What is Hertzian contact theory?

The Hertzian contact (Hertz 1881, 1882) is referred to the frictionless contact between two bodies. Spherical contact is a special case of the Hertz contact, which is between two spheres, or between a sphere and the surface of a half space.

What is elastic contact?

1. Elastic contact properties. In the simplest case, the elastic contact deformations can be modeled by a linear spring law. However, for spherical particles, a Hertzian law is more appropriate. Young’s modulus and Poisson’s ratio of the solid material can be used directly.

What is the Hertz model?

The Hertz model. The most widely used model for data processing in AFM nanoindentation experiments is the Hertz model. In particular, if the AFM tip has a spherical shape and if the indentation depth is significantly smaller than the tip radius then the loading data are fitted into the equation [7, 13, 14]:

What is Hertz law?

[′hərt·səs ‚lȯ] (mechanics) A law which gives the radius of contact between a sphere of elastic material and a surface in terms of the sphere’s radius, the normal force exerted on the sphere, and Young’s modulus for the material of the sphere.

How do you calculate contact pressure?

Contact pressure = Applied Load/ Area of contact.

What is the contact pressure between two bodies?

Suppose that two elastic bodies are in contact at a single point. If the bodies are pressed with a force, say F, the contact, because of deformation, will not be in a single point but will be over a small area of the surface of each body. This surface is called the pressure surface.

Who is Hertz and his contribution?

How do you calculate contact stress?

Calculate the contact stress distribution between a cylinder having a radius of curvature R1 = 500 mm pressed against another cylinder having R2 = 1000 mm by a force P′ = 1 kN/mm, as shown in Fig. 3.125. The two cylinders are made of the same steel having Young’s modulus = 210 GPa and Poisson’s ratio ν = 0.3.

What are contact stresses?

Contact stress is damage to the tissue of the body caused by contact between soft tissue and a hard object. Contact stress may be internal or external. External contact stress is most often caused by a part of the body coming into contact with a hard surface such as a desk or machinery.

What is contribution of Hertz?

Heinrich Hertz, in full Heinrich Rudolf Hertz, (born February 22, 1857, Hamburg [Germany]—died January 1, 1894, Bonn, Germany), German physicist who showed that Scottish physicist James Clerk Maxwell’s theory of electromagnetism was correct and that light and heat are electromagnetic radiations.

What is contact stress analysis?

2.2 Contact stress analysis Contact stress calculations are based on Hertzian pressure analysis between two cylinders (represented by the teeth in contact under compression load).

How is the stress of the Hertzian contact derived?

1.1 The Hertzian Contact The original theory was derived for two non-conforming surfaces that in an no load situation would result in a point or line contact. When the load was applied there is some elastic deformation that takes place to provide a larger area so that the stresses are not in\\fnite.

What is the point of contact in Hertz theory?

• Contact is a point or line when there are no applied forces or moments. • Area of contact is dependent on the force applied due to elastic deformation. • Non-adhesive, meaning the two surfaces require no force to separate. • Hertz Contact theory maintains both surfaces are frictionless.

What was Hertz’s theory of non adhesive elastic contact?

Hertzian theory of non-adhesive elastic contact In Hertz’s classical theory of contact, he focused primarily on non-adhesive contact where no tension force is allowed to occur within the contact area. The following assumptions are made in determining the solutions of Hertzian contact problems: The strains are small and within the elastic limit.

What is the MATLAB code for Hertzian contact?

The elastic approach (also know as rigid body approach) is given by the following expression: Corresponding Matlab code for Hertz solution can be found here. The online Hertz contact calculator can be found here. Further details of the contact theory can be found in Contact Mechanics by James Barber .