Outer-ligament-enhanced tetra-missing rib auxetic structures with high specific stiffness and broadband elastic bandgaps

This paper presents two designs for auxetic metamaterials: the outer-ligament-enhanced tetra-missing rib auxetic structure (O-TMR) and the outer-ligament-enhanced enhanced tetra-missing rib auxetic structure (OE-TMR). These designs build upon the traditional (T-TMR) and enhanced (E-TMR) tetra-missing rib structures by strategically altering the width of their outer ligaments. The mechanical properties and bandgap characteristics of the introduced auxetic structures are comprehensively investigated through theoretical analysis and finite element (FE) simulations. We systematically examined the effects of key geometric parameters on bandgap behavior, revealing that widening the outer ligaments not only enhances the structural specific stiffness but also significantly broadens the bandgap. The effective Young’s modulus of the O-TMR is increased by 45.57% compared to the traditional T-TMR, and that of the OE-TMR shows a 54.57% improvement over E-TMR. Additionally, when the effective densities are identical, both the O-TMR and OE-TMR exhibit lower starting frequencies and broader relative bandwidths than their traditional counterparts. Experimental measurements were conducted to verify the predicted bandgap characteristics, demonstrating good agreement between simulations and tests. These designs effectively alleviate the inherent stiffness-bandgap trade-off, providing lightweight, high-strength solutions with improved vibration attenuation capabilities for advanced engineering applications. • Outer-ligament-enhanced auxetic structures are proposed by strategically widening the outer ligaments. • The OE-TMR achieves 54.47% higher Young’s modulus and 71.56% broader relative width of the bandgaps. • The OE-TMR enables quasi-continuous broad bandgaps with a separation interval as small as 45.65 Hz, overcoming the traditional bandgap separation with larger intervals. • Combined FEM and experimental validation confirm the improved vibration attenuation performance of the outer-ligament enhanced auxetic structures.