International Journal of Fracture

, Volume 209, Issue 1–2, pp 235–240 | Cite as

Evaluation of Gurson yield function dependencies through large-scale void growth simulations

Brief Note


Numerical simulation of void growth from thousands of randomly distributed particles is used to assess the functional dependence of the Gurson model. Shock loading of the model region followed by a ramped pressure release creates a smoothly varying velocity field in which the void growth is inertially stabilized. The pressure, effective stress, and void fraction are obtained from the simulation for comparison with the Gurson model. The results show that the pressure-void fraction relation from the model reasonably follows the simulation data, but the numerical data exhibit significantly greater void fraction dependence on the effective stress than the Gurson model.


Void growth Porosity Ductile failure Gurson model 



The authors wish to acknowledge use of Frontier time on the Department of Defense High Performance Computers for this work.


  1. Becker R (2017) Direct numerical simulation of ductile spall failure. Int J Fract. doi: 10.1007/s10704-017-0198-y
  2. Callaghan K, Becker R (2017) Something about spall. In: Proceedings of the 20th conference on shock compression in condensed matter, St. Louis, MO., (AIP, 2018), p. Submitted for publicationGoogle Scholar
  3. Green R (1972) A plasticity theory for porous solids. Int J Mech Sci 14(4):215. doi: 10.1016/0020-7403(72)90063-X CrossRefGoogle Scholar
  4. Grüneisen E (1926) Handbuch der Physik, Zustand des festen Körpers, vol 10. Springer, Berlin, pp 1–59. doi: 10.1007/978-3-642-99531-6-1 Google Scholar
  5. Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part I—yield criteria and flow rules for porous ductile media. J Eng Mater Technol 99(1):2. doi: 10.1115/1.3443401 CrossRefGoogle Scholar
  6. Hopkinson B (1914) A method of measuring the pressure produced in the detonation of high explosives or by the impact of bullets. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, vol 213, p 437.
  7. Kuhn H, Downey C (1971) Deformation characteristics and plasticity theory of sintered powder materials. Int J Powder Metall 7(1):15Google Scholar
  8. Nahshon K, Hutchinson J (2008) Modification of the Gurson model for shear failure. Eur J Mech A Solids 27(1):1. doi: 10.1016/j.euromechsol.2007.08.002 CrossRefGoogle Scholar
  9. Nichols AL (2015) ALE3D. An arbitrary Lagrange/Eulerian 2D and 3D code system. Lawrence Livermore National Laboratory, V4.26 edn. LLNL-SM-681737Google Scholar
  10. Steinberg DJ, Cochran SG, Guinan MW (1980) A constitutive model for metals applicable at high-strain rate. J Appl Phys 51(3):1498. doi: 10.1063/1.327799 CrossRefGoogle Scholar
  11. Stewart JB, Cazacu O (2011) Analytical yield criterion for an anisotropic material containing spherical voids and exhibiting tension compression asymmetry. Int J Solids Struct 48(2):357. doi: 10.1016/j.ijsolstr.2010.10.009
  12. Torre C (1948) Theorie und Verhalten der zusammengepressten Pulver. Berg-Hüttenmänn. Monatsh. Montan. Hochschule Leoben 93:62Google Scholar
  13. Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fract 17(4):389. doi: 10.1007/BF00036191 CrossRefGoogle Scholar
  14. Vadillo G, Reboul J, Fernndez-Sez J (2016) A modified Gurson model to account for the influence of the Lode parameter at high triaxialities. Eur J Mech A Solids 56:31. doi: 10.1016/j.euromechsol.2015.09.010 CrossRefGoogle Scholar
  15. Wen J, Huang Y, Hwang K, Liu C, Li M (2005) The modified Gurson model accounting for the void size effect. Int J Plast 21(2):381. doi: 10.1016/j.ijplas.2004.01.004 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. (outside the USA) 2017

Authors and Affiliations

  1. 1.Impact Physics BranchU.S. Army Research Laboratory, Aberdeen Proving GroundAberdeenUSA
  2. 2.Academy of Applied ScienceConcordUSA
  3. 3.Department of Aerospace EngineeringUniversity of Maryland, College ParkCollege ParkUSA

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