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:
The profile of the stress and the displacement are determined by the formulas below ():
where is the average pressure which is given by the equation:
while is the elasticity of the substrate or the conical intender as well.
These formulas are restricted to relatively small values.
Poisson’s ratio of the substrate dimensionless,
Young’s modulus of elasticity of the substrate, [Pa],
Equivalent elastic constant , [Pa],
Normal load , [N]
 Valentin L. Popov, Hanbook of Contact Mechnics, Exact Solutions of Axisymmetric Contact Problems, pg. 13
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