Extended Data Fig. 6: The shape function, β(ℓ), characterizing self-similar nucleation patches is particularly simple during the nucleation phase, until the topological transition to 1D rupture occurs at ℓ*.
From: How frictional ruptures and earthquakes nucleate and evolve
a. The shape function β(ℓ) for a self-similar growth of a penny crack shown in the inset. Note that, in this case, β = π/2 for ℓ < ℓ* = W, where ℓ* is the value of ℓ at which the topological transition takes place. b. Mode I (g1(v)) and mode II (g2(v)) solutions of self-similar Broberg problems23. Here, plane stress conditions are imposed so that the dilatational (cd) and shear (cs) wave speeds are related by \({c}_{d}=\sqrt{2/(1-\rho )}{c}_{s}\), where ρ = 1/3 is the Poisson ratio.
