Geometrically Frustrated, Mechanical Metamaterial Membranes: Large-Scale Stress Accumulation and Size-Selective...

Area of Science:

• Materials Science
• Mechanical Engineering
• Physics

Background:

• Geometric frustration in elastic plates limits Gaussian curvature to scales dependent on thickness.
• Metamaterials offer novel mechanical properties through engineered structures.
• Understanding curvature accumulation in thin structures is crucial for material design.

Purpose of the Study:

• To investigate the impact of geometric frustration on dilational mechanical metamaterial membranes.
• To compare curvature accommodation in frustrated metamembranes versus elastic plates.
• To analyze the influence of frustration on the assembly thermodynamics of metamembranes.

Main Methods:

• Development of a continuum elastic theory.
• Implementation of a discrete numerical model.
• Analysis of axisymmetric, trumpetlike metamembranes.

Main Results:

• Frustrated metamembranes accumulate hyperbolic curvatures at mesoscopic scales, independent of constituent size.
• A crossover to weaker power-law growth in elastic strain energy with size was observed compared to elastic membranes.
• A severalfold increase in the size range of self-limitation for frustrated metamembranes was demonstrated.

Conclusions:

• Geometric frustration enables unique curvature properties in metamembranes, distinct from elastic plates.
• Metamembranes exhibit enhanced self-assembly capabilities due to size-independent curvature accumulation.
• These findings have implications for designing advanced mechanical metamaterials with tunable assembly properties.