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Determining the contact area in elastic-indentation problems

# Determining the contact area in elastic-indentation problems,10.1243/03093247V094230,Journal of Strain Analysis for Engineering Design,J. R. BARBER

Determining the contact area in elastic-indentation problems
A general relationship is established, determining the contact area in the indentation of an elastic half-space. Contact pressure is shown to increase. monotonically with load throughout the contact area.
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## Citation Context (4)

• ...For all other cases, the contact area is a non-decreasing function of w (Barber 1974), and consequently the incremental sti¬ ness d F=dw is also a non-decreasing function of w. The expression (4.2) can be extended to cover the case of non-contact by de› ning the function F(w) such that F = 0 for w < 0...
• ...Now, in a frictionless indentation problem for the half-space, the maximum normal surface displacement must occur in an area of positive contact pressure (Barber 1974), and in the auxiliary problem the only loaded area is A, throughout which u2 = 1. It follows that all points in A are points of maximum u2 and hence that p2(x;y) > 0 for all points in A. We also have ¯ U(x;y) > 0 ex hypothesi , and hence the integrand on the ...

### J. R. Barber. Bounds on the electrical resistance between contacting elastic rough b...

• ...He uses a theorem proved in an earlier paper [15] which states that the value of b which satisfies the required condition that the contact pressure is zero at the inner boundary may be determined by making OP/Ob = 0, where P is the total pressure on the annulus...

### G. M. L. Gladwell, et al. On the approximate solution of elastic contact problems for a circular...

• ...In order to find this radius, we make use of a variational formulation of the contact condition discussed in a previous paper [6]...

### J. R. Barber. Indentation of the semi-infinite elastic solid by a concave rigid punc...

• ...The case of contact by a flat annular punch is especially simple, since the contact radii are known ap riori .O therwise, the determination of contact radii in these non-adhesive cases follow from a result by Barber that essentially states that the contact area maximizes the value of the contact force [4]...

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