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Mechanical design of negative stiffness honeycomb materials

  • Dixon M Correa
  • Carolyn Conner Seepersad
  • Michael R Haberman
Research article
Part of the following topical collections:
  1. Multidisciplinary Design Optimization

Abstract

A mechanical system exhibits negative stiffness when it requires a decrease in applied force to generate an increase in displacement. Negative stiffness behavior has been of interest for use in vibro-acoustic damping materials, vibration isolation mechanisms, and mechanical switches. This non-intuitive mechanical response can be elicited by transversely loading a curved beam structure of appropriate geometry, which can be designed to exhibit either one or two stable positions. The current work investigates honeycomb structures whose unit cells are created from curved beam structures that are designed to provide negative stiffness behavior and a single stable position. These characteristics allow the honeycomb to absorb large amounts of mechanical energy at a stable plateau stress, much like traditional honeycombs. Unlike traditional honeycombs, however, the mechanism underlying energy-absorbing behavior is elastic buckling rather than plastic deformation, which allows the negative stiffness honeycombs to recover from large deformations. Accordingly, they are compelling candidates for applications that require dissipation of multiple impacts. A detailed exploration of the unit cell design shows that negative stiffness honeycombs can be designed to dissipate mechanical energy in quantities that are comparable to traditional honeycomb structures at low relative densities. Furthermore, their unique cell geometry allows the designer to perform trade-offs between density, stress thresholds, and energy absorption capabilities. This paper describes these trade-offs and the underlying analysis.

Keywords

Honeycombs Negative stiffness Bistability Energy absorption Elastic stiffness Stress threshold 

Abbreviations

Δth

Normalized displacement threshold

b

Out-of-plane depth for a negative stiffness beam

d

Transverse displacement

E0

Specific initial stiffness

Es

Modulus of elasticity

F

Normalized force

f

Transverse force

Fth

Force threshold

h

Apex height for a negative stiffness beam

I

Area moment of inertia

l

Length of a negative stiffness beam

Q

Ratio of apex height to thickness for a negative stiffness beam

t

In-plane thickness for a negative stiffness beam

w(x)

Beam-shape coordinate along the vertical axis

x

Beam-shape coordinate along the horizontal axis

Δ

Normalized displacement

εmax

Maximum strain

ρ

Relative density

σpl

Critical stress level

σth

Stress threshold

σys

Yield strength

Notes

Acknowledgements

We gratefully acknowledge Professor Desiderio Kovar and Mr. Sergio Cortes for their help in generating the experimental data in Fig. 5. Tim Klatt was instrumental in generating the negative stiffness honeycomb configuration illustrated in Fig. 2 and conducting preliminary proof-of-concept studies to refine the design. We gratefully acknowledge the funding from the Department of Defense Small Business Innovation Research (SBIR) Program under SBIR Topic N142-085 in collaboration with the Maritime Applied Physics Corporation (MAPC).

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Copyright information

© Correa et al. 2015

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.

Authors and Affiliations

  • Dixon M Correa
    • 1
  • Carolyn Conner Seepersad
    • 1
  • Michael R Haberman
    • 1
    • 2
  1. 1.Mechanical Engineering DepartmentThe University of Texas at AustinAustinUSA
  2. 2.Applied Research LaboratoriesThe University of Texas at AustinAustinUSA

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