Total force on a contact area between a rigid conical indenter and an elastic half-space related to the contact radius

Description

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized stresses that develop as two curved surfaces come in contact and deform slightly under the imposed loads. This amount of deformation is dependent on the modulus of elasticity of the material in contact. In the case of indentation of an elastic half-space using a rigid conical indenter, the total force applied on the contact area is related to the contact radius and the angle between the plane and the side surface of the cone.

Related formulas

Variables

FTotal force on the contact area (N)
πpi
EModulus of elasticity ( Young's modulus) (Pa)
νPoisson's ratio (dimensionless)
aContact radius (m)
θAngle between the plane and the side surface of the cone (radians)