Numerical studies of ductile failure including the third stress invariant

Abaqus Explicit (2012) SIMULIA, Providence

Anandarajah A (2010) Computational methods in elasticity and plasticity. Solids and porous media. Springer, New York

Aravas N (1987) On the numerical integration of a class of pressure-dependent plasticity models. Int J Numer Methods Eng 24:1395–1416

Barsoum I, Faleskog J (2007) Rupture in combined tension and shear: experiments. Int J Solids Struct 44:1768–1786

Benzerga AA (2002) Micromechanics of coalescence in ductile fracture. J Mech Phys Solids 50:1331–1362

Benzerga AA, Leblond J-B (2010) Ductile fracture by void growth to coalescence. In: Aref H, van der Giessen E (eds) Advances in applied mechanics, vol 44. Academic Press, New York, pp 169–305

Besson J (2001) Eprouvettes axisymétriques entaillées, chapter 10. In: François D (ed) Hermès Science, Paris, pp 319–351

Besson J (2010) Continuum models of ductile fracture: a review. Int J Damage Mech 19(1):3–52

Bonora N (1999) Identification and measurements of ductile damage parameters. J Strain Anal Eng Des 34:463–478

Borja RI, Sama KM, Sanz PF (2003) On the numerical integration of three-invariant elastoplastic constitutive models. Comput Methods Appl Mech Eng 192:1227–1258

Chaboche J-L, Cailletaud G (1996) Integration methods for complex plastic constitutive equations. Comput Methods Appl Mech Eng 133:125–155

Chu CC, Needleman A (1980) Void nucleation effects in biaxially stretched sheets. J Eng Mater Technol 102:249–256

Cowie JG, Azrin M, Olson GB (1989) Microvoid formation during shear deformation of ultrahigh strength steels. Metall Trans A 20A:143–153

Foster CD, Regueiro RA, Fossum AF, Borja RI (2005) Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials. Comput Methods Appl Mech Eng 194:5109–5138

Gao X, Kim J (2006) Modeling of ductile fracture: significance of void coalescence. Int J Solids Struct 43:6277–6293

Gologanu M, Leblond J-B, and Devaux J (1997) Recent extensions of Gurson’s model for porous ductile metals. In: Suquet P (ed) CISM lectures series. Springer, Berlin, pp 61–106

Gurson AL (1975) Plastic flow and fracture behavior of ductile materials incorporating void nucleation, growth and interaction. PhD thesis, Brown University, Providence

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 99:2–15

Hancock JW, Mackenzie AC (1976) On the mechanism of ductile fracture in high-strength steels subjected to multi-axial stress-states. J Mech Phys Solids 24:147–169

McClintock FA (1968) A criterion for ductile fracture by the growth of holes. J Appl Mech 33:363

McClintock FA, Kaplan SM, Berg CA (1966) A criterion for ductile fracture by the growth of holes. Int J Fract 2:3614–3627

Nahshon K, Hutchinson J (2008) Modification of the gurson model for shear failure. Eur J Mech A Solids 27:1–17

Nahshon K, Xue Z (2009) A modified gurson model and its application to punch-out experiments. Eng Fract Mech 76:997–1009

Pardoen T, Hutchinson JW (2000) An extended model for void growth and coalescence. J Mech Phys Solids 48:2467–2512

Pardoen T, Scheyvaerts F, Simar A, Tekoglu C, Onck PR (2010) Multiscale modeling of ductile failure in metallic alloys. C R Phys 11:326–345

Rice JR, Tracey DM (1969) On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17:201–217

Scheyvaerts F, Pardoen T, Onck PR (2010) A new model for void coalescence by internal necking. Int J Damage Mech 19(1):95–126

Sean McElwain DL, Roberts AP, and Wilkins AH (2006) Yield criterion for porous materials sujected to complex stress states. Acta Mater 54:1995–2002

Sean McElwain DL, Roberts AP, and Wilkins AH (2006) Yield functions for porous materials with cubic symmetry using different definitions of yield. Adv Eng Mater 8:870–876

Simo J, Hughes TJR (1998) Computational inelasticity. Springer, New York

Tamagnini C, Castellanza R, Nova R (2002) A generalized backward euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials. Int J Numer Anal Meth Geomech 26:963–1004

Thomason PF (1990) Ductile fracture of metals. Pergamon Press, Oxford

Tvergaard V (1981) Influence of voids on shear bands instabilities under plane strain conditions. Int J Fract 17:389–407

Tvergaard V (1989) Numerical study of localization in a void-sheet. Int J Solids Struct 10:1143–1156

Tvergaard V (1990) Materials failure by void growth to coalescence. In: Hutchinson JW, Wu T (eds) Advances in applied mechanics, vol 27. Academic Press, New York, pp 83–151

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

Tvergaard V, Nielsen KL (2010) Relations between a micro-mechanical model and a damage model for ductile failure in shear. J Mech Phys Solids 58:1243–1252

Wang X, Wang LB, Xu LM (2004) Formulation of the return mapping algorithm for elastoplastic soil models. Comput Geotech 31:315–338

Xue L (2008) Constitutive modeling of void shearing effect in ductile fracture of porous materials. Eng Fract Mech 75(11):3343–3366