Roads and Bridges - Drogi i Mosty
11, 4, 2012, 295-310

The numerical modeling of failure of S235JR steel using Gurson-Tvergaard-Needleman material model

Paweł Kossakowski Mail
Kielce University of Technology, Faculty of Civil Engineering and Architecture


The paper presents assumptions of the Gurson-Tvergaard-Needleman (GTN) model for a porous materials, which is now one of the basic damage material models applied in the analysis of the load-bearing capacity of metal engineering structures. The practical information about the selection of GTN material parameters and performing numerical calculations is given. An example of the numerical simulation of the failure of tensile element made of S235JR steel is presented. The calculation procedure, the determined GTN microstructure parameters and the obtained results are described. The simulations included the strength analysis and the study of the micro-defects growth occurring during the plasticity process is presented. As a result the critical volume void fraction was determined which can be used as a microvoid criterion corresponding to the expected S235JR steel failure.


bridge, failure, Gurson-Tvergaard-Needleman Material Model, GTN, S235JR steel

Full Text:



Cotrell A.H.: Własności mechaniczne materii. PWN, Warszawa, 1970

Gurson A.L.: Continuum theory of ductile rupture by void nucleation and growth. Part I – Yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology, Transactions of the ASME, 99, 1, 1977, 2 - 15

Tvergaard V.: Influence of voids on shear band instabilities under plane strain conditions. International Journal of Fracture, 17, 4, 1981, 389 - 407

Tvergaard V., Needleman A.: Analysis of the cup-cone fracture in a round tensile bar. Acta Metallurgica, 32, 1, 1984, 157 - 169

PN-EN 1993-1-1:2006 Eurokod 3: Projektowanie konstrukcji stalowych – Część 1-1: Reguły ogólne i reguły dla budynków

PN-EN 1993-2:2010 Eurokod 3: Projektowanie konstrukcji stalowych – Część 2: Mosty stalowe

PN-EN 1993-1-10:2007 Eurokod 3: Projektowanie konstrukcji stalowych – Część 1-10: Dobór stali ze względu na odporność na kruche pękanie i ciągliwość międzywarstwową

Sedlacek G., Feldmann M., Kühn B., Tschickardt D., Höhler S., Müller C., Hensen W., Stranghöner N., Dahl W., Langenberg P., Münstermann S., Brozetti J., Raoul J., Pope R., Bijlaard F.: Commentary and worked examples to EN 1993-1-10 “Material toughness and through thickness properties” and other toughness oriented rules in EN 1993. JRC Scientific and Technical Reports, European Commission Joint Research Centre, Luxemburg, 2008

Kossakowski P.G.: An analysis of the load-carrying capacity of elements subjected to complex stress states with a focus on the microstructural failure. Archives of Civil and Mechanical Engineering, 10, 2, 2010, 15 - 39

Kossakowski P.G., Trąmpczyński W.: Numeryczna symulacja zniszczenia stali S235JR z uwzględnieniem wpływu uszkodzeń mikrostrukturalnych. Przegląd Mechaniczny, 70, 4, 2011, 15 - 22

Kossakowski P.G.: Simulation of ductile fracture of S235JR steel using computational cells with microstructurally-based length scales. Journal of Theoretical and Applied Mechanics, 50, 2, 2012, 589 - 607

Tvergaard V.: Material failure by void growth to coalescence. Advances in Applied Mechanics, 27, New York 1990, 83 - 151

Nahshon K., Hutchinson J.W.: Modification of the Gurson Model for shear failure. European Journal of Mechanics - A/Solids, 27, 1, 2008, 1 - 17

Faleskog J., Gao X., Shih C.F.: Cell model for nonlinear fracture analysis - I. Micromechanics calibration. International Journal of Fracture, 89, 4, 1998, 355 - 373

Richelsen A.B., Tvergaard V.: Dilatant plasticity or upper bound estimates for porous ductile solids. Acta Metallurgica et Materialia, 42, 8, 1994, 2561 - 2577

Zhang Z.L., Thaulow C., Řdegĺrd J.: A Complete Gurson model approach for ductile fracture. Engineering Fracture Mechanics, 67, 2, 2000, 155 - 168

Xia L., Shih C.F.: Ductile crack growth - I. A numerical study using computational cells with microstructurally-based length scales. Journal of the Mechanics and Physics of Solids, 43, 2, 1995, 233 - 259

PN-EN 10002-1:2004 Metale - Próba rozciągania - Część 1: Metoda badania w temperaturze otoczenia

Określenie struktury materiałów (pobranych z konstrukcji), analiza porównawcza z parametrami stali wzorcowej, Raport z badań w ramach projektu nr R04 007 01, Politechnika Warszawska, Warszawa, 2008

Abaqus 6.10 Analysis User’s Manual, Dassault Systčmes Simulia Corporation, Providence, 2010

The numerical modeling of failure of S235JR steel using Gurson-Tvergaard-Needleman material model

Kossakowski, Paweł. The numerical modeling of failure of S235JR steel using Gurson-Tvergaard-Needleman material model. Roads and Bridges - Drogi i Mosty, [S.l.], v. 11, n. 4, p. 295-310, apr. 2012. ISSN 2449-769X. Available at: <>. Date accessed: 22 Apr. 2019. doi: