Geometric role in designing pneumatically actuated pattern-transforming metamaterials

When a metamaterial, composed of an elastomer with periodic circular holes sealed by elastomeric membranes, is subject to a compressive load, it can undergo a pattern transformation, yielding a large transformation strain. Such pattern transformation can be broadly tuned by changing the geometric parameters of the metamaterial. We numerically, analytically and experimentally survey the design space of the geometric parameters, and investigate their effects on the pattern transformation. Our finite element simulations reveal that the slenderest wall thickness and the pattern of the holes play key roles in determining the critical load for the pattern transformation, the transformation strain, and the transformation type. To quantify the effects of these geometric parameters, we further analytically model the pattern transformation of the metamaterial by simplifying it to a network of rigid rectangles linked by deformable beams. Finally, we experimentally characterize the pattern transformation of the metamaterials with different geometric parameters. The experimental, numerical, and analytical results are in good agreement with each other. Our work provides design guidelines for this metamaterial.