Geometry and Mechanics of Ribbon Gridshells
Abstract
Mechanical metamaterials exhibit anomalous properties induced from non-trivial mesoscopic constituents. Inspired from architectural and industrial structures, we introduce arrangements of long, narrow ribbons intersecting at prescribed angles as a model thin-sheet metamaterial. These ribbon gridshells are shown to display highly non-linear behavior driven by the geometric constraints, nonetheless unlike most complex mechanical systems, we are able to explicitly write out the coarse-grained governing equations and to classify their solutions in terms of the intersection patterns of the ribbons. It is shown that the structure can assume arbitrary, tunable Gaussian curvature distributions, allowing us to formulate an inverse design problem, solvable under a suitably defined local condition. An analysis of the soft modes, confirmed by experiment and numerics, reveals rich mechanics which may exhibit both a rigid and an anomalously soft behaviors.
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BibTeX
@misc{castro2026geometry,
title = {{Geometry and Mechanics of Ribbon Gridshells}},
author = {Daniel Castro and Joo-Won Hong and Étienne Reyssat and José Bico and Benoît Roman and Hillel Aharoni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.38365},
eprint = {2609.38365},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38365},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometry and Mechanics of Ribbon Gridshells
AU - Daniel Castro
AU - Joo-Won Hong
AU - Étienne Reyssat
AU - José Bico
AU - Benoît Roman
AU - Hillel Aharoni
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.38365
UR - https://arxiv.org/abs/2609.38365
AB - Mechanical metamaterials exhibit anomalous properties induced from non-trivial mesoscopic constituents. Inspired from architectural and industrial structures, we introduce arrangements of long, narrow ribbons intersecting at prescribed angles as a model thin-sheet metamaterial. These ribbon gridshells are shown to display highly non-linear behavior driven by the geometric constraints, nonetheless unlike most complex mechanical systems, we are able to explicitly write out the coarse-grained governing equations and to classify their solutions in terms of the intersection patterns of the ribbons. It is shown that the structure can assume arbitrary, tunable Gaussian curvature distributions, allowing us to formulate an inverse design problem, solvable under a suitably defined local condition. An analysis of the soft modes, confirmed by experiment and numerics, reveals rich mechanics which may exhibit both a rigid and an anomalously soft behaviors.
ER -