Dear fellow contact mechanicists,
it is well known that the elastic edge singularity for the contact pressure in the vicinity of a singular contact boundary with a smooth boundary line is analogous to the elastic stress singularity for a crack with a smooth crack frontline, and of the form p(s) ~ s^(-1/2).
Now, what happens at a singular sharp corner of the contact boundary, e.g., under the indentation by a rigid square flat punch? I would assume, the exponent of the pressure singularity depends on the inner angle \theta of the corner, and will be p ~ 1/s (?) for \theta = 0, p ~ s^(-1/2) for \theta = \pi (the known edge singularity), and there is no singularity for \theta = 2\pi.
Are there asymptotic analytic solutions for this kind of singular indentation problems?
For the "crack analogue", the corresponding task has been solved in the work
Xu, L.; Kundu, T.: Stress Singularities at Crack Comers. Journal of Elasticity, 39, 1–16 (1995).
However, I think, the "analogue" only works for the edge singularity; for example, for a right-angled crack corner the singularity should be \sigma(s) ~ s^(-0.9) (approximately), but in a boundary element simulation for the indentation by a square flat punch, I obtain the asymptotic behavior p ~ s^(-0.7) (approximately).
Best regards,
Emanuel
I don’t understand are you talking of indentation by a rigid punch with corner at various angle? There is a lot of literature on that check hills and barber and comninou including their books
Michele Ciavarella : I am not talking about a rigid corner in a plane that includes the normal direction of the half-space (for which, indeed, there are a lot of works about indentation by rigid or elastic wedges and so on), but a corner in the surface plane of the half-space.
For example, consider a rigid flat punch with a square planform indenting the elastic half-space; the contact domain is a square. But what is the nature of the pressure singularity at the corners of this square?
Emanuel Willert I see the point and I agree that, after thousands of papers on the 2D problem, you may like to study the 3D one, despite there will be no good theory if the singularity is not the usual LEFM one!
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