Depth of indentation of a Contact Area between two spheres

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. The area of contact between two spheres is a circle. The radius of the circle is related to the applied load.
The depth of indentation is related to the radius of the contact area and the effective radius.

Related formulas

Variables

dThe depth of indentation of the Contact Area (m)
aRadius of the circle of the contact area (m)
RThe effective radius (m)