Design of Isotropic Morphing Multi-stable Corrugated Shell Structures on Elastic Walls

Multi-stability is used to achieve complex shape reconfigurations and realize structures that can be quickly deployed. As such, multi-stable behavior can be exploited in a wide range of mechanical and aerospace engineering applications where shape change without the need for conventional mechanisms is crucial. In this work, first, we present a new design of multi-stable corrugated shell structures on elastic walls. Then, we show how geometrical and material parameters for isotropic domes with zig-zag corrugations can result in multi-stable structures. To achieve this goal, an extensive virtual testing program was carried out in Abaqus to investigate the effects of thickness and aspect ratio of the corrugations. For each structure under consideration, its multi-stable behavior is verified using a geometrically nonlinear static analysis using the Newton-Raphson algorithm. In particular, each analysis incorporates two steps to capture the load-displacement curve. The first step introduces the load through a solid ball head indenter which can only translate vertically. Whereas the second step brings the indenter back to its original position and the dome is allowed to recover freely. To have a more realistic description of the mechanics beyond this problem, hard contact between the dome and indenter is assumed. Furthermore, both of these surfaces are allowed to separate in the second step. Finally, for each structure showing multi-stability, a high fidelity geometrically nonlinear elastoplastic analysis is conducted, and the influence of plastic effects on the multi-stable behavior is discussed.