Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

An extended finite element method (X-FEM) for three-dimensional crack modelling is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three-dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd.

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Extended finite element method for three-dimensional crack modelling

Several aspects of the mechanics of cracks originating at sites of fretting are considered. It is argued that the problem may be distilled into three separate parts: the contact problem itself in full or partial slip, the initiation of a crack from a surface suffering severe distress, and the propagation of a crack under combined contact and bulk loading. The first of these may be solved by either a classical or numerical means, whilst the last merely requires the careful use of fracture mechanics. However, it is the second element which remains elusive to quantify, and the influence of the intrinsic length scales in the problem, including contact length, surface roughness and amplitude of relative tangential displacement on initiation conditions, is discussed and explored.

Mechanics of Fretting Fatigue

THE appearance of a treatise in English upon the mathematical theory of elasticity is an event the potential importance of which may be judged by the that the author, in his frequent suggestions for collateral reading, refers to only three such, those of Southwell, Timoshenko, and Love. In spirit and content Sokolnikoff}s book differs greatly from each and all of these. It may be described by a possible sub-title: “A pure mathematician surveys topics related to certain problems in the mathematical theory of elasticity”. It is symptomatic of the change in outlook of American mathematics over the past few decades. Mathematical Theory Of Elasticity Prof. I. S. Sokolnikoff with the collaboration of Asst. Prof. R. D. Speche. Pp. xi + 373. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 22s. 6d.

Mathematical Theory Of Elasticity

A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques

http://courses.washington.edu/mengr541/ramulu/541/projects/project3.pdf

Recent developments in the understanding of fretting fatigue

The contact problem and stress state for indentation by a flat punch with rounded edges is studied. For the contact problem itself analytical solutions are obtained for both surface pressure and interior stress fields. Cases of normal indentation and frictional contact, the latter in both sliding or partial slip conditions, are all treated. The transition from the Hertzian configuration to the contact between a nominally flat pad and contacting flat surface is discussed, and it is found that the strength of the contact decays surprisingly slowly. Regarding the von Mises yield parameter, there is a range of configurations for which the strength is actually higher than the Hertzian one, and the strength decays only when the corner radii are very small. The present solution is therefore a realistic alternative to the classical rigid-flat punch idealization, and has particular application to fretting fatigue tests.

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The influence of rounded edges on indentation by a flat punch

Prediction of fretting crack propagation based on a short crack methodology

Results available in the literature for the problem of two contacting bodies, suffering Hertzian contact and with an assumed proportional shear, are reviewed. The general case of the proble...

Some useful results in the tangentially loaded hertzian contact problem

The values of stresses resulting from point or line Hertzian contact (including frictional traction) are deduced as a special case of the general elliptical geometry problem, and are compared with known solutions.

D.A. Hills

Papers

Recent developments in the understanding of fretting fatigue

The influence of rounded edges on indentation by a flat punch

Prediction of fretting crack propagation based on a short crack methodology

Some useful results in the tangentially loaded hertzian contact problem

A note on the hertz contact problem: A correlation of standard formulae: