Constitutive Modeling of Polyamide Split Hopkinson Pressure Bars for the Design of a Pre-stretched Apparatus

  • A. BracqEmail author
  • G. Haugou
  • H. Morvan
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


This paper aims to model the constitutive behavior of polyamide material used in the Split Hopkinson Pressure bars (SHPB). The Hopkinson bars apparatus is employed for the mechanical characterization of many materials under high strain rates at large strains. Nevertheless, testing soft materials is a challenging task regarding their low impedance properties and the difficulty to achieve a dynamic equilibrium. To address that issue, polyamide (nylon) SHPB are employed. However, the application of the pre-stretched technique to tensile apparatus using polyamide bars may provide a flexible mechanical characterization device reaching moderate to high strain rates at large strains. It requires bars of several meters where wave attenuation and dispersion are dominant. Moreover, the design of such apparatus is extremely complex with respect to the sample shape and rigidity as well as connectors. While analytical techniques are proposed in the literature, they are not sufficient to provide guidance in the design and the optimization of a pre-stretched apparatus.

Therefore, the aim of the present study is to develop a finite element model of polyamide SHPB. Various experimental tests are conducted using compressive polyamide SHPB. These tests are computationally modeled using the Radioss explicit FE code through an axisymmetric analysis. The generalized Maxwell model is chosen to consider the viscoelastic material properties. An optimization procedure by inverse method is applied using both experimental and numerical strain signals to identify the material coefficients.

Experimental tests are repeatable for each test configuration. The viscoelastic model parameters of the bars are identified through one configuration and validated against three others. This model gives very satisfactory results and presents interesting predictive abilities.


Hopkinson bars Viscoelastic bars Experimental testing Constitutive modeling Inverse technique 


  1. 1.
    Kolsky, H.: An investigation of the mechanical properties of materials at very high rates of loading. Proc. Phys. Soc. Sect. B. 62(11), 676–700 (1949)CrossRefGoogle Scholar
  2. 2.
    Van Sligtenhorst, C., Cronin, D.S., Wayne Brodland, G.: High strain rate compressive properties of bovine muscle tissue determined using a split Hopkinson bar apparatus. J. Biomech. 39(10), 1852–1858 (2006)CrossRefGoogle Scholar
  3. 3.
    Salisbury, C.P., Cronin, D.S.: Mechanical properties of ballistic gelatin at high deformation rates. Exp. Mech. 49(6), 829–840 (2009)CrossRefGoogle Scholar
  4. 4.
    Cronin, D.S.: Ballistic gelatin characterization and constitutive modeling. In: Proulx, T. (ed.) Dynamic Behavior of Materials, Volume 1: Proceedings of the 2011 Annual Conference on Experimental and Applied Mechanics, pp. 51–55. Springer New York, New York (2011)CrossRefGoogle Scholar
  5. 5.
    Morin, D., Haugou, G., Bennani, B., Lauro, F.: Experimental characterization of a toughened epoxy adhesive under a large range of strain rates. J. Adhes. Sci. Technol. 25(13), 1581–1602 (2011)CrossRefGoogle Scholar
  6. 6.
    Morin, D., Haugou, G., Lauro, F., Bennani, B., Bourel, B.: Elasto-viscoplasticity Behaviour of a structural adhesive under compression loadings at low, moderate and high strain rates. J. Dyn. Behav. Mater. 1(2), 124–135 (2015)CrossRefGoogle Scholar
  7. 7.
    Bracq, A., Haugou, G., Delille, R., Lauro, F., Roth, S., Mauzac, O.: Experimental study of the strain rate dependence of a synthetic gel for ballistic blunt trauma assessment. J. Mech. Behav. Biomed. Mater. 72, 138–147 (2017)CrossRefGoogle Scholar
  8. 8.
    Haugou, G., Leconte, N., Morvan, H.: Design of a pre-stretched tension Hopkinson bar device: Configuration, tail corrections, and numerical validation. Int. J. Impact Eng. 97, 89–101 (2016)CrossRefGoogle Scholar
  9. 9.
    Haugou, G., Morvan, H., Leconte, N.: Direct compression loading using the pre-stretched bar technique: Application to high strains under moderate strain rates. In: Kimberley, J., Lamberson, L., Mates, S. (eds.) Dynamic Behavior of Materials, Volume 1, pp. 169–173. Springer International Publishing, Cham (2018)CrossRefGoogle Scholar
  10. 10.
    Bustamante, M., Cronin, D.S., Singh, D.: Experimental testing and computational analysis of viscoelastic wave propagation in polymeric split hopkinson pressure bar. In: Kimberley, J., Lamberson, L., Mates, S. (eds.) Dynamic Behavior of Materials, vol. Volume 1, pp. 67–72. Springer, Cham (2018)CrossRefGoogle Scholar
  11. 11.
    Bracq, A., et al.: Characterization of a visco-hyperelastic synthetic gel for ballistic impacts assessment. In: Kimberley, J., Lamberson, L., Mates, S. (eds.) Dynamic Behavior of Materials, Volume 1: Proceedings of the 2017 Annual Conference on Experimental and Applied Mechanics, pp. 109–113. Springer, Cham (2018)CrossRefGoogle Scholar
  12. 12.
    Oliveira, I., Teixeira, P., Ferreira, F., Reis, A.: Inverse characterization of material constitutive parameters for dynamic applications. Procedia Eng. 114, 784–791 (2015)CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2019

Authors and Affiliations

  1. 1.Laboratory LAMIH UMR CNRS 8201, University of Valenciennes and Hainaut CambrésisValenciennesFrance

Personalised recommendations