Study on the definition of equivalent plastic strain under non-associated flow rule for finite element formulation

Barlat, 1991, A six-component yield function for anisotropic metals, International Journal of Plasticity, 7, 693, 10.1016/0749-6419(91)90052-Z Barlat, 2003, Plane stress yield function for aluminum alloy sheets – Part 1: Theory, International Journal of Plasticity, 19, 1297, 10.1016/S0749-6419(02)00019-0 Barlat, 2005, Linear transformation-based anisotropic yield functions, International Journal of Plasticity, 21, 1009, 10.1016/j.ijplas.2004.06.004 Barlat, 2007, On linear transformations of stress tensors for the description of plastic anisotropy, International Journal of Plasticity, 23, 876, 10.1016/j.ijplas.2006.10.001 Barlat, 2011, An alternative to kinematic hardening in classical plasticity, International Journal of Plasticity, 27, 1309, 10.1016/j.ijplas.2011.03.003 Bishop, 1951, XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses, Philosophical Magazine Series 7, 42, 414, 10.1080/14786445108561065 Bron, 2004, A yield function for anisotropic materials – application to aluminum alloys, International Journal of Plasticity, 20, 937, 10.1016/j.ijplas.2003.06.001 Cazacu, 2002, A new anisotropic yield criterion for aluminum alloys, Advanced Materials Forum I, 230-2, 537 Cazacu, 2004, A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals, International Journal of Plasticity, 20, 2027, 10.1016/j.ijplas.2003.11.021 Cazacu, 2004, New anisotropic constitutive models for HCP sheet forming simulations, 1046 Cazacu, 2006, Orthotropic yield criterion for hexagonal closed packed metals, International Journal of Plasticity, 22, 1171, 10.1016/j.ijplas.2005.06.001 Chung, 1996, Finite element simulation of sheet forming based on a planar anisotropic strain-rate potential, International Journal of Plasticity, 12, 93, 10.1016/S0749-6419(95)00046-1 Cleja-Ţigoiu, 2013, Orientational anisotropy and strength-differential effect in orthotropic elasto-plastic materials, International Journal of Plasticity, 47, 80, 10.1016/j.ijplas.2013.01.005 Cvitanic, 2008, A finite element formulation based on non-associated plasticity for sheet metal forming, International Journal of Plasticity, 24, 646, 10.1016/j.ijplas.2007.07.003 Gao, 2011, On stress-state dependent plasticity modeling: significance of the hydrostatic stress, the third invariant of stress deviator and the non-associated flow rule, International Journal of Plasticity, 27, 217, 10.1016/j.ijplas.2010.05.004 Gawad, 2013, Hierarchical multi-scale modeling of texture induced plastic anisotropy in sheet forming, Computational Materials Science, 66, 65, 10.1016/j.commatsci.2012.05.056 Hecker, 1976, Experimental studies of yield phenomena in biaxially loaded metals, 1 Hill, 1948, A theory of the yielding and plastic flow of anisotropic metals, Proceedings of the Royal Society of London Series A. Mathematical and Physical Sciences, 193, 281, 10.1098/rspa.1948.0045 Hu, 2007, Constitutive modeling of orthotropic sheet metals by presenting hardening-induced anisotropy, International Journal of Plasticity, 23, 620, 10.1016/j.ijplas.2006.08.004 Karafillis, 1993, A general anisotropic yield criterion using bounds and a transformation weighting tensor, Journal of the Mechanics and Physics of Solids, 41, 1859, 10.1016/0022-5096(93)90073-O Park, 2012, Non-associated flow rule with symmetric stiffness modulus for isotropic-kinematic hardening and its application for earing in circular cup drawing, International Journal of Solids and Structures, 49, 3582, 10.1016/j.ijsolstr.2012.02.015 Rousselier, 2009, A novel approach for anisotropic hardening modeling. Part I: Theory and its application to finite element analysis of deep drawing, International Journal of Plasticity, 25, 2383, 10.1016/j.ijplas.2009.04.002 Rousselier, 2010, A novel approach for anisotropic hardening modeling. Part II: Anisotropic hardening in proportional and non-proportional loadings, application to initially isotropic material, International Journal of Plasticity, 26, 1029, 10.1016/j.ijplas.2010.01.001 Safaei, 2013, An evolutionary anisotropic model for sheet metals based on non-associated flow rule approach, Computational Materials Science Safaei, 2013, Evaluation of anisotropic constitutive models: Mixed anisotropic hardening and non-associated flow rule approach, International Journal of Mechanical Sciences, 73, 53, 10.1016/j.ijmecsci.2013.04.003 Simo, 1998, Computational inelasticity Stoughton, 2002, A non-associated flow rule for sheet metal forming, International Journal of Plasticity, 18, 687, 10.1016/S0749-6419(01)00053-5 Stoughton, 2004, A pressure-sensitive yield criterion under a non-associated flow rule for sheet metal forming, International Journal of Plasticity, 20, 705, 10.1016/S0749-6419(03)00079-2 Stoughton, 2006, Review of Drucker’s postulate and the issue of plastic stability in metal forming, International Journal of Plasticity, 22, 391, 10.1016/j.ijplas.2005.03.002 Stoughton, 2008, On the existence of indeterminate solutions to the equations of motion under non-associated flow, International Journal of Plasticity, 4, 583, 10.1016/j.ijplas.2007.07.002 Stoughton, 2009, Anisotropic hardening and non-associated flow in proportional loading of sheet metals, International Journal of Plasticity, 25, 1777, 10.1016/j.ijplas.2009.02.003 Taherizadeh, 2010, A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming, International Journal of Plasticity, 26, 288, 10.1016/j.ijplas.2009.07.003 Taherizadeh, 2011, Evaluation of advanced anisotropic models with mixed hardening for general associated and non-associated flow metal plasticity, International Journal of Plasticity, 27, 1781, 10.1016/j.ijplas.2011.05.001 Van Houtte, P., 1995. The MTM-FHM Software System Version 2, Department of Metallurgy and Materials Engineering, KU Leuven. Van Houtte, 2005, Deformation texture prediction: from the Taylor model to the advanced Lamel model, International Journal of Plasticity, 21, 589, 10.1016/j.ijplas.2004.04.011 Van Houtte, 2011, A full-field strategy to take texture-induced anisotropy into account during FE simulations of metal forming processes, JOM, 63, 37, 10.1007/s11837-011-0189-9 Vegter, 2006, A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states, International Journal of Plasticity, 22, 557, 10.1016/j.ijplas.2005.04.009 Yoon, 1999, Elasto-plastic finite element method based on incremental deformation theory and continuum based shell elements for planar anisotropic sheet materials, Computer Methods in Applied Mechanics, 174, 23, 10.1016/S0045-7825(98)00275-8 Yoon, 2000, Earing predictions based on asymmetric nonquadratic yield function, International Journal of Plasticity, 16, 1075, 10.1016/S0749-6419(99)00086-8 Yoon, 2004, Plane stress yield function for aluminum alloy sheets – Part II: FE formulation and its implementation, International Journal of Plasticity, 20, 495, 10.1016/S0749-6419(03)00099-8 Yoon, 2006, Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function, International Journal of Plasticity, 22, 174, 10.1016/j.ijplas.2005.03.013 Yoon, 2007, Earing prediction in cup drawing based on non-associated flow rule, 685 Yoon, 2011, A new analytical theory for earing generated from anisotropic plasticity, International Journal of Plasticity, 27, 1165, 10.1016/j.ijplas.2011.01.002