Ordered patches cap the stability of disordered frameworks
Abstract
Structural disorder can stabilize frameworks against pressure-induced failure, yet the ordered regions it contains limit this gain. We show that, in rigid-jointed frames under hydrostatic pressure, an ensemble containing arbitrarily large patches of a crystal at positive density, whose centres carry a scaled crystal prestress, cannot stay linearly stable once those patches are stressed beyond the crystal's threshold for localizable instabilities. A homogeneous loss of positive definiteness while all Bloch modes, including the acoustic limit, remain stable cannot localize, leaving a window for stabilization. Extending an acoustic criterion to prestress, we show for all point groups that such a window requires a strain that keeps the crystal's symmetry. Unless the patches are shielded from stress, disorder cannot protect a crystal against a failure that breaks its symmetry, and protects a cubic crystal at most against volume collapse. In two-dimensional Truchet frames, planted ordered domains bring the threshold within 1% of the bound, and correlations short of long-range order localize failure on ordered clusters. Across 876 slender-strut nets, 798 fail first by a localizable instability; the other 78 have a median window of 7.6%. Stability gained through disorder is capped by the localizable instabilities of the local order it permits.
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BibTeX
@misc{nam2026ordered,
title = {{Ordered patches cap the stability of disordered frameworks}},
author = {Joohan Nam},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38501},
eprint = {2610.38501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38501},
}
RIS
TY - UNPB
TI - Ordered patches cap the stability of disordered frameworks
AU - Joohan Nam
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38501
UR - https://arxiv.org/abs/2610.38501
AB - Structural disorder can stabilize frameworks against pressure-induced failure, yet the ordered regions it contains limit this gain. We show that, in rigid-jointed frames under hydrostatic pressure, an ensemble containing arbitrarily large patches of a crystal at positive density, whose centres carry a scaled crystal prestress, cannot stay linearly stable once those patches are stressed beyond the crystal's threshold for localizable instabilities. A homogeneous loss of positive definiteness while all Bloch modes, including the acoustic limit, remain stable cannot localize, leaving a window for stabilization. Extending an acoustic criterion to prestress, we show for all point groups that such a window requires a strain that keeps the crystal's symmetry. Unless the patches are shielded from stress, disorder cannot protect a crystal against a failure that breaks its symmetry, and protects a cubic crystal at most against volume collapse. In two-dimensional Truchet frames, planted ordered domains bring the threshold within 1% of the bound, and correlations short of long-range order localize failure on ordered clusters. Across 876 slender-strut nets, 798 fail first by a localizable instability; the other 78 have a median window of 7.6%. Stability gained through disorder is capped by the localizable instabilities of the local order it permits.
ER -