0
REVIEW ARTICLES

Stress integration procedures for inelastic material models within the Finite Element Method

[+] Author and Article Information
Miloš Kojić

Faculty of Mechanical Engineering and Center for Scientific Research, Serbian Academy of Science and Arts, University of Kragujevac, 34000 Kragujevac, Serbia, Yugoslavia; kojic@knez.uis.kg.ac.yu

Appl. Mech. Rev 55(4), 389-414 (Jul 30, 2002) (26 pages) doi:10.1115/1.1482088 History: Online July 30, 2002
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.

References

Simo JC and Hughes TJR (1998), Computational Inelasticity, Springer-Verlag, NY.
Bathe KJ (1982), Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, NJ.
Bathe KJ (1996), Finite Element Procedures, Prentice-Hall, Englewood Cliffs, NJ.
Kojic M (1997), Computational Procedures in Inelastic Analysis of Solids and Structures, Center Sci Res Serbian Academy Sci Art and Univ Kragujevac, Kragujevac, Serbia.
Kojic M and Bathe KJ, Inelastic Analysis of Solids and Structures, Springer-Verlag, Berlin-Heidelberg, to be published.
Ilyushin  AA (1946), Some problems in the theory of plastic deformation, Prikl. Mat. Mekh. 7, 245–272, (1943); English translation, RMB-12, Grad Div Appl Math, Brown Univ.
Mendelson A (1968), Plasticity: Theory and Application, The Macmillan Co, NY.
Nayak  GC and Zienkiewicz  OC (1972), Elasto-plastic stress analysis. A generalization for various constitutive relations including strain softening, Int. J. Numer. Methods Eng. 5, 113–135.
Hinton E and Owen DRJ (1980), Finite Elements in Plasticity: Theory and Practice, Pineridge Press, Swansea, UK.
Chen F and Han DJ (1988), Plasticity for Structural Engineers, Springer-Verlag, NY.
Desai CS and Siriwardane HJ (1984), Constitutive Laws for Engineering Materials, Prentice-Hall, Englewood Cliffs, NJ.
Chen WF and Mizuno E (1990), Nonlinear Analysis in Soil Mechanics, Elsevier, Amsterdam.
Wood DM (1994), Soil Behavior and Critical State Soil Mechanics, Cambridge Univ Press, Cambridge.
Desai  CS, Somasundaram  S, and Frantziskonis  G (1986), A hierarchical approach for constitutive modelling of geologic materials, Int. J. Numer. Analyt. Meth. Geomech. 10, 225–257.
Prevost  JH (1977), Mathematical modelling of monotonic and cyclic undrained clay behavior, Int. J. Numer. Analyt. Meth. Geomech. 1, 195–216.
Dragon  A and Mroz  Z (1979), A continuum model for plastic-brittle behavior of rock and concrete, Int. J. Eng. Sci. 17, 121–137.
Desai  CS, Phan  HV, and Sture  S (1981), Procedure, selection and application of plasticity models for a soil, Int. J. Numer. Analyt. Meth. Geomech. 5, 295–311.
Desai  CS and Faruque  O (1984), Constitutive model for (geological) materials, J. Eng. Mech. 110, 1391–1408.
Desai  CS and Zhang  D (1987), Viscoplastic model for geologic materials with generalized flow rule, Int. J. Numer. Analyt. Meth. Geomech. 11, 603–620.
Desai  CS and Siriwardane  JH (1980), A concept of correction functions account for non-associative characteristics of geologic media, Int. J. Numer. Analyt. Meth. Geomech. 4, 377–387.
Langen  H Van and Vermeer  PA (1990), Automatic step size correction for non-associated plasticity problems, Int. J. Numer. Methods Eng. 29, 579–598.
Bathe  KJ, Snyder  MD, Cimento  AP, and Rolph  WD (1980), On some current procedures and difficulties in finite element analysis of elastic-plastic response, Comput. Struct. 12, 607–624.
