Strain gradient solutions of half-space and half-plane contact problems

2012 ◽  
Vol 64 (4) ◽  
pp. 1363-1386 ◽  
Author(s):  
Xin-Lin Gao ◽  
Song-Sheng Zhou
Keyword(s):  
Half Space ◽  
Half Plane ◽  
Strain Gradient ◽  
Contact Problems ◽  
Plane Contact

Plane contact problems with frictional heating for a vertically layered half-space

2011 ◽  
Vol 54 (9-10) ◽  
pp. 1805-1813 ◽  
Author(s):  
Roman Kulchytsky-Zhyhailo ◽  
Stanisław J. Matysiak ◽  
Dariusz M. Perkowski
Keyword(s):  
Half Space ◽  
Frictional Heating ◽  
Contact Problems ◽  
Plane Contact ◽  
Layered Half Space

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.

Solution of Contact Problems for Half-Space by Boundary Element Methods Based on Singular Solutions of Flamant and Boussinesq’s Problems

2020 ◽  
Vol 12 (02) ◽  
pp. 2050015 ◽  
Author(s):  
Natela Zirakashvili
Keyword(s):  
Boundary Element ◽  
Half Space ◽  
Half Plane ◽  
Strain State ◽  
Plane Deformation ◽  
Contact Problems ◽  
Boundary Element Methods ◽  
Singular Solutions ◽  
Normal Contact ◽  
Distributed Load

The paper considers normal contact problems formulated as follows: an indenter with negligible weight presses the surface half-space with a certain force, i.e., normal stress acts on the contact surface and tangential stress is zero. In particular, we consider two types of distributed load that correspond to the following cases: when half-space is subjected to frictionless flat rigid indenter, and when half-space is subject to frictionless cylindrical rigid indenter. The paper considers plane deformation. Problems are solved by boundary element methods (BEM), which are based on singular solutions of Flamant (BEMF) and Boussinesq (BEMB) problems. The stress–strain state of the half-plane, particularly the constructed contours (isolines) of stresses in half-plane, was studied. The results obtained by BEMF and BEMB are discussed and compared.

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