Skip to main content
SpringerLink
Log in

Numerical implementation of strain rate dependent thermo viscoelastic constitutive relation to simulate the mechanical behavior of PMMA

  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

In this work, a nonlinear viscoelastic constitutive relation was implemented to describe the mechanical behavior of a transparent thermoplastic polymer polymethyl methacrylate (PMMA). The quasi-static and dynamic response of the polymer was studied under different temperatures and strain rates. The effect of temperature was incorporated in elastic and relaxation constants of the constitutive equation. The incremental form of constitutive model was developed by using Poila–Kirchhoff stress and Green strain tensors theory. The model was implemented numerically by establishing a user defined material subroutine in explicit finite element (FE) solver LS-DYNA. Finite element models for uniaxial quasi-static compressive test and high strain rate split Hopkinson pressure bar compression test were built to verify the accuracy of material subroutine. Numerical results were validated with experimental stress strain curves and the results showed that the model successfully predicted the mechanical behavior of PMMA at different temperatures for low and high strain rates. The material model was further engaged to ascertain the dynamic behavior of PMMA based aircraft windshield structure against bird impact. A good agreement between experimental and FE results showed that the suggested model can successfully be employed to assess the mechanical response of polymeric structures at different temperature and loading rates.

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

Similar content being viewed by others

References

  • Arruda, E.M., Boyce, M.C., Jayachandran, R.: Effects of strain rate, temperature and thermomechanical coupling on the finite strain deformation of glassy polymers. Mech. Mater. 19(2), 193–212 (1995)

    Article  Google Scholar 

  • Bai, J., Sun, Q.: On the integrated design technique of windshield against bird strike. Mech. Pract. 27(1), 14–18 (2005)

    Google Scholar 

  • Chen, W., Lu, F., Cheng, M.: Tension and compression tests of two polymers under quasi-static and dynamic loading. Polym. Test. 21(2), 113–121 (2002)

    Article  Google Scholar 

  • Drozdov, A.D.: Modelling the nonlinear viscoelastic behavior of amorphous glassy polymers. Math. Comput. Model. 30(5), 49–72 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • Frank, G.J., Brockman, R.A.: A viscoelastic–viscoplastic constitutive model for glassy polymers. Int. J. Solids Struct. 38(30), 5149–5164 (2001)

    Article  MATH  Google Scholar 

  • Gao, Z.Z., Liu, Z.Q., Liu, W., Yue, Z.F.: Experimental and constitutive investigation on tensile and compressive behavior of MDYB-3 at different temperatures and loading rates. Int. J. Polym. Mater. 60(5), 340–350 (2011)

    Article  Google Scholar 

  • Huang, F.Z., Guo, W.G.: Mechanical behavior of MDYB-3 PMMA at different temperatures and strain rates. J. Mater. Sci. Eng. 25(4), 582–586 (2007)

    MathSciNet  Google Scholar 

  • Jenq, S.T., Hsiao, F.B., Lin, I.C., Zimcik, D.G., Nejad, E.M.: Simulation of a rigid plate hit by a cylindrical hemi-spherical tip-ended soft impactor. Comput. Mater. Sci. 39(3), 518–526 (2007)

    Article  Google Scholar 

  • Johnson, A.F., Holzapfel, M.: Numerical prediction of damage in composite structures from soft body impacts. J. Mater. Sci. 41(20), 6622–6630 (2006)

    Article  Google Scholar 

  • Lee, O.S., Kim, M.S.: Dynamic material property characterization by using split Hopkinson pressure bar (SHPB) technique. Nucl. Eng. Des. 226(2), 119–125 (2003)

    Article  Google Scholar 

  • Li, Z., Lambros, J.: Strain rate effects on the thermomechanical behavior of polymers. Int. J. Solids Struct. 38(20), 3549–3562 (2001)

    Article  MATH  Google Scholar 

  • LS-DYNA Aerospace Working Group, Ver 12.1.: Modeling Guidelines Document (2012)

