Geometrically Frustrated, Mechanical Metamaterial Membranes: Large-Scale Stress Accumulation and Size-Selective Assembly
Year: 2025
Type: article
Abstract: We study the effect of geometric frustration on dilational mechanical metamaterial membranes. While shape frustrated elastic plates can only accommodate nonzero Gaussian curvature up to size scales that ultimately vanish with their elastic thickness, we show that frustrated 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, trumpetlike frustrated metamembranes, revealing a nontrivial 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 severalfold increase in the size range of self-limitation of metamembranes relative to elastic membranes.
Source: Physical Review Letters
Authors: Michael Wang, Sourav Roy, Christian Santangelo, Gregory Grason
Institution: Syracuse University
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407770560