Analysis of a Frictional Contact Problem with Adhesion

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The discussion focuses on modeling a frictional contact problem with adhesion, specifically under the conditions where body forces and surface tractions are set to zero. The relevance of the Cauchy stress tensor is highlighted, suggesting that normal forces should be treated as pressure, while friction requires a comprehensive tensor approach. A continuity requirement on the stress tensor is emphasized, indicating that it must remain consistent across the interface of contacting bodies. Additionally, the importance of coupling the model with force laws relating stress to strain for the materials involved is noted. The conversation underscores the need for a solid understanding of both mathematical and physical principles in addressing such contact problems.
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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).
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"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.
 

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