Behavior of architected instability-based metamaterials (AIMs) under out-of-plane geometric variations

Architected instability-based metamaterials (AIMs), composed of multistable elementary building blocks, can undergo highly reversible geometric phase transformations, making them ideal for dynamic systems such as energy-dissipating structures and micro-electro-mechanical devices (MEMS). While prior research has largely focused on in-plane geometries and global responses, limited studies have explored how out-of-plane geometry affects the critical mechanical behavior of AIMs. Here, we study a representative class of AIMs constructed from curved beam-based building blocks, ${\text{AIMs}}^{\text{cb}}$, and investigate how their out-of-plane geometry influences key performance metrics. ${\text{AIMs}}^{\text{cb}}$ rely on elastic buckling of slender beams to achieve reversibility, which limits their strength and energy dissipation. Their limited geometric tunability also constrained their utility in MEMS requiring diverse multistable behaviors. To address these limitations, we introduce a new geometric control parameter, $k$, to adjust the out-of-plane geometry of ${\text{AIMs}}^{\text{cb}}$ and tune their mechanical properties. Our results show that $k$ governs the localization of maximum strain, thereby controlling the reversibility and robustness of the multistable response. Using finite element simulations, digital image correlation, and cyclic compression experiments, we demonstrate that ${\text{AIMs}}^{\text{cb}}$ with $k>0$ achieve up to 62.1% higher compressive strength and 45.6% greater energy dissipation, while also enabling a broader range of tunable multistable behaviors. The simplicity of fabricating out-of-plane geometries further enhances the practical applicability of ${\text{AIMs}}^{\text{cb}}$, extending their use from energy-focused applications such as packaging, shock absorption, and impact protection to adaptive systems including MEMS and other multistability-driven devices.