Zienkiewicz  OC, Valliappan  S, and King  IP (1969), Elasto-plastic solutions of engineering problems; initial stress finite element approach, Int. J. Numer. Methods Eng. 1, 75–100.
Siriwardane  HJ and Desai  CS (1983), Computational procedures for non-linear three-dimensional analysis with some advanced constitutive laws, Int. J. Numer. Analyt. Meth. Geomech. 7, 143–171.
Bicanic  NP (1989), Exact evaluation of contact stress state in computational elasto-plasticity, Eng. Comput. 6, 67–73.
Marques  JMMC (1984), Stress computation in elastoplasticity, Eng. Comput. 1, 43–51.
Marques  JMMC and Owen  DRJ (1984), Some reflections on elastoplastic stress calculation in finite element analysis, Comput. Struct. 18(6), 1135–1139.
Bushnell  D (1977), A strategy for the solution of problems involving large deflections, plasticity and creep, Int. J. Numer. Methods Eng. 11, 683–708.
Faruque  MO and Desai  CS (1985), Implementation of a general constitutive model for geological materials, Int. J. Numer. Analyt. Meth. Geomech. 9, 415–436.
Marcal  PV (1965), A stiffness method for elastic-plastic problems, Int. J. Mech. Sci. 7, 229–238.
Rice JR and Tracey DM (1973), Computational fracture mechanics, in Numerical and Computer Methods in Structural Mechanics, SJ Fendes (ed), Academic Press, NY.
Drysdale  WH and Zak  AR (1985), A theory for rate-dependent plasticity, Comput. Struct. 20(1–3), 259–264.
Penny RK and Marriott (1971), Design for Creep, McGraw-Hill, London.
Penny  RK (1967), The creep of spherical shells containing discontinuities, Int. J. Mech. Sci. 9, 373–388.
Parkes DAC and Webster JJ (1974), Finite element solutions for two transient creep problems, in Creep and Fatigue in Elevated Temperature Applications, 1 Mech Eng Publ, London, 157, 1–9.
Burke  MA and Nix  WD (1979), A numerical analysis of void growth in tension creep, Int. J. Solids Struct. 15, 55–71.
Hyde TH, Webster JJ, Hardy SJ, and Yahaioui K (1984), Elastic-plastic-creep analysis of the thermal ratchetting of thick, enlarged tubes and comparisons with experimental results, in Pressure Vessel Technology, Vol. 1, Design and Analysis, ASME, NY, 418–442.
Desai  CS and Fishman  KL (1991), Plasticity-based constitutive model with associated testing for joints, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 28, 15–26.
Krieg  RD and Krieg  DB (1977), Accuracies of numerical solution methods for the elastic-perfectly plastic model, ASME J. Pressure Vessel Technol. 99, 510–515.
Schreyer  HL, Kulak  RF, and Kramer  JM (1979), Accurate Numerical Solutions for Elastic-Plastic Models, ASME J. Pressure Vessel Technol. 101, 226–234.
Simo  JC and Taylor  RL (1985), Consistent tangent operators for rate-independent elastoplasticity, Comput. Methods Appl. Mech. Eng. 48, 101–118.
Ortiz  M and Popov  EP (1985), Accuracy and stability of integration algorithms for elastoplastic constitutive relations, Int. J. Numer. Methods Eng. 21, 1561–1576.
Wilkins ML (1964), Calculation of elastic-plastic flow, in Methods in Computational Physics3 , B Alder (ed), Academic Press, New York and London, 211–263.
Ortiz  M, Pinsky  PM, and Taylor  RL (1983), Operator split methods for the numerical solution of the elastoplastic dynamic problem, Comput. Methods Appl. Mech. Eng. 39, 137–157.
Simo  JC and Ortiz  M (1985), A unified approach to finite deformation elastoplasticity based on use of hyperelastic constitutive equations, Comput. Methods Appl. Mech. Eng. 49, 221–245.
