Controlled snapping sequence and energy absorption in multistable mechanical metamaterial cylinders

Abstract

Mechancial metamaterials comprising bistable unit cells utilize a sinusoidal beam to enable significant deformation between stable states, which is associated with energy absorption. A stack of similar bistable unit cells, i.e., multistable metamaterials, will snap to a second stable state in a seemingly random sequence that is influenced by minute variations in manufacturing. However, it is desirable to tailor the energy absorbed and the snapping sequence to obtain predictable geometric reconfiguration in multistable cylindrical metamaterials. Additive Manufacturing (AM) processes, such as Fused Deposition Modeling (FDM), are able to produce these structures with flexible filaments, such as Thermoplastic Polyurethane (TPU), to enable flexible, multistable cylindrical structures. In this study, we investigated experimentally and computationally the mechanical behavior and controlled snapping sequence of bistable lattices incorporated into cylindrical shells. Individual layers are printed using FDM and assembled into a cylinder. Experimental and computational results for uniaxial tension and compression tests, applied along the length of the cylinder, are used to evaluate the non-linear mechanical behavior and quantify energy absorption of the system during both loading (tension) and unloading (compression). It was shown that energy absorption during loading was always greater than unloading and increased with an increasing number of layers. The energy absorbed by individual layer was approximately 1.25 J in loading and 0.52 J in unloading for a layer with sinusoidal beam thickness of 1.5 mm. The direction dependence of the energy absorption is attributed to the printed configuration of the lattices. Individual layers can be stacked to tailor the amount of energy absorption. In addition, the energy absorbed and the snapping sequence of the multistable cylinder could be controlled by changing the thickness of the sinusoidal beams in each layer. The variation of energy absorbed is strongly influenced by the thickness of the sinusoidal beam. By increasing the beam thickness from 1 mm to 2 mm, energy absorption increased by approximately a factor of three. Beam thickness accurately controlled the snap-through behavior in experimental samples, but the computational model experienced re-distribution of strain and snap-close forces that cause less predictable snap-through behavior in unloading (compression). The design, analysis and control of snapping sequence of cylindrical shells with multistable states provides new opportunities in practical application of control of elastic waves, energy absorption and reconfigurable structures.