Variational Approach in Elastic-Indentation Problems

2005 ◽  
Author(s):  
Roman V. Riznychuk
Keyword(s):  
Variational Method ◽  
Half Space ◽  
Contact Stress ◽  
Variational Approach ◽  
Stress Singularity ◽  
Elastic Half Space ◽  
Contact Spot ◽  
Rigid Punch ◽  
Elliptical Contact ◽  
Indentation Problem

The indentation problem of rigid punch with curvilinear base on elastic half-space is solved by variational method. The method is based on Betti theorem and on condition of absence of stress singularity at the edge of contact spot. Variation condition of absence of stress singularity at the edge of contact spot gives the equations connecting the displacement and the size and the shape of the contact spot and gives the expression for contact stress under curvilinear base of punch. The case of elliptical contact spot is considered.

Elliptic Elastic Contact Between High Order Symmetrical Surfaces

2006 ◽  
Vol 128 (4) ◽  
pp. 908-914 ◽  
Author(s):  
Emanuel N. Diaconescu
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Elastic Contact ◽  
Square Root ◽  
Rigid Punch ◽  
Elliptical Contact ◽  
Space Boundary ◽  
Contact Parameters ◽  
Polynomial Surface

This paper proves that a generalized Hertz pressure (the product of Hertz square root and an even polynomial of degree 2n with respect to coordinates) applied over elastic half-space boundary generates a polynomial normal displacement of degree 2n+2. Polynomial surface coefficients are combinations of elliptical integrals. The equation of rigid punch surface generating this pressure is derived, as well as the conditions in which an elliptical contact occurs. For second order surfaces, n=0, these results yield all Hertz formulas, whereas new formulas are derived for contact parameters between fourth, sixth, and eight order surfaces.

Description of the Nanoindentation Unloading Behavior of Brittle Ceramics with a Modified Surface

2007 ◽  
Vol 336-338 ◽  
pp. 2422-2425
Author(s):  
Zong Huai Li ◽  
Jiang Hong Gong ◽  
Zhi Jian Peng ◽  
He Zhuo Miao
Keyword(s):  
Half Space ◽  
Contact Stress ◽  
Physical Meaning ◽  
Elastic Half Space ◽  
Quadratic Polynomial ◽  
Modified Surfaces ◽  
Modified Surface ◽  
Force Displacement

The nanoindentation unloading behavior of some brittle ceramics with modified surfaces was analyzed. It was found that the unloading data may be described well with a quadratic polynomial. The physical meaning of the quadratic polynomial in describing the nanoindentation unloading behavior was then discussed by considering the effect of residual contact stress on the force-displacement relationship. It was suggested that the quadratic polynomial may be considered as a modified form of the basic forcedisplacement relationship for the contact of an isotropic elastic half-space by a rigid conical punch.

Penetration of a Half Space by a Rectangular Cylinder

1979 ◽  
Vol 46 (3) ◽  
pp. 587-591 ◽  
Author(s):  
A. Cemal Eringen ◽  
F. Balta
Keyword(s):  
Half Space ◽  
Stress Singularity ◽  
Elastic Solid ◽  
Interatomic Interaction ◽  
Elastic Half Space ◽  
Rigid Block ◽  
Field Equations ◽  
Displacement Fields ◽  
Rectangular Cylinder ◽  
Stress And Displacement Fields

The stress and displacement fields are determined in an elastic half space loaded by a rectangular frictionless, rigid block normally at its surface. The semi-infinite solid is considered to be an elastic solid with nonlocal interatomic interaction. The field equations of the nonlocal elasticity and boundary conditions are employed to treat this contact problem. Interestingly the classical stress singularity at the edges of the block are not present in the nonlocal solutions. Consequently the critical applied load for the initiation of penetration of the rigid cylinder into the semi-infinite solid can be determined without recourse to any criterion foreign to the theory. The stress field obtained is valid even for penetrators of submicroscopic width.

The solution of the contact between a tilted circular rigid punch and an elastic half-space

Wear ◽  
1995 ◽  
Vol 184 (1) ◽  
pp. 93-95 ◽  
Author(s):  
R.L. Munisamy ◽  
D.A. Hills ◽  
D. Nowell
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Rigid Punch

Contact Area Variation in Elastic Indentation Problems

2009 ◽  
Author(s):  
Roman Riznychuk
Keyword(s):  
Contact Problem ◽  
Pressure Distribution ◽  
Half Space ◽  
Analytical Solutions ◽  
Contact Area ◽  
Elastic Half Space ◽  
Exact Expression ◽  
Rigid Punch ◽  
Contact Pressure Distribution ◽  
Area Variation

Contact problem of the frictionless indentation of elastic half-space by smooth rigid punch of curved profile is investigated. An exact expression of the contact pressure distribution for a curved profile punch in terms of integral involving the pressure distribution for sequence of flat punches is derived. The method is illustrated and validated by comparison with some well-known analytical solutions.

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