Analysis of a Frictional Contact Problem with Adhesion

[vw17]

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).

 

[jbriggs444]

"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.