Analysis of a Frictional Contact Problem with Adhesion

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SUMMARY

The discussion focuses on modeling a frictional contact problem with adhesion, specifically under the conditions where the density of body forces (f_0) and the density of surface tractions (f_2) are both set to zero. The participants emphasize the relevance of the Cauchy stress tensor in capturing the complexities of the problem, particularly under no-slip conditions, which necessitate continuity in the stress tensor across interfaces. The conversation suggests that coupling this model with force laws relating stress to strain for the involved materials is essential for a comprehensive analysis.

PREREQUISITES
  • Cauchy stress tensor concepts
  • Understanding of frictional contact mechanics
  • Knowledge of no-slip boundary conditions
  • Fundamentals of stress-strain relationships in materials
NEXT STEPS
  • Research the application of the Cauchy stress tensor in contact mechanics
  • Explore models of frictional contact problems with adhesion
  • Study the implications of no-slip conditions in material interfaces
  • Learn about stress-strain relationships for various materials in contact
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Mathematicians, engineers, and researchers involved in contact mechanics, particularly those focusing on frictional interactions and adhesion in material science.

vw17
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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).
Capture ph.PNG
 

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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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