Skip to main content

Advertisement

Log in

Stiffness and Energy Dissipation of Polymer Matrix Composites Containing Embedded Metallic Negative Stiffness Structures

  • Research paper
  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Background

Conventional composites used in damping applications exhibit an undesirable tradeoff between stiffness and energy dissipation. Recent research demonstrates that it is possible to simultaneously achieve increased stiffness and energy dissipation for a configuration of a viscoelastic polymer matrix placed in parallel with a negative stiffness structure (NSS). This configuration resulted in energy dissipation equal to the sum of its components but is difficult to implement in practice.

Objective

In this paper, an alternative configuration is investigated in which the NSS is embedded simultaneously in series and parallel with the matrix. The main objectives are to examine the tradeoff between the stiffness and energy dissipation of the composite and to identify the mechanisms for enhanced energy dissipation.

Methods

To achieve this, FEA models were used to match the stiffness of a polymer matrix with that of a metallic NSS. Multiple specimens were manufactured and tested under quasi-static compressive loads to determine the force versus displacement curves and calculate the energy dissipation and stiffness.

Results

These tests demonstrate that the total energy dissipation of the composite can be greater than the sum of its components, while maintaining the benefit of increasing the stiffness and damping capacity simultaneously. The results also demonstrate that the applied strain rate plays a critical role in activating the NSS, which is essential to achieve the desired increase in energy dissipation.

Conclusions

The results indicate that localized strain and strain rate at the interface between the NSS and polymer matrix are the main contributors to achieving energy dissipation beyond the sum of its components. Furthermore, it was demonstrated that the strain rate affects the activation of the NSS and therefore composites containing mechanically activated NSS must be designed for the strain rate of interest.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Dall’Astaa A, Ragnib L (2006) "Experimental tests and analytical model of high damping rubber dissipating devices," Eng Structures 28:1874–1884

  2. Chung DDL (2003) Structural composite materials tailored for damping. J Alloy Compd 355:216–223

    Article  Google Scholar 

  3. Zhao X, Yang J, Zhao D, Lu Y, Wang W, Zhang L, Nishi T (2015) Natural rubber/nitrile butadiene rubber/hindered phenol composites with high-damping properties. Int J Smart Nano Mater 6(4):239–250

    Article  Google Scholar 

  4. Byers L, Gandhi F (2009) Embedded absorbers for helicopter rotor lag damping. J Sound Vib 325:705–721

    Article  Google Scholar 

  5. Gu HS, Itoh Y (2010) Ageing Behaviour of Natural Rubber and High Damping Rubber Materials Used in Bridge Rubber Bearings. Adv Struct Eng 13(6):1105–1113

    Article  Google Scholar 

  6. Rasuo B (2010) Experimental study of structural damping of composite helicopter blades with different cores. Plast, Rubber Compos 39(1):1–5

    Article  Google Scholar 

  7. Kumar R, Kant R, Pandey S, Asfer M, Bhattacharya B, Panigrahi PK, Bhattacharya S (2013) Passive Vibration Damping Using Polymer Pads With Microchannel Arrays. J Microelectromech Syst 22(3):695–707

    Article  Google Scholar 

  8. Vér IL, Beranek LL (2006) "Chapter 8, Sound-Absorbing Materials and Sound Absorbers, K. Attenborough, L. Vér. Chapter 14, Structural Damping, E.E. Ungar, J.A. Zpfe," in Noise and Vibration Control Engineering, Hoboken, NJ, John Wiley & Sons, Inc.

  9. Sun CT, Lu YP (1995) Vibration Damping of Structural Elements, Englewood Cliff. Prentice Hall, NJ

    Google Scholar 

  10. Jarzynski J (1990) "Chapter 10. Mechanisms of Sound Attenuation in Materials," in Sound and Vibration Damping with Polymers, Washington D.C., Am Chem Soc pp. 116–207

  11. Koutsawa Y, Haberman MR, Cherkaoui M (2009) Multiscale design of a rectangular sandwich plate with viscoelastic core and supported at extents by viscoelastic materials. Int J Mech Mater Des 5:29–44

    Article  Google Scholar 

  12. Callister WD, Rethwisch DG (2009) Materials Science and Engineering and Introduction, Hoboken. Wiley, NJ

    Google Scholar 

  13. Onda Corporation, "Acoustic tables," [Online]. Available: http://www.ondacorp.com/tecref_acoustictable.shtml. Accessed 20 Feb 2016

  14. Lakes RS (Eds), Golden K, Grimmert G, James R, Milton G, Sen P (1998) "Elastic freedom in cellular solids and composite materials," in Mathematics of Multiscale Materials, NY, Berlin, Springer, pp. 129–153

  15. Lakes RS (2001) Extreme Damping in Composite Materials with a Negative Stiffness Phase. Phys Rev Lett 86(13):2897–2900

    Article  Google Scholar 

  16. Wang YC, Ludwigson M, Lakes RS (2004) Deformation of extreme viscoelastic metals and composites. Mater Sci Eng 370:41–49

    Article  Google Scholar 

  17. Lakes RS, Lee T, Bersie A, Wang YC (2001) Extreme damping in composite materials with negative stiffness inclusions. Nature 410:565–567

    Article  Google Scholar 

  18. Qiu J, Lang JH, Slocum AH (2004) A Curved-Beam Bistable Mechanism. J Microelectromech Syst 13(2):137–146

    Article  Google Scholar 

  19. Shan S, Kang SH, Raney JR, Wang P, Fang L, Candido F, Lewis JA, Bertoldi K (2015) Multistable Architected Materials for Trapping Elastic Strain Energy. Adv Mater 27(29):4296–4301

