Conical Indenter

The conical intender is characterized by its inclination angle . After applying a rigid body motion (resulting in normal load ) on an elastic substrate, the intender deforms the substrate and creates elastic deformation and effective contact radius as shown in the figure.

Displacement depth , inclination angle and contact radius are all related to other geometrically. The contact radius can be calculated using the relation:

(1)

The profile of the stress and the displacement are determined by the formulas below ([1]):

(2)

where is the average pressure which is given by the equation:

(3)

while is the elasticity of the substrate or the conical intender as well.
These formulas are restricted to relatively small values.

Definitions:

Poisson’s ratio of the substrate dimensionless,
Young’s modulus of elasticity of the substrate, [Pa],
Equivalent elastic constant  , [Pa],