◽  
Frictionless Contact ◽  
Couple Stresses ◽  
Linear Elastic ◽  
Contact Width

In this paper, a frictionless contact of a rigid flat-ended indentor on a linear elastic half plane is investigated by taking the influence of surface and couple stresses into account. The surface elasticity and couple stress theories are utilized to form a mathematical model. The Green’s function method together with the equilibrium condition of the indentor is employed to formulate the key equations governing the contact pressure. A collocation technique and a set of available fundamental solutions of a half plane under the surface loading are adopted to determine the unknown contact pressure. Results from a numerical study reveal that the presence of both surface and couple stresses significantly alters the distribution of the contact pressure from that predicted by the classical linear elasticity, and the size-dependent characteristics of predicted solutions are obviously observed when the contact width is comparable to the internal length scales of the surface and bulk materials.

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