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arXiv · 2406.16790

Geometrically frustrated, mechanical metamaterial membranes: Large-scale stress accumulation and size-selective assembly

Micheal Wang·Sourav Roy·Christian D. Santangelo·Gregory M. Grason
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Abstract

We study the effect of geometric frustration on dilational mechanical metamaterial membranes. While shape frustrated elastic plates can only accommodate non-zero Gaussian curvature up to size scales that ultimately vanish with their elastic thickness, we show that frustrated {\it metamembranes} accumulate hyperbolic curvatures up to mesoscopic length scales that are ultimately independent of the size of their microscopic constituents. A continuum elastic theory and discrete numerical model describe the size-dependent shape and internal stresses of axisymmetric, trumpet-like frustrated metamembranes, revealing a non-trivial crossover to a much weaker power-law growth in elastic strain energy with size than in frustrated elastic membranes. We study a consequence of this for the self-limiting assembly thermodynamics of frustrated trumpets, showing a several-fold increase the size range of self-limitation of metamembranes relative to elastic membranes.

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Micheal Wang, Sourav Roy, Christian D. Santangelo, Gregory M. Grason. 2024-06-24. Geometrically frustrated, mechanical metamaterial membranes: Large-scale stress accumulation and size-selective assembly. https://arxiv.org/abs/2406.16790

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