Skip to main content

The Mechanical Behavior of Viscoelastic Materials in the Frequency Domain

  • Conference paper
  • First Online:
Proceedings of DINAME 2017 (DINAME 2017)

Part of the book series: Lecture Notes in Mechanical Engineering ((ABCMSMSE))

Included in the following conference series:

  • 673 Accesses

Abstract

In the last few decades, a growing need for new materials for several applications led to the development and increase of studies in new theories such as viscoelasticity. Many efforts have been done to understand and characterize the mechanical behavior of these materials. The purpose of this work is to determine the viscoelastic Poisson’s ratio in the frequency domain, \(\nu ^*(\omega )\), for a viscoelastic material in order to characterize its three-dimensional behavior. To do so, the work is based on the elastic-viscoelastic correspondence principle (EVCP) and the time-temperature superposition principle (TTSP). Measurements of the complex shear modulus, \(G^*(\omega )\), and the complex modulus, \(E^*(\omega )\), were performed using a dynamic mechanical analyzer (DMA). To consider eventual uncertainties, each specific mechanical test was carried out using three test-specimens.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alotta, G., Barrera, O., Cocks, A.C., Paola, M.D.: On the behaviour of a three-dimensional fractional viscoelastic constitutive model. Meccanica 52(9), 2127–2142 (2017). https://doi.org/10.1007/s11012-016-0550-8

  2. Armenkas, A.E.: Advanced Mechanics of Materials and Applied Elasticity. CRC Press, Florida (2005)

    Google Scholar 

  3. Arzoumanidis, G.A., Liechti, K.M.: Linear viscoelastic property measurement and its significance for some nonlinear viscoelasticity models. Mech. Time-Depend. Mater. 7, 209–250 (2003). https://doi.org/10.1023/B:MTDM.0000007357.18801.13

  4. Bonfiglio, P., Pompoli, F.: A simplified compression test for the estimation of the Poisson’s ratio of viscoelastic foams. Polym. Test. 61, 324–332 (2017). https://doi.org/10.1016/j.polymertesting.2017.05.040

  5. Borges, F.C.L., Castello, D.A., Magluta, C., Rochinha, F.A., Roitman, N.: An experimental assessment of internal variables constitutive models for viscoelastic materials. Mech. Syst. Signal Process. 50–51 (2015). https://doi.org/10.1016/j.ymssp.2014.04.023

  6. Charpin, L., Sanahuja, J.: Creep and relaxation Poisson’s ratio: Back to the foundations of linear viscoelasticity. Application to concrete. Int. J. Solids Struct. 110–111 (2017). https://doi.org/10.1016/j.ijsolstr.2017.02.009

  7. Christensen, R.M.: Theory of Viscoelasticity—An Introduction. Academic Press, New York (1982)

    Google Scholar 

  8. Dae Han, C., Kim, J.K.: On the use of time-temperature superposition in multicomponent/multiphase polymer systems. Polymer 34(12), 2533–2539 (1993). https://doi.org/10.1016/0032-3861(93)90585-X

  9. Dauvillier, B.S., Feilzer, A.J., De Gee, A.J., Davidson, C.L.: Visco-elastic parameters of dental restorative materials during setting. J. Dent. Res. 79(3), 818–823 (2000). https://doi.org/10.1177/00220345000790030601

  10. Dealy, J., Plazek, D.: Time-temperature superposition—a users guide. Rheol. Bull. 78, 16–31 (2009)

    Google Scholar 

  11. Deng, S., Hou, M., Ye, L.: Temperature-dependent elastic moduli of epoxies measured by DMA and their correlations to mechanical testing data. Polym. Test. 26(6), 803–813 (2007). https://doi.org/10.1016/j.polymertesting.2007.05.003

  12. Estrada-Royval, I.-A., Díaz-Díaz, A.: Post-curing process and visco-elasto-plastic behaviour of two structural adhesives. Int. J. Adhes. Adhes. 61(9), 9–111 (2015). https://doi.org/10.1016/j.ijadhadh.2015.06.001

  13. Graziani, A., Bocci, M., Canestrari, F.: Complex Poisson’s ratio of bituminous mixtures: measurement and modeling. Mater. Struct. 47, 1131–1148 (2014). https://doi.org/10.1617/s11527-013-0117-2

  14. Greaves, G.N., Greer, A.L., Lakes, R.S., Rouxel, T.: Poisson’s ratio and modern materials. Nat. Mater. 10(11), 823–837 (2011). https://doi.org/10.1038/nmat3134

  15. Hernández, W.P., Castello, D.A., Ritto, T.G.: Uncertainty propagation analysis in laminated structures with viscoelastic core. Comput. Struct. 164(2), 23–37 (2016). https://doi.org/10.1016/j.compstruc.2015.10.006