Ortiz  M and Simo  JC (1986), An analysis of a new class of integration algorithms for elastoplastic constitutive relations, Int. J. Numer. Methods Eng. 23, 353–366.
Simo  JC and Govindjee  S (1988), Exact closed-form solution of the return mapping algorithm in plane stress elasto-viscoplasticity, Eng. Comput. 5, 254–258.
Simo  JC and Taylor  RL (1986), A return mapping algorithm for plane stress elastoplasticity, Int. J. Numer. Methods Eng. 22, 649–670.
Simo  JC (1987a), A J2-flow theory exhibiting a corner-like effect and suitable for large-scale computation, Comput. Methods Appl. Mech. Eng. 62, 169–194.
Simo  JC (1987b), On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects, Comput. Methods Appl. Mech. Eng. 60, 153–173.
Pinsky  PM (1987), A finite element formulation for elastoplasticity based on a three-field variational equation, Comput. Methods Appl. Mech. Eng. 61, 41–60.
Simo  JC, Ju  JW, Pister  KS, and Taylor  RL (1988a), Assessment of cap model: consistent return algorithms and rate-dependent extension, J. Eng. Mech. 114, 191–218.
Simo  JC, Kennedy  JG, and Govindjee  S (1988b), Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms, Int. J. Numer. Methods Eng. 26, 2161–2185.
Ortiz  M and Martin  JB (1989), Symmetry-preserving return mapping algorithms and incrementally external paths: A unification of concept, Int. J. Numer. Methods Eng. 28, 1839–1853.
Simo  JC, Kennedy  JG, and Taylor  RL (1989), Complementary mixed finite element formulations for elastoplasticity, Comput. Methods Appl. Mech. Eng. 74, 177–206.
Peric  D (1993), On a class of constitutive equations in viscoplasticity: formulation and computational issues, Int. J. Numer. Methods Eng. 36, 1365–1393.
Luccioni  B, Oller  S, and Danesi  R (1996), Coupled plastic-damaged model, Comput. Methods Appl. Mech. Eng. 129, 81–89.
Svedberg  T and Runesson  K (1998), An algorithm for gradient-regularized plasticity coupled to damage based on a dual mixed FE-formulation, Comput. Methods Appl. Mech. Eng. 161, 49–65.
Alawaji  H, Runesson  K, Sture  S, and Axelsson  K (1992), Implicit integration in soil plasticity under mixed control for drained and undrained response, Int. J. Numer. Analyt. Meth. Geomech. 16, 737–756.
De Borst  R and Feenstra  P (1990), Studies in anisotropic plasticity with reference to the Hill criterion, Int. J. Numer. Methods Eng. 29, 315–336.
Jeremic  B and Sture  S (1998), Tensor object in finite element programming, Int. J. Numer. Methods Eng. 41, 113–126.
Sture  S, Runesson  K, and Macari-Pasqualino  (1989), Analysis and calibration of a three-invariant plasticity model for granular materials, Ing. Arch. 59, 253–266.
Crisfield MA (1987), Consistent schemes for plasticity computation with the Newton-Raphson method, in Computational Plasticity Models, Software, and Applications, Vol 1, DRJ Owen et al. (eds), Pineridge Press, Swansea, 133–159.
Braudel  HJ, Abouaf  M, and Chenot  L (1986), An implicit and incremental formulation for the solution of elastoplastic problems by the finite element method, Comput. Struct. 22, 801–814.
Jetteur  P (1986), Implicit integration algorithm for elastoplasticity in plane stress analysis, Eng. Comput. 3, 251–253.
Dodds  RH (1987), Numerical techniques for plasticity computations in finite element analysis, Comput. Struct. 26, 767–779.
Ramm  E and Matzenmiller  E (1988), Consistent linearization in elasto-plastic shell analysis, Eng. Comput. 5, 289–299.
Mitchell  GP and Owen  DRJ (1988), Numerical solutions for elastic-plastic problems, Eng. Comput. 5, 274–284.
