The Role of Geometry in the Design of the Pattern-transforming Metamaterials*

We numerically, analytically and experimentally study how geometry alters the behaviors of the pattern-transforming metamaterials. These metamaterials contain periodic circular holes sealed by elastomeric membranes, which can buckle under critical pressure differentials and undergo a pattern transformation, yielding a large transformation strain. The results of finite element simulations reveal the key roles of the slenderest wall thickness and size of holes in determining the critical pressure differentials, transformation strains and transformation type. According to the fact uncovered in the simulations that the deformations mainly occur in the slender regions, we introduce a 1D analytical model that features a network of rigid rectangles linked by deformable slender beams, which can qualitatively capture the results observed in the simulations. Finally, we experimentally verified the crucial role of geometry and found an excellent agreement among numerical, analytical and experimental results. Our study provides a clear guideline for the design of the pattern-transforming metamaterials.