Skip to main content
SpringerLink
Log in

Simulations for mechanical properties of polymer composites: investigations into suitability of numerical models for TPU-CNT with Mooney–Rivlin (\(N = 1\)) and friction

  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

With rising demand to develop versatile composite materials for modern applications, computer-based solutions to arrive at the material characteristics are now preferred. This necessity is due to the large cost involved for the nanoadditives, as well as elaborate and precise setups required for detailed load tests or experiments. Even with the numerical simulations, considerable information has to arrive from experiments for these highly nonlinear viscoelastic materials. Stress accumulation and relaxation are important aspects that need prediction before considering composites for applications. Being a relatively new engineering domain, the significant information to use commercial codes like Ansys®, MSC®, or Abaqus® are now scattered in literature and the solvers themselves are still evolving. Our attempt through this work is to provide a comprehensive basic set of information on the same, while using Ansys® for arriving at the material characteristics of Thermoplastic Polyurethane-Carbon Nanotube (TPU-CNT) polymer composite. A simulation procedure to study stress relaxation behavior with Maxwell’s Prony relaxation parameters is detailed, suitability of incorporating basic hyperelastic models, such as Mooney–Rivlin and Ogden available in the solver, is compared, and the influence of coefficient of friction (COF) in the numerical simulations is investigated. On appropriate validation with available experimental results, we found that hyper-viscoelastic model is best suited for TPU-CNT with maximum error as low as 5% during stress relaxation phase (for 1800 s), in comparison with 15% and 25% for viscoelastic and hyperelastic models. During the short loading phase of the material, none of the models are accurate. The two-parameter first-order equation-based Mooney–Rivlin model fed with uniaxial load test information was satisfactory for low strain predictions in comparison with higher-order Ogden model. COF is found to significantly affect the solution, and a value of about 0.3 was found suitable for the present 0.05% TPU-CNT composite. Further, we present the transient stress contours to show how the stress relaxation within the composite material would be predicted with each model.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

Data Availability

Data to the present work is available with the data repository of the research group. It can be shared and made available to the reviewers on request.

References

  • ANSYS Learning Hub: https://www.ansys.com/services/ansys-learning-hub. Accessed 05-07-2021

  • Aurilia, M., Piscitelli, F., Sorrentino, L., Lavorgna, M., Iannace, S.: Detailed analysis of dynamic mechanical properties of TPU nanocomposite: the role of the interfaces. Eur. Polym. J. 47(5), 925–936 (2011)

    Article  Google Scholar 

  • Avalle, M., Romanello, E.: Tribological characterization of modified polymeric blends. Proc. Struct. Integr. 8, 239–255 (2018). ISSN 2452-3216

    Google Scholar 

  • Bower, A.F.: Applied Mechanics of Solids. CRC Press, Boca Raton (2009)

    Book  Google Scholar 

  • Dilibal, S., Sahin, H., Celik, Y.: Experimental and numerical analysis on the bending response of the geometrically gradient soft robotics actuator. Arch. Mech. 70(5), 391–404 (2018)

    MATH  Google Scholar 

  • Fazekas, B., Goda, T.J.: Determination of the hyper-viscoelastic model parameters of open-cell polymer foams and rubber-like materials with high accuracy. Mater. Des. 156, 596–608 (2018)

    Article  Google Scholar 

  • Ferry, J.D.: Viscoelastic Properties of Polymers. Wiley, New York (1980)

    Google Scholar 

  • Goh, S.M., Charalambides, M.N., Williams, J.G.: Determination of the constitutive constants of non-linear viscoelastic materials. Mech. Time-Depend. Mater. 8(3), 255–268 (2004)

    Article  Google Scholar 

  • Gu, S., Yan, B., Liu, L., Ren, J.: Carbon nanotube–polyurethane shape memory nanocomposites with low trigger temperature. Eur. Polym. J. 49(12), 3867–3877 (2013)

    Article  Google Scholar 

  • Guo, S., Zhang, C., Wang, W., Liu, T., Tjiu, W.C., He, C., Zhang, W.-D.: Preparation and characterization of polyurethane/multiwalled carbon nanotube composites. Polym. Polym. Compos. 16(8), 501–507 (2008)

    Google Scholar 

  • Holzapfel, G.A.: On large strain viscoelasticity: continuum formulation and finite element applications to elastomeric structures. Int. J. Numer. Methods Eng. 39(22), 3903–3926 (1996)