Pramono  E and Willam  K (1989), Implicit integration of composite yield surfaces with corners, Eng. Comput. 6, 186–197.
Pramono  E and Wiliam  KJ (1988), Fracture energy-based plasticity formulation of plane concrete, J. Eng. Mech. 115, 11–1204.
Borja  RI and Lee  RS (1990), Cam-Clay plasticity, Part I: Implicit integration of elasto-plastic constitutive relations, Comput. Methods Appl. Mech. Eng. 78, 49–72.
Borja  RI (1991), Cam-Clay plasticity, Part II: Implicit integration of constitutive equation based on a nonlinear elastic stress predictor, Comput. Methods Appl. Mech. Eng. 88, 225–240.
Weber  G and Anand  L (1990), Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids, Comput. Methods Appl. Mech. Eng. 79, 173–202.
Runesson  K, Sture  S, and Willam  K (1988), Integration in computational plasticity, Comput. Struct. 30, 119–130.
Runesson  K, Samuelsson  A, and Bernspang  L (1986), Numerical technique in plasticity including solution advancement control, Int. J. Numer. Methods Eng. 36, 1365–1393.
Runesson  K (1987), Implicit integrations of elastoplastic relations with reference to soils, Int. J. Numer. Analyt. Meth. Geomech. 11, 315–321.
Runesson  K and Larsson  R (1993), Properties of incremental solutions for dissipative material, J. Eng. Mech. 119, 647–666.
Matthies  HG (1989), A decomposition method for the integration of the elastic-plastic rate problem, Int. J. Numer. Methods Eng. 28, 1–11.
Kuhn H and Tucker A (1951), Nonlinear programming, in Proc of 2nd Berkeley Symp on Mathematical Statistics and Probability, J Neyman (ed), Univ California Press, Berkeley and LA, 481–492.
Koiter WT (1960), General theorems for elastic-plastic solids, in Progress in Solid Mechanics, S Sneddon and R Hill (eds), North-Holland, Amsterdam, pp. 165.
Bathe KJ, Chaudhary AB, Dvorkin EN, and Kojic M (1984), On the solution of nonlinear finite element equations, in Proc of Int Conf on Computer-Aided Analysis and Design of Concrete Structures I, F Damjanic et al. (eds), Pineridge Press, Swansea, UK, 289–299.
Kojic  M and Bathe  KJ (1987a), The effective-stress-function algorithm for thermo-elasto-plasticity and creep, Int. J. Numer. Methods Eng. 24, 1509–1532.
Kojic  M and Bathe  KJ (1987b), Thermo-elastic-plastic and creep analysis of shell structures, Comput. Struct. 26, 135–143.
Willam  KJ (1978), Numerical solution of inelastic rate processes, Comput. Struct. 8, 511–531.
Snyder MD and Bathe KJ (1978), Finite element analysis of thermo-elastic-plastic and creep response, Report 82448-10, Acoustic and Vibration Lab, Mech Eng Dept, MIT.
Snyder  MD and Bathe  KJ (1981), A solution procedure for thermo-elastic-plastic and creep problems, Nucl. Eng. Des. 64, 49–80.
Kojic  M (1996), The governing parameter method for implicit integration of viscoplastic constitutive relations for isotropic and orthotropic metals, Comput. Mech. 19, 49–57.
Kojic M (1993), A General Concept for Implicit Stress Integration of Inelastic Constitutive Relations, (in Serbian), Center Sci Res Serbian Academy Sci Art and Univ Kragujevac, Kragujevac, Serbia.
Kojic M (1992), An implicit procedure for stress integration of a general anisotropic von Mises material, Proc of Int Conf on Comput Plasticity, COMPLAS III, Pineridge Press, Swansea, UK.
Kojic M, Begovic D, and Grujovic N (1995a), A computational procedure for implicit stress integration of anisotropic thermo-plastic and/or anisotropic creep constitutive relations of metals, in Computational Plasticity, DRJ Owen and E Onate (eds), Pineridge Press, Swansea, UK, 249–259.
