= Solution
For dry <friction>, the tangential contact force opposes sliding and has limiting magnitude $\mu_fN_c$, where $N_c\geq0$ is the compressive <normal force> and $\mu_f=\tan\phi$. Sticking requires $|F|\leq\mu_fN_c$; impending sliding reaches equality.
The cohesionless <Mohr-Coulomb failure criterion> applies the same local condition on internal planes: yield begins when some plane has $|\tau_{\rm shear}|=N_c\tan\phi$. In the tension-positive Cauchy convention used here, $N_c=-N$ for a compressive plane, so
$$
\boxed{|F|\leq-N\tan\phi\quad(N\leq0),\qquad |F|=-N\tan\phi\text{ at yield}.}
$$
A cohesive material would add a positive intercept, but the later formulas in this paper are explicitly the zero-<cohesion> case. The model does not supply a tensile strength law.
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