Formulation of the return mapping algorithm for elastoplastic soil models

ADINA R&D, Inc. Theory and modeling guide, vol. I: ADINA, Report ARD 02-7, 2002;490–3 Aravas, 1987, On the numerical integration of a class of pressure-dependent plasticity models, Int. J. Numer. Meth. Eng., 24, 1395, 10.1002/nme.1620240713 Armero, 2002, On the formulation of closed-point projection algorithms in elastoplaticity – part I: the variational structure, Int. J. Numer. Meth. Eng., 53, 297, 10.1002/nme.278 Bathe, 1996 Borja, 1991, Cam-Clay plasticity, part II: implicit integration of constitutive equation based on a nonlinear elastic stress predictor, Comput. Meth. Appl. Mech. Eng., 88, 225, 10.1016/0045-7825(91)90256-6 Borja, 1990, Cam-Clay plasticity, part I: implicit integration of elasto-plastic constitutive relations, Comput. Meth. Appl. Mech. Eng., 78, 49, 10.1016/0045-7825(90)90152-C Borja, 2003, On the numerical integration of three-invariant elstoplastic constitutive models, Comput. Meth. Appl. Mech. Eng., 192, 1227, 10.1016/S0045-7825(02)00620-5 Chen, 1990 Chowdhury, 1998, Consequences of the tij-concept and a new modeling approach, Comput. Geotech., 23, 131, 10.1016/S0266-352X(98)00017-2 Eterovic, 1990, A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures, Int. J. Numer. Meth. Eng., 30, 1099, 10.1002/nme.1620300602 Gajo, 1999, A kinematic hardening constitutive model for sands: the multiaxial formulation, Int. J. Numer. Anal. Meth. Geomech., 23, 925, 10.1002/(SICI)1096-9853(19990810)23:9<925::AID-NAG19>3.0.CO;2-M Jeremic, 1997, Implicit integration in elastoplastic geotechanics, Mech. Cohesivie-Frictional Mater., 2, 165, 10.1002/(SICI)1099-1484(199704)2:2<165::AID-CFM31>3.0.CO;2-3 Kojic, 1987, Thermo-elastic–plastic and creep analysis of shell structures, Comput. Struct., 26, 135, 10.1016/0045-7949(87)90243-4 Kojic, 1987, The `effective-stress-function' algorithm for thermo-elasto-plasticity and creep, Int. J. Numer. Meth. Eng., 24, 1509, 10.1002/nme.1620240808 Kojic M, Bathe KJ. Inelastic Analysis of solids and structures. Goettingen: Springer (to appear) Krieg, 1977, Accuracies of numerical solution methods for elastic-perfectly plastic model, J. Pressure Vessel Technol. ASME, 99, 510, 10.1115/1.3454568 Matsuoka, 1974, Stress–strain deformation and strength characteristics of soil under three different principal stresses, Proc. JSCE, 232, 59 Matsuoka H, Nakai T. Stress–strain relationship of soil based on the “SMP”. In: Proc. Specialty Session 9, IXICSMFE, Tokyo 1977; p. 153–62 Nakai, 1986, A generalized elastoplastic constitutive model for clay in three-dimensional stresses, Soils Foundations, 26, 81, 10.3208/sandf1972.26.3_81 Nakai, 1984, A new mechanical quantity for soils and its application to elastoplastic constitutive models, Soils Foundations, 24, 82, 10.3208/sandf1972.24.2_82 Ortiz, 1985, Accuracy and stability of integration algorithms for elastoplastic constitutive relations, Int. J. Numer. Meth. Eng., 21, 1561, 10.1002/nme.1620210902 Ortiz, 1986, An analysis of a new class of integration algorithm for elastoplastic costitutive relations, Int. J. Numer. Meth. Eng., 23, 353, 10.1002/nme.1620230303 Perez-Foguet, 2002, On the formulation of closed-point projection algorithms in elastoplasticity – part II: globally convergent schemes, Int. J. Numer. Meth. Eng., 53, 331, 10.1002/nme.279 Simo, 1992, Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory, Comput. Meth. Appl. Mech. Eng., 99, 61, 10.1016/0045-7825(92)90123-2 Simo, 1998 Tamagnini, 2002, A generalized backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials, J. Numer. Anal. Meth. Geomech., 26, 963, 10.1002/nag.231 Wang, 2001, A stress integration algorithm for J3-dependent elasto-plasticity models, vol. 1, 542 Wang, 2002, Numerical modelling of shear bands by element bands, Int. J. Numer. Meth. Eng., 54, 1131, 10.1002/nme.464 Wang, 2003, Kinematic modelling of shear band localization using discrete finite elements, Int. J. Numer. Anal. Meth. Geomech., 27, 289, 10.1002/nag.274 Wang, 2003, Formulation and study of thermal–mechanical coupling for saturated porous media, Comput. Struct., 81, 1019, 10.1016/S0045-7949(02)00476-5 Xu, 2004, Numerical simulation of shear band in clayey soils using finite deformation theory, J. Geotech. Eng. (in Chinese), 26, 225 Zhang, 1995, Explicit consistent tangent moduli with a return mapping algorithm for pressure-dependent elastoplasticity models, Comput. Meth. Appl. Mech. Eng., 121, 29, 10.1016/0045-7825(94)00707-T Zhang, 1995, A class of generalized mid-point algorithms for the Gurson–Tvergaard material model, Int. J. Numer. Meth. Eng., 38, 2033, 10.1002/nme.1620381206