Closed-Form Solutions for a Piecewise Quadratic Half-Plane Contact Problem

2010 ◽  
Vol 45 (7) ◽  
pp. 505-511 ◽  
Author(s):  
M Davies ◽  
D A Hills
Keyword(s):  
Contact Problem ◽  
Closed Form ◽  
Half Plane ◽  
Closed Form Solutions ◽  
Plane Contact ◽  
Plane Contact Problem

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.

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 RELATIVE PORE VOLUME UNDER INDENTATION OF POROUS MATERIALS

2021 ◽  
Vol 83 (4) ◽  
pp. 462-470
Author(s):  
V.B. Zelentsov ◽  
A.D. Zagrebneva ◽  
P.A. Lapina ◽  
S.M. Aizikovich ◽  
Wang Yun-Che
Keyword(s):  
Porous Material ◽  
Contact Problem ◽  
Porous Layer ◽  
Pore Volume ◽  
Lower Boundary ◽  
Contact Stresses ◽  
Plane Contact ◽  
Plane Contact Problem ◽  
Static Contact ◽  
Rigidity Modulus

Investigation of the function of the relative volume of pores under the load action is carried out on the base of the solution of the static contact problem of the indentation of a layer made of a material with voids or unfilled pores. A rigid strip indenter with a flat base is pressed into a porous layer that is adhered to a non-deformable base along the lower boundary. The formulated 3D problem of the indentation of a porous layer is reduced to solving the plane contact problem of the indentation of a porous strip. The plane contact problem is reduced to solving an integral equation for unknown contact stresses, the solution of which is constructed by the method of successive approximations in the form of an asymptotic expansion in the dimensionless parameter of the problem. The obtained contact stresses and the force acting on the indenter made it possible to study the influence of the nonclassical moduli of the layer porous material (the connectivity modulus and pore rigidity modulus) on the main contact characteristics and on the distribution of the function of the relative pore volume. The connectivity modulus increase leads to an increase in the compliance of the layer porous material, the pore rigidity modulus increase leads to an increase in the rigidity of the layer porous material. The maximum value of the distribution function of the relative pore volume in the porous material of the layer is achieved under the indenter base centre, regardless of the change in the porous material non-classical moduli.

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