Depth of the contact region between a rigid conical indenter and an elastic half-space

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 angle between thecontact and deform slightly under the imposed loads. This amount of deformation is dependent on the modulus of elasticity of the material in contact. It gives the contact stress as a function of the normal contact force, the radii of curvature of both bodies and the modulus of elasticity of both bodies.
In the case of indentation of an elastic half-space using a rigid conical indenter, the depth of the contact region is related to the contact radius and the angle between the plane and the side surface of the cone.

Related formulas

Variables

ϵDepth of the contact region (m)
aRadius of the contact area (circle) (m)
θAngle between the plane and the side surface of the cone (radians)