Never better than 5/6: The fundamental limit of energy absorption efficiency for negative-stiffness curved-beam honeycombs

Abstract

In recent years, the design and development of negative-stiffness metamaterials and metastructures have been considered a research field with great potential for applications such as energy absorption and vibration isolation. As a particular example, it is known that the reaction force of a typical negative-stiffness honeycomb (NSH) metastructure under compression will not monotonically increase with displacement, but manifests successive local extremums. This makes it an attractive choice as a concept for energy-absorbing applications, especially for recurrent low-velocity collision scenarios. Here, we analytically derive the equations of the piecewise-defined force–displacement functions for the general case of an NSH two-dimensional lattice metastructure followed by finding the optimal geometric design parameters. Using analytical methods, we demonstrate that there is a fundamental upper limit of 5/6 to the energy absorption efficiency of such metastructures. The obtained theoretical results are validated by finite-element numerical simulations and experimental compression tests. The findings of this study enable designers to identify optimal geometries of NSH metastructures for different practical applications with particular requirements on maximum reaction force and displacement.

Keywords

• Negative-stiffness honeycomb metastructure
• Mechanical metamaterial
• Energy absorption efficiency
• Optimal structural design
• Elastic deformation