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The effect of material density on load rate sensitivity in nonlinear viscoelastic material models

  • Ivica Kožar
  • Tea Rukavina
Original
  • 36 Downloads

Abstract

This work presents the results of a numerical sensitivity analysis of material density on crack propagation in nonlinear viscoelastic softening material models. Two basic material models are analyzed: Maxwell and Kelvin material models, under the loading with changing rate (slow or fast impact loading). The material is discretized as a lattice model, and the analysis is performed on simple examples consisting of several lattice bars. The mathematical description is based on the theory of dynamical systems, i.e., it is a system of nonlinear differential equations for Kelvin, and a system of nonlinear differential-algebraic equations for Maxwell material model. Sensitivity of displacements on mass and load rate accompanies the analysis.

Keywords

Nonlinear softening Maxwell material model Nonlinear softening Kelvin material model Load rate sensitivity Global parameter sensitivity 

Notes

Acknowledgements

The Croatian Science Foundation Grant No. 9068 Multi-scale concrete model with parameter identification supported this work. The support is gratefully acknowledged.

References

  1. 1.
    Hirsh, M.W., Smale, S., Devaney, R.L.: Differential Equations, Dynamical Systems and An Introduction to Chaos. Elsevier, Amsterdam (2004)Google Scholar
  2. 2.
    Kožar, I., Ožbolt, J.: Some aspects of load-rate sensitivity in visco-elastic microplane material model. Comput. Concrete 7(4), 317 (2010)CrossRefGoogle Scholar
  3. 3.
    Herv, G., Gatuingt, F., Ibrahimbegovic, A.: On numerical implementation of a coupled rate-dependent damage-plasticity constitutive model for concrete in application to high rate dynamics. Int. J. Eng. Comput. 22(5–6), 583 (2005)zbMATHGoogle Scholar
  4. 4.
    Travaš, V., Ožbolt, J., Kožar, I.: Failure of plain concrete beam at impact load: 3D finite element analysis. Int. J. Fract. 160(1), 31 (2009)CrossRefGoogle Scholar
  5. 5.
    Bede, N., Ožbolt, J., Sharma, A., Irhan, B.: Dynamic fracture of notched plain concrete beams: 3D finite element study. Int. J. Impact Eng. 77, 176 (2015)CrossRefGoogle Scholar
  6. 6.
    Marino, S., Hogue, I.B., Ray, C.J., Kirschner, D.E.: A methodology for performing global uncertainty and sensitivity analysis in systems biology. J. Theor. Biol. 254(1), 178 (2008)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Marenic, E., Ibrahimbegovic, A.: Homogenized elastic properties of graphene for moderate deformations. Coupled Syst. Mech. 4(2), 137 (2015)CrossRefGoogle Scholar
  8. 8.
    Bolander, J.E., Sukumar, N.: Irregular lattice model for quasistatic crack propagation. Phys. Rev. B 71(9), 094106 (2005)CrossRefGoogle Scholar
  9. 9.
    Nikolić, M., Karavelić, E., Ibrahimbegovic, A., Miščević, P.: Lattice element models and their peculiarities. Arch Comput. Methods Eng. 25(3), 753–784 (2018)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kožar, I., Ožbolt, J., Pecak, T.: Load-rate sensitivity in 1D non-linear viscoelastic model. Key Eng. Mater. 488, 731 (2012)Google Scholar
  11. 11.
    Pan, W., Li, X., Wang, L., Guo, N., Yang, Z.: Influence of contact stiffness of joint surfaces on oscillation system based on the fractal theory. Arch. Appl. Mech. 88(4), 525–541 (2018)CrossRefGoogle Scholar
  12. 12.
    Ožbolt, J., Li, Y., Kožar, I.: Microplane model for concrete with relaxed kinematic constraint. Int. J. Solids Struct. 38(16), 2683 (2001)CrossRefGoogle Scholar
  13. 13.
    Kun, F., Raischel, F., Hidalgo, R., Herrmann, H.: Extensions of fibre bundle models. In: Bhattacharyya, P., Chakrabarti, B. (eds.) Modelling Critical and Catastrophic Phenomena in Geoscience, pp. 627–637 (2007)Google Scholar
  14. 14.
    Murčinková, Z., Novák, P., Kompiš, V., Žmindák, M.: Homogenization of the finite-length fibre composite materials by boundary meshless type method. Arch. Appl. Mech. 88(5), 789–804 (2018)CrossRefGoogle Scholar
  15. 15.
    Dong, L., Wadley, H.: Mechanical properties of carbon fiber composite octet-truss lattice structures. Compos. Sci. Technol. 119, 26 (2015)CrossRefGoogle Scholar
  16. 16.
    Kožar, I., Torić Malić, N., Rukavina, T.: Inverse model for pullout determination of steel fibers. Coupled Syst. Mech. 7, 197 (2018)Google Scholar
  17. 17.
    Kožar, I., Ibrahimbegović, A., Rukavina, T.: Material model for load rate sensitivity. Coupled Syst. Mech. 7, 141 (2018)Google Scholar
  18. 18.
    Lozzi-Kožar, D., Kožar, I.: Estimation of the eddy thermal conductivity for lake botonega. Eng. Rev. 37(3), 322 (2017)zbMATHGoogle Scholar
  19. 19.
    Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.C.: Past, present and future of nonlinear system identification in structural dynamics. Mech. Syst. Signal Process. 20(3), 505 (2006)CrossRefGoogle Scholar
  20. 20.
    Ibrahimbegovic, A.: Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods. Springer, Berlin (2009)CrossRefGoogle Scholar
  21. 21.
    Simo, J., Hughes, T.: Computational Inelasticity. Springer, New York (1998)zbMATHGoogle Scholar
  22. 22.
    Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Springer, Berlin (1998)zbMATHGoogle Scholar
  23. 23.
    Ermentrout, B.: Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. Siam, Philadelphia (2002)CrossRefGoogle Scholar
  24. 24.
    Mathematica, W.: Wolfram research Inc. Champaign, Illinois (2009)Google Scholar
  25. 25.
    Perumal, T.M., Gunawan, R.: Understanding dynamics using sensitivity analysis: caveat and solution. BMC Syst. Biol. 5(1), 41 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Rijeka, Faculty of Civil EngineeringRijekaCroatia
  2. 2.Université de Technologie de Compiègne - Sorbonne Universités, Laboratoire Roberval de MécaniqueCompiègneFrance

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