Pressure distribution on a Contact Area between a rigid cylinder 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 contact and deform slightly under the imposed loads. This amount of deformation is dependent on the modulus of elasticity of the material in contact. If a rigid cylinder is pressed into an elastic half-space, it creates a pressure distribution. The contact area is a circle (the base of the cylinder)

Related formulas

Variables

prPressure on the Contact Area (Pa)
p0Maximum contact Pressure (Pa)
rDistance from the center of the circle of the contact area (m)
aRadius of the cylinder (m)