= Initial delay in Griffith growth under proportional loading
{title2=$G(s,t)=t^2G(s,1)$}
For linear antiplane elasticity with body forces and Dirichlet data proportional to time, uniqueness gives $u(s,t)=tu(s,1)$ at any fixed crack length $s$. The minimized elastic-plus-load potential and its <energy release rate> scale quadratically. The local <Griffith fracture criterion> laws are $\dot\ell\geq0$, $G(\ell,t)\leq G_c$ and $\dot\ell(G_c-G)=0$, with positive toughness $G_c$.
If $G(s,1)$ is finite and continuous near the initial length, it is bounded there by $M$. Continuity of the crack path keeps it in that neighborhood for a positive interval. Choose the interval short enough that $t^2M<G_c$; complementarity then forces zero growth throughout it. This proves a positive initial waiting time without assuming the crack is stationary in advance.
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