Kojic  M, Grujovic  N, Slavkovic  R, and Kojic  A (1995b), Elastic-plastic orthotropic pipe deformation under external load and internal pressure, AIAA J. 33, 2354–2358.
Kojic  M, Zivkovic  M, and Kojic  A (1995c), Elastic-plastic analysis of orthotropic multilayered beam, Comput. Struct. 57, 205–211.
Kojic  M, Grujovic  N, Slavkovic  R, and Zivkovic  M (1996), A general orthotropic von Mises plasticity material model with mixed hardening: model definition and implicit stress integration procedure, ASME J. Appl. Mech. 63, 376–382.
Kojic  M, Slavkovic  R, Grujovic  N, and Vukicevic  M (1994), Implicit stress integration algorithm for modified Cam-clay material, Theor. Appl. Mech. (Yugoslavian) 20, 95–118.
Kojic M and Vukicevic M (1997), Elastic-plastic analysis of soil by using bounding surface Cam-clay model, in Computational Plasticity, DRJ Owen, E Onate, and E Hinton (eds), CIMNE, Barcelona, 1691–1695.
Kojic  M, Vlastelica  I, and Zivkovic  M (2002), Implicit stress integration procedure for small and large strains of the Gurson material model, Int. J. Numer. Methods Eng. 53, 2701–2720.
Kojic M, Slavkovic R, Grujovic N, and Zivkovic M (1995d), Implicit stress integration procedure for the generalized cap model in soil plasticity, in Computational Plasticity, DRJ Owen and E Onate (eds), Pineridge Press, Swansea, UK, 1809–1820.
Kojic M (2000a), Inelastic analysis of shell-type structures, IASS-IACM 2000 4th Int Coll Comput Shell Spat Struct, June 5–7 2000, Chania-Crete, Greece.
Kojic M, Zivkovic M, Slavkovic R, Grujovic N, and Vlastelica I (2000b) A procedure for large strain elastic-plastic analysis of shells, IASS-IACM 2000 4th Int Coll Comput Shell Spat Struct, June 5–7 2000, Chania-Crete, Greece.
Nagtegaal  JC (1982), On the implementation of inelastic constitutive equations with special reference to large deformation problems, Comput. Methods Appl. Mech. Eng. 33, 469–484.
Larsson  R and Runesson  K (1996), Implicit integration and consistent linearization for yield criteria of the Mohr-Coulomb type, Int J Mech Cohesive-Frict. Mater. Struct. 1, 367–383.
Jeremic  B and Sture  S (1997), Implicit integrations in elasto-plastic geotechnics, Int. J. Mech. Cohesive-Frict. Mater. Struct. 2, 1–19.
Miehe  C (1996), Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational elasticity, Comput. Methods Appl. Mech. Eng. 134, 223–240.
Hill R (1978), Aspects of invariance in solid mechanics, in Advances in Applied Mechanics, CS Yih (ed), 18 , Academic Press, NY, 1–75.
Hughes  TJR and Winget  J (1980), Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis, Int. J. Numer. Methods Eng. 20, 1862–1867.
Rashid  MM (1993), Incremental kinematics for finite element applications, Int. J. Numer. Methods Eng. 36, 3937–3956.
Kojic  M and Bathe  KJ (1987c), Studies of finite element procedures-stress solution of a closed elastic strain path with stretching and shearing using the updated Lagrangian-Jaumann formulation, Comput. Struct. 26, 175–179.
Dienes  JK (1979), On the analysis of rotation and stress rate in deforming bodies, Acta Mech. 32, 217–232.
Dafalias  YF (1983), Corotational rates for kinematic hardening at large plastic deformations, ASME J. Appl. Mech. 50, 561–565.
Lee  EH, Mallet  RL, and Wertheimer  TB (1983), Stress Analysis for Anisotropic Hardening in Finite-Deformation Plasticity, ASME J. Appl. Mech. 50, 554–560.
Pinsky  PM, