Fig. 2.

Comparison of measured $\mathrm{\Delta }{\epsilon }_{ij}$ with the self-similar solution. (A, Top) We consider a self-similar bilaterally expanding rupture initiating at zero initial length and propagating at a constant rate under uniform remote shear stress, ${\sigma }_{xy}^0$, and residual frictional shear stress, ${\sigma }_{xy}^r$. The propagation length is given by $l=C_{f}t$. (Bottom) Close-up of the self-similar solution, ${\overline{\epsilon }}_{xy}=\left({\epsilon }_{xy}-{\epsilon }_{xy}^0\right)/\left({\epsilon }_{xy}^0-{\epsilon }_{xy}^r\right)$, at $y=0$ shows a pronounced shear stress peak propagating ahead of the singular rupture tip. (B) Comparison of $\mathrm{\Delta }{\epsilon }_{ij}$ measured at $y=3.5$ mm, $x=x_2$ (blue) during a rupture event of Fig. 1B with both the singular LEFM predictions and the self-similar solution. Time is relative to the rupture tip arrival, $t_{\text{tip}}$. The singular term of the LEFM solution is plotted in black ($C_f=0.96C_R$, $\mathrm{\Gamma }=0.6$ J/m²). Although it captures $\mathrm{\Delta }{\epsilon }_{xx}$ and $\mathrm{\Delta }{\epsilon }_{yy}$ well, the singular term fails to describe $\mathrm{\Delta }{\epsilon }_{xy}$ for $t-t_{\text{tip}}<0$. Shown in red, the corresponding self-similar solution [$C_f=0.96C_R$, ${\epsilon }_{xy}^0-{\epsilon }_{xy}^r\approx 0.06\cdot {10}^{-3},l=100$ mm result in $\mathrm{\Gamma }\left(l=100\hspace{0.17em}\text{mm}\right)$ J/m²] entirely captures all measured strain components including the initial shear strain, ${\epsilon }_{xy}^0$, and the shear stress peak far before the rupture tip arrival. The difference in $\mathrm{\Delta }{\epsilon }_{xy}$ in the two solutions highlights the importance of nonsingular contributions.