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- TL;DR Summary
- What is the correct boundary condition for limiting friction?
Suppose I have a block of deformable material on a rough surface. I want to have the boundary condition for the stress tensor that takes into account of friction. If the mass of my block is m, and of density \rho and the coefficient of friction is \mu as well as gravity g. The resultant force is given by R=mg=\rho gdV, so the frictional force per unit mass is \mu\rho g$. Linking to the tangential part of the stress tensor, this yields: \hat{\mathbf{n}}\cdot\boldsymbol{\sigma}\cdot\hat{\mathbf{t}}=\mu\rho g<br />
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Does this reasoning seem okay?