Flexibility of a Contact Area of an Isotropic Elastic Body

1985 ◽  
Vol 52 (1) ◽  
pp. 62-66 ◽  
Author(s):  
C. M. Szalwinski
Keyword(s):  
Elastic Body ◽  
Contact Area ◽  
Tangential Component ◽  
Isotropic Elastic Body ◽  
Elliptical Contact

From Cerruti’s solution to the problem of the plane and Cattaneo’s traction distributions, instantaneous and secant flexibilities are derived for an elliptical contact area which includes a region of slip. The results apply to force histories where the tangential component is constantly directed. Some of the results differ from those reported by Mindlin and Deresiewicz [4]. Ellipticity affects normal and tangential flexibilities differently but is independent of the extent of slip.

Elliptical Contact Area Between Elastic Bodies Bounded by High Order Surfaces

2005 ◽  
Author(s):  
Emanuel N. Diaconescu
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Fourth Order ◽  
Contact Area ◽  
High Order ◽  
Normal Displacement ◽  
Hertz Theory ◽  
Elastic Bodies ◽  
Surface Normal ◽  
Elliptical Contact

Hertz theory fails when contacting surfaces are expressed by a sum of even polynomials of higher powers than two. An alternative analytical solution implies the knowledge of contact area. In the case of elliptical domains, there are some published proposals for the correlation between pressure distribution and surface normal displacement. This paper identifies the class of high order surfaces which lead to elliptical contact domains and solves a contact between fourth order surfaces.

A Numerical Study of the Partial Slip Elliptical Contact under Fretting Conditions

2013 ◽  
Vol 371 ◽  
pp. 576-580 ◽  
Author(s):  
Sergiu Spînu ◽  
Dorin Gradinaru
Keyword(s):  
Contact Area ◽  
State Of The Art ◽  
Numerical Study ◽  
Partial Slip ◽  
Elastic Materials ◽  
Elastic Mismatch ◽  
Numerical Tools ◽  
Elliptical Contact ◽  
Contact Parameters ◽  
Circular Contact

The technologically important elliptical contact undergoing fretting is simulated using previously advanced state-of-the-art numerical tools. The influence of contact ellipse eccentricity on various contact parameters is assessed. An analogy with the circular contact is found when tractions equations are written in dimensionless coordinates in case of similarly elastic materials. However, when an elastic mismatch is introduced, the stick area no longer follows proportionally the established contact area.

scholarly journals A Finite Element-Based Elastic-Plastic Model for the Contact of Rough Surfaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Finite Element ◽  
Contact Force ◽  
Contact Area ◽  
Rough Surfaces ◽  
Constitutive Relations ◽  
Element Model ◽  
Tangential Component ◽  
Asperity Contact ◽  
Elastic Plastic ◽  
Force Components

Three-dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the asperity constitutive relations from a finite element model of the elastic-plastic interaction proposed by Kogut and Etsion (2002), in which asperity scale constitutive relations are derived using piecewise approximate functions. An analytical fusion technique is developed to combine the piecewise asperity level constitutive relations. Shoulder-shoulder asperity contact yields a slanted contact force consisting of two components, one in the normal direction and a half-plane tangential component. Statistical summation of the asperity level contact force components and asperity level contact area results in the total contact force and total contact area formulae between two rough surfaces. Approximate equations are developed in closed form for contact force components and contact area.

Adhesive Contact of Bodies Having an Elliptical Contact Area

2005 ◽  
Author(s):  
K. L. Johnson ◽  
J. A. Greenwood
Keyword(s):  
Closed Form ◽  
Contact Area ◽  
Adhesive Contact ◽  
Contact Radius ◽  
General Shape ◽  
Elliptical Contact ◽  
Jkr Theory ◽  
Two Bodies

The so-called JKR theory of adhesion between elastic spheres in contact (Johnson, Kendall & Roberts 1971, Sperling 1964) has been widely used in micro-tribology. In this paper the theory is extended to solids of general shape and curvature. It is assumed that the area of contact is elliptical which turns out to be approximately true, though the eccentricity is different from that for non-adhesive contact. Closed form expressions are found for the variation with load of contact radius and displacement, as a function of the ratio of principal relative curvatures of the two bodies in contact. The pull-off force is found to decrease with increasing eccentricity from its value of 3πΔγR/2 in the case of contact of spheres of radius R.

Elastic-Plastic Microcontact Model for Elliptical Contact Areas and Its Application to a Treillis Point in Overhead Electrical Conductors

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Frédéric Lévesque ◽  
Sylvain Goudreau ◽  
Louis Cloutier
Keyword(s):  
Contact Force ◽  
Critical Points ◽  
Contact Area ◽  
Transmission Lines ◽  
Electrical Transmission ◽  
Contact Areas ◽  
Elastic Plastic ◽  
Elliptical Contact ◽  
Rigid Plane ◽  
Electrical Conductors

Aeolian vibrations represent a threat to the integrity of electrical transmission lines. The fretting fatigue of conductors is thus a major concern. The modelization of the contact conditions at critical points is an important tool in assessing the life of conductors. Treillis points around the last point of contact between the conductor and the pieces of equipment are such critical points. We observe a fully plastic contact condition at these points. Finite element results for the contact between an ellipsoid and a rigid plane and between two wires at different angles are compared with an elastic-plastic microcontact model for elliptical contact areas. These numerical results are then compared with experimental ones for the contact between two wires of a conductor (ACSR Bersfort), showing a very similar relationship between the contact force and the observed contact area. We have a good correlation between the microcontact model and the finite elements ones in the fully plastic contact regime on both the contact area and the contact force for a given interference between bodies. The use of the elastic-plastic microcontact model for elliptical contacts presented in this paper proves to be a strong tool in getting a better understanding of the mechanical behavior at those critical points.

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