  16. Hilton, H.: Clarifications of Certain Ambiguities and Failings of Poisson’s Ratios in Linear Viscoelasticity. J. Elast. 104(1), 303–318 (2011). https://doi.org/10.1007/s10659-010-9296-z

  17. Hilton, H.: Elastic and Viscoelastic poisson’s ratios: the theoretical mechanics perspective. Mater. Sci. Appl. 8, 291–332 (2017)

    Google Scholar 

  18. Kumar, N.P.: Viscoelastic characterization and effective damping of a carbon/polyurethane laminate. Master thesis, Rochester Institute of Technology, New York (2016)

    Google Scholar 

  19. Lack, I., Krupa, I., Stach, M., Kuma, A., Juriov, J., Chodk, I.: Thermal lag and its practical consequence in the dynamic mechanical analysis of polymers. Polym. Test. 19, 775–771 (2000). https://doi.org/10.1016/S0142-9418(99)00046-X

  20. Lakes, R., Wineman, A.: On poisson’s ratio in linearly viscoelastic solids. J. Elast. 85(1), 45–63 (2006). https://doi.org/10.1007/s10659-006-9070-4

  21. Lakes, R.S.: Viscoelastic measurement techniques. Rev. Sci. Instrum. 75(4), 797-810 (2004). https://doi.org/10.1063/1.1651639

  22. Lee, E.H.: Stress analysis for linear viscoelastic materials. Rheol. Acta. 1(4-6), 426–430 (1961). https://doi.org/10.1007/BF01989085

  23. Menard, K.: Dynamic mechanical analysis—a practical introduction. CRC Press LLC, Florida (2008)

    Book  Google Scholar 

  24. Placet, V., Foltête, E.: Is Dynamic Mechanical Analysis (DMA) a non-resonance technique?. EPJ Web Conf. 6, (2010). https://doi.org/10.1051/epjconf/20100641004

  25. Pritz, T.: The Poisson’s loss factor of solid viscoelastic materials. J. Sound Vib. 306(3), 790–802 (2007). https://doi.org/10.1016/j.jsv.2007.06.016

  26. Rao, K.V., Dayananda, G.N., Ananthapadmanabha, G.S.: Viscoelastic characterisation of an epoxy based shape memory polymer (SMEP). Indian J. Adv. Chem. Sci. 2, 64–67 (2014)

    Google Scholar 

  27. Rouleau, L., Deu, J.-F., Legay, A., Le Lay, F.: Application of KramersKronig relations to timetemperature superposition for viscoelastic materials. Mech. Mater. 65(10), 66–75 (2013). https://doi.org/10.1016/j.mechmat.2013.06.001

  28. Rouleau, L., Pirk, R., Pluymers, B., Desmet, W.: Characterization and modeling of the viscoelastic behavior of a self-adhesive rubber using dynamic mechanical analysis tests. J. Aerosp. Technol. Manag. 7(2), 200–208 (2015). https://doi.org/10.5028/jatm.v7i2.474

  29. Shaw, M.T., MacKnight, W.J.: Introduction to Polymer Viscoelasticity. Wiley, New York (2005)

    Book  Google Scholar 

  30. Swaminathan, G., Shivakumar, K.: A re-examination of DMA testing of polymer matrix composites. J. Reinf. Plast. Comp. 28(8), 979–994 (2008). https://doi.org/10.1177/0731684407087740

  31. Tschoegl, N.W., Knauss, W.G., Emri, I.: Poisson’s ratio in linear viscoelasticity a critical review. Mech. Time-Depend. Mater. 6(1), 3–51 (2002). https://doi.org/10.1023/A:101441150317

  32. Tschoegl, N.W.: The Phenomenological Theory of Linear Viscoelastic Behavior: an introduction. Springer, Berlin (1989)

    Book  Google Scholar 

  33. Van Gurp, M., Palmen, J.: Time-temperature superposition for polymeric blends. Rheol. Bull. 67(1), 5–8 (1998)

    Google Scholar 

  34. Williams, M.L., Landel, R.F., Ferry, J.D.: The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 77(14), 3701–3707 (1955). https://doi.org/10.1021/ja01619a008

  35. Yu, H., Kongsmo, R., Patil, N., He, J., Breiby, D.W., Zhang, Z.: On determining the Poisson’s ratio of viscoelastic polymer microparticles using a flat punch test. Int. J. Mech. Sci. 128129, 150–158 (2017). https://doi.org/10.1016/j.ijmecsci.2017.04.019

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Daniel A. Castello .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Henriques, I.R., Borges, L.A., Castello, D.A. (2019). The Mechanical Behavior of Viscoelastic Materials in the Frequency Domain. In: Fleury, A., Rade, D., Kurka, P. (eds) Proceedings of DINAME 2017. DINAME 2017. Lecture Notes in Mechanical Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-91217-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91217-2_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91216-5

  • Online ISBN: 978-3-319-91217-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics