A GTN-like Model for Plastic Porous Materials

L. Siad, S. C. Gangloff


An extended version of the well-known Gurson-Tvergaard-Needleman (GTN) isotropic hardening model is presented in this paper. The yield function of the proposed constitutive model possesses the distinctiveness to explicitly depend upon the third stress invariant. The presented constitutive model is used to analyze the necking of a round tensile bar. As long as softening initiation of specimen is not reached, the obtained numerical results highlight similarities and good agreement with those provided by the use of the GTN model. However, discrepancy shows up as soon as specimen failure starts.


constitutive modelling; ductile failure; necking; porous microstructures; tensile test; numerical simulations

Full Text:



V. Tvergaard, “Materials failure by void growth to coalescence”, in: Advances in Applied Mechanics, Vol. 27, pp. 83–151, Academic Press, New York, 1994

A. A. Benzerga, J. -B. Leblond, “Ductile fracture by void growth to coalescence”, in: Advances in Applied Mechanics, Vol. 44, pp. 169–305, Academic Press, New York, 2010

D. L. S. McElwain, A. P. Roberts, A. H. Wilkins, “Yield criterion of porous materials subjected to complex stress states”, Acta Materialia, Vol. 54, No. 8, pp. 1995-2002, 2006

L. Siad, “Ductile damage analysis based on a J3-GTN-like model”, Journal of Multiscale Modelling, Vol. 3, pp. 1-27, 2011

V. Tvergaard, A. Needleman, “Analysis of the cup-cone fracture in a round tensile bar”, Acta Metallurgica, Vol. 32, No. 1, pp.157–169, 1984

N. Aravas, “On the numerical integration of a class of pressure-dependent plasticity models”, International Journal for Numerical Methods in Engineering, Vol. 24, No. 7, pp.1395–1416, 1987

J. Simo, .J.R. Hughes, Computational inelasticity, Springer, 1998

A. Anandarajah, Computational Methods in Elasticity and Plasticity. Solids and Porous Media, Springer, 2010

J. Besson, ‘Eprouvettes axisymétriques entaillées’’, in D. François, éditeur, Essais mécaniques et lois de comportement, pp. 319–351. Hermès Science, Paris, 2001

N. Bonora, “Identification and measurements of ductile damage parameters”, The Journal of Strain Analysis for Engineering Design, Vol. 34, No. 6, pp. 463–478, 1999

eISSN: 1792-8036     pISSN: 2241-4487