Direct Evaluation of Pressure Distribution of Frictionless Axisymmetric Indentation Problems

The pressure distribution between a rigid frictionless axisymmetric punch and an elastic half-space can be evaluated if the punch shape can be expressed by a polynomial function. However, there is a lack of investigation on how to calculate the pressure distribution when the punch shape cannot be expressed by a polynomial formula. This paper shows that with the help of a mathematical software, the pressure distribution can be evaluated directly from its corresponding analytical solutions. Using this technique, we evaluate the pressure distributions of a cosine punch and a hyperbolic cosine punch, and compare the results with Hertz’s solution.