This calculator allows calculating pressure 
, displacement (elastic deformation) 
, average pressure 
and resultant force 
for the case of indentation of elastic half-space by a rigid truncated paraboloid. The substrate is elastic, the geometric parameters, 
– radius of curvature, 
– radius of the blunt end, indentation depth 
and material parameters 
are the inputs (see the figure and definitions below).
A truncated paraboloid is characterized by the blunt radius that covers the base, the contact radius 
and the curvature . The intender is described by the profile:
(1) 
The contact radius 
can be deduced numerically using the relation that connects the geometrical parameters to each other:
(2) 
Other parameters: Load force , displacement 
and the stress profile 
are given by the following formulas:
(3) 
(4) 
(5) ![\begin{align*} \omega(r;a) &= \frac{2a}{\pi R}\sqrt{a^2-b^2}\arcsin\left(\frac{a}{r}\right) \nonumber\\ &-\frac{1}{\pi R}\left[(r^2-b^2)\arcsin\left(\frac{\sqrt{a^2-b^2}}{\sqrt{r^2-b^2}}\right) - \sqrt{a^2-b^2}\sqrt{r^2-a^2}\right], r>a. \end{align*}](https://quicklatex.com/cache3/37/ql_74844671816fe7d8d0302d5e96f97737_l3.png "Rendered by QuickLaTeX.com")
Equations were taken from [1].
Definitions:
Poisson’s ratio 
dimensionless,
Young’s modulus of elasticity 
, [Pa],
Equivalent elastic constant 
, [Pa],
Normal load 
, [N]
