Analysis of a Frictional Contact Problem with Adhesion

In summary, the conversation discusses a mathematician's work with a model representing a contact problem and the hypothesis of f_0=0 and f_2=0, where f_0 is the density of body forces and f_2 is the density of surface tractions. It is suggested that the Cauchy stress tensor could capture the density of body forces, and the continuity requirement of the stress tensor inside and outside the body is mentioned. The conversation also touches on the need for force laws for the various material objects involved.
  • #1
vw17
1
0
Hi,
I'd to work with a model which represents a contact problem. I want to suppose that f_0=0 and f_2=0 where f_0 is a density of body forces and f_2 is a density of surface tractions .
I am mathematician so I don't know if the hypothesis that I'd to suppose will make the problem have a sense in physics or no?
the problem is attached below (pdf).
Capture ph.PNG
 

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  • ANALYSIS OF A FRICTIONAL CONTACT PROBLEM - Copie.pdf
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  • #2
"Density of body forces" sounds like something which would be captured by the Cauchy stress tensor. If it were just a normal force between surfaces, you could call it "pressure". But with friction, I think you want the whole tensor.

It's a bit above my level of education, but I think that you will find that given a no-slip condition that there is a continuity requirement on the stress tensor -- it has to be the same inside the body as outside.

I'd expect you to next couple this with force laws (stress versus strain) for the various material objects involved.
 

1. What is a frictional contact problem with adhesion?

A frictional contact problem with adhesion is a type of mechanical engineering problem that involves the interaction between two surfaces in contact, where adhesion forces between the surfaces play a significant role in the frictional behavior.

2. What factors affect the analysis of a frictional contact problem with adhesion?

The analysis of a frictional contact problem with adhesion is affected by factors such as the material properties of the surfaces, the magnitude of the applied load, the surface roughness, and the presence of any lubricants or contaminants.

3. How is the adhesion force quantified in a frictional contact problem?

The adhesion force in a frictional contact problem is typically quantified using the JKR theory, which states that the adhesion force is proportional to the contact area and the surface energy of the materials.

4. What are some common methods used for solving frictional contact problems with adhesion?

Some common methods used for solving frictional contact problems with adhesion include finite element analysis, boundary element method, and analytical solutions based on simplified assumptions.

5. What are the applications of studying frictional contact problems with adhesion?

The study of frictional contact problems with adhesion has applications in various fields such as mechanical engineering, materials science, and tribology. It can help in designing better surface coatings, improving the performance of mechanical systems, and understanding the behavior of biological systems.

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