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)

Equations were taken from [1].

Definitions:

Poisson’s ratio dimensionless,
Young’s modulus of elasticity , [Pa],
Equivalent elastic constant  , [Pa],
Normal load , [N]