Pre-failure response spectra predict finite-amplitude fragility (opens in new tab)

Failure theories often identify a single leading route to failure: the most unstable mode, weakest link, minimum-action escape path, or optimal perturbation. Yet finite-amplitude susceptibility depends not only on the nearest route but on how much of perturbation space lies near dangerous directions. We cast this distinction as a fragility problem: for each perturbation direction, the failure distance is the smallest amplitude that crosses a pre...