This calculator considers the indentation of an elastic half-plane by a rigid body with sinusoidal profile. This is a two-dimensional case. Equations are given below the calculator.

It is assumed here that the sinusoidal profile is given by the following equation:

(1)

where is the amplitude of the profile, is the period of the function.

In this case, the contact half-length is given as follows:

(2)

where is applied pressure (load divided by the period), is pressure at which the full contact would occur.

Pressure is given as follows:

(3)

where is the reduced elastic modulus, and are the Young’s moduli and Poisson’s ratios of the bodies.

This solution is known as Westergaard’s solution [1].

[1]. Contact Mechanics, J.R. Barber, 2018.