    Article  MATH  Google Scholar 

  • Jyoti, J., Singh, B.P., Rajput, S., Singh, V.N., Dhakate, S.R.: Detailed dynamic rheological studies of multiwall carbon nanotube-reinforced acrylonitrile butadiene styrene composite. J. Mater. Sci. 51(5), 2643–2652 (2016)

    Article  Google Scholar 

  • Keerthiwansa, G.W.R., Javořík, J., Kledrowetz, J., Nekoksa, P.: Elastomer testing: the risk of using only uniaxial data for fitting the Mooney-Rivlin hyperelastic-material model. Mater. Tehnol. (2018). https://doi.org/10.17222/mit.2017.085

    Article  Google Scholar 

  • Lakes, R.S.: Viscoelastic measurement techniques. Rev. Sci. Instrum. 75(4), 797–810 (2004)

    Article  Google Scholar 

  • Mansour, G., Tsongas, K., Tzetzis, D., Tzikaset, K.: Dynamic mechanical characterization of polyurethane/multiwalled carbon nanotube composite thermoplastic elastomers. Polym.-Plast. Technol. Eng. 56(14), 1505–1515 (2017)

    Article  Google Scholar 

  • Mofidi, M.: Tribology of elastomers. PhD thesis, Luleå tekniska universitet (2007)

  • Pawlikowski, M.: Non-linear approach in hyper-viscoelastic constitutive modelling of polyurethane nanocomposite. Mech. Time-Depend. Mater. 18(1), 1–20 (2014)

    Article  Google Scholar 

  • Ryszkowska, J., Jurczyk-Kowalska, M., Szymborski, T.: Dispersion of carbon nanotubes in polyurethane matrix. Physica E 39, 124–127 (2007)

    Article  Google Scholar 

  • Simo, J.C.: On a fully three-dimensional finite-strain viscoelastic damage model: formulation and computational aspects. Comput. Methods Appl. Mech. Eng. 60(2), 153–173 (1987)

    Article  MATH  Google Scholar 

  • Sun, W., Yuan, Y.-X.: Optimization Theory and Methods: Nonlinear Programming, vol. 1. Springer, Berlin (2006)

    MATH  Google Scholar 

  • TA Instruments: Application of Time-Temperature Superposition Principles to DMA. Thermal Analysis Application Brief (last accessed 2022). https://www.tainstruments.com/pdf/literature/TA144.pdf (last modified 2017-09-06 20:08)

  • Tapia-Romero, M.A., Dehonor-Gómez, M., Lugo-Uribe, L.E.: Prony series calculation for viscoelastic behavior modeling of structural adhesives from DMA data. Ing. Investig. Tecnol. 21(2), 1–10 (2020)

    Google Scholar 

  • Taylor, R.L., Pister, K.S., Goudreau, G.L.: Thermomechanical analysis of viscoelastic solids. Int. J. Numer. Methods Eng. 2(1), 45–59 (1970)

    Article  MATH  Google Scholar 

  • Wex, C., et al.: Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review. Biomed. Eng., Biomed. Tech. 60(6), 577–592 (2015)

    Google Scholar 

  • Wu, Y., Wang, H., Li, A.: Parameter identification methods for hyperelastic and hyper-viscoelastic models. Appl. Sci. 6(12), 386 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

We thank the Ansys® support team for engaging in technical discussions throughout the course of the present research. The authors declare that they have no conflict of interest.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, TKM College of Engineering, Kollam, 691005, India

    Goutham B. Raj

  2. Department of Mechanical Engineering, Rajagiri School of Engineering and Technology, Kakkanad, Ernakulam, 682039, India

    Ajanas Saludheen, Ajith Kumar Arumugham-Achari & Tony Chacko

  3. Department of Mechanical Engineering, National Institute of Technology, Tiruchirappalli, 620001, India

    Nivish George

Authors
  1. Goutham B. Raj
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ajanas Saludheen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ajith Kumar Arumugham-Achari
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nivish George
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tony Chacko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ajith Kumar Arumugham-Achari.

Additional information

Publisher’s Note

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

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Raj, G.B., Saludheen, A., Arumugham-Achari, A.K. et al. Simulations for mechanical properties of polymer composites: investigations into suitability of numerical models for TPU-CNT with Mooney–Rivlin (\(N = 1\)) and friction. Mech Time-Depend Mater 27, 705–726 (2023). https://doi.org/10.1007/s11043-022-09565-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11043-022-09565-w

Keywords

Search

Navigation