    Article  Google Scholar 

  20. Rafsanjani A, Akbarzadeh A, Pasini D (2015) Snapping Mechanical Metamaterials under Tension. Adv Mater 27(39):5931–5935

    Article  Google Scholar 

  21. Pontecorvo ME, Barbarino S, Murray GJ, Gandhi FS (2012) Bistable Arches for Morphing Applications. J Intell Mater Syst Struct 24(3):274–286

    Article  Google Scholar 

  22. Harne RL, Wu Z, Wang KW (2016) Designing and Harnessing the Metastable States of a Modular Metastructure for Programmable Mechanical Properties Adaptation. J Mech Des 138(2):1–9

    Article  Google Scholar 

  23. Restrepo D, Mankame ND, Zavttieri P (2015) Phase Transforming Cellular Materials. Extreme Mechanics Letters 4:52–60

    Article  Google Scholar 

  24. Florijn B, Coulais C, van Hecke M (2014) Programmable Mechanical Metamaterials. Phys Rev Lett 113(17):175503

    Article  Google Scholar 

  25. Correa DM, Klatt T, Cortes S, Haberman M, Kovar D, Seepersad C (2015) Negative stiffness honeycombs for recoverable shock isolation. Rapid Prototyp J 21(2):193–200

    Article  Google Scholar 

  26. Correa DM, Seepersad CC, Haberman MR (2015) Mechanical design of negative stiffness honeycomb materials. Integr Mater Manuf Innov 4(10):1–11

    Google Scholar 

  27. Fulcher BA, Shahan DW, Haberman MR, Seepersad CC, Wilson PS (2014) "Analytical and Experimental Investigation of Buckled Beams as Negative Stiffness Elements for Passive Vibration and Shock Isolation Systems," J Vib Acoust 136(031009):1–12

  28. Cortes S, Allison J, Morris C, Haberman MR, Seepersad CC, Kovar D (2017) Design, Manufacture, and Quasi-Static Testing of Metallic Negative Stiffness Structures within a Polymer Matrix. Exp Mech 57(8):1183–1191

    Article  Google Scholar 

  29. Morris C, Bekker L, Spadaccini C, Haberman M, Seepersad C (2019) Tunable Mechanical Metamaterial with Constrained Negative Stiffness for Improved Quasi-Static and Dynamic Energy Dissipation. Adv Eng Mater 21(7):1900163

    Article  Google Scholar 

  30. Vangbo M (1998) An Analytical Analysis of a Compressed Bistable Buckled Beam. Sens Actuators, A 69(3):212–216

    Article  Google Scholar 

  31. Klatt T, Haberman MR (2013) A nonlinear negative stiffness metamaterial unit cell and small-on-large multiscale material model. J Appl Phys 114:033503

    Article  Google Scholar 

  32. Steel AK , "AK Steel,"  (2007) [Online]. Available: http://www.aksteel.com/pdf/markets_products/stainless/precipitation/17-4_ph_data_bulletin.pdf. Accessed 2 Apr 2016

  33. Online Metals, "Stainless sheet 17–4 Cond. A," [Online]. Available: https://www.onlinemetals.com/merchant.cfm?pid=9850&step=4&showunits=inches&id=305&top_cat=0#. Accessed 7 May 2016

  34. Citim, "Metal additive manufacturing," [Online]. Available: http://www.citim.de/en/metal-additive-manufacturing. Accessed 10 May 2016

  35. Fritzen F, Kochmann DM (2014) Material instability-induced extreme damping in composites: a computational study. Int J S Struct 51:4101–4112

    Article  Google Scholar 

  36. Kotanchik J, Woods W, Weinberger R (1945) Investigation of Methods of Supporting Single-Thickness Specimens in a Fixture for Determination of Compressive Stress-Strain Curves. National Advisory Committee for Aeronautics, Virginia

    Google Scholar 

  37. Luecke WE, Ma L, Graham SM, Adler MA(2009) "Repeatability and reproducibility of compression strength measurements conducted according to ASTM E9," Natl Inst Stand Technol

  38. Kashdan L, Seepersad C, Haberman M, Preston SW (2012) "Design, fabrication, and evaluation of negative stiffness elements using SLS," Rapid Prototyp J 18:194–200

  39. Haberman MR, Berthelot Y, Cherkaoui M (2006) Micromechanical Modeling of Particulate Composites for Damping of Acoustic Waves. J Eng Mater Technol 128:320–329

    Article  Google Scholar 

  40. Qi HJ, Boyce MC (2005) Stress–strain behavior of thermoplastic polyurethanes. Mech Mater 37(8):817–839

    Article  Google Scholar 

  41. Lakes RS, Drugan WJ (2002) Dramatically stiffer elastic composite materials due to a negative stiffness phase? J Mech Phys Solids 50(5):979–1009

    Article  Google Scholar 

Download references

Acknowledgements

We acknowledge Dr. David Bourell for allowing the use of scientific equipment required for this study and Stratasys Direct Manufacturing, Austin, TX for assistance with their stainless steel powder products. We also acknowledge Jared Allison and Clint Morris for their support and guidance on the NSS design process and FEA modeling.

Funding

The authors acknowledge the National Science Foundation for supporting this research under grant CMMI #1435548. We also acknowledge the “Ministerio de Ciencia y Tecnología”, MICIT and the “Consejo Nacional para Investigaciones Científicas y Tecnológicas”, CONICIT for their support under the scholarship # 117–2012.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Cortes.

Ethics declarations

Conflicts of Interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cortes, S., Cobo-Losey, N., Haberman, M.R. et al. Stiffness and Energy Dissipation of Polymer Matrix Composites Containing Embedded Metallic Negative Stiffness Structures. Exp Mech 61, 843–858 (2021). https://doi.org/10.1007/s11340-021-00705-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-021-00705-w

Navigation