  • LS-DYNA Keyword User Manual, Ver. 971.: Liverrmore Software Technology Corporation (2006)

  • LS-DYNA Theory Manual v1.0.: Liverrmore Software Technology Corporation (2006)

  • Meguid, S.A., Mao, R.H., Ng, T.Y.: FE analysis of geometry effects of an artificial bird striking an aeroengine fan blade. Int. J. Impact Eng. 35(6), 487–498 (2008)

    Article  Google Scholar 

  • Meyers, M.A.: Dynamic Behavior of Materials. Wiley, New York (1994)

    Book  MATH  Google Scholar 

  • Moy, P., Gunnarsson, C.A., Weerasooriya, T., Chen, W.: Stress–strain response of PMMA as a function of strain-rate and temperature. Dyn. Behav. Mater. 1, 125–133 (2011)

    Article  Google Scholar 

  • Richeton, J., Ahzi, S., Makradi, A., Vecchio, K.S.: Constitutive modeling of polymer materials at impact loading rates. J. Phys. IV (Proc.) 134, 103–107 (2006)

    Google Scholar 

  • Suo, T., Li, Y., Liu, Y.: Study on temperature and strain rate effects on mechanical behavior of aeronautical PMMA [J]. J. Mater. Sci. Eng. 4, 018 (2006)

    Google Scholar 

  • Tang, Z.P.: Mechanical behavior of epoxy resin under high strain rates. He fei: master’s degree thesis of University of Science and Technology of China (1981)

  • Wang, F.S., Yue, Z.F.: Numerical simulation of damage and failure in aircraft windshield structure against bird strike. Mater. Des. 31, 687–695 (2010)

    Article  Google Scholar 

  • Wang, L.L., Zhou, F.H., Sun, Z.J., Wang, Y.Z., Shi, S.Q.: Studies on rate-dependent macro-damage evolution of materials at high strain rates. Int. J. Damage Mech 19(7), 805–820 (2010)

    Article  Google Scholar 

  • Weerasooriya, T., Moy, P., Casem, D., Cheng, M., Chen, W.: Fracture toughness of PMMA as a function of loading rate. In: Proceedings of the SEM Annual Conference on Experimental Mechanics, pp. 5–7 (2006)

  • Welsh, C.J., Centonze, V.: Aircraft transparency testing artificial birds. Report AEDC-TR-86-2, US Air Force (1986)

  • Yapeng, S., Jiaju, Y., Shuchan, C.: The finite element analysis of three dimensional viscoelastic large-deformation problem by updated-Lagrangian approach. Chin. J. Comput. Mech. 2, 005 (1987)

    Google Scholar 

  • Zhou, F.H., Wang, L.L., Hu, S.S.: A damage-modified nonlinear visco-elastic constitutive relation and failure criterion of PMMA at high strain-rates [J]. Explos. Shock Waves 4, 006 (1992)

    Google Scholar 

  • Zhu, S., Tong, M., Wang, Y.: Experiment and numerical simulation of a full-scale aircraft windshield subjected to bird impact. In: 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, pp. 4–7. Palm Springs (2009)

Download references

Acknowledgments

This work is supported by 973 Program (2012CB025904), 111 Project (B07050) and National Natural Science Foundation of China (51221001).

Author information

Authors and Affiliations

  1. Engineering Simulation and Aerospace Computing (ESAC), Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, China

    Uzair Ahmed Dar, Wei Hong Zhang & Ying Jie Xu

Authors
  1. Uzair Ahmed Dar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Hong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ying Jie Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Uzair Ahmed Dar or Wei Hong Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dar, U.A., Zhang, W.H. & Xu, Y.J. Numerical implementation of strain rate dependent thermo viscoelastic constitutive relation to simulate the mechanical behavior of PMMA. Int J Mech Mater Des 10, 93–107 (2014). https://doi.org/10.1007/s10999-013-9233-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10999-013-9233-y

Keywords

Search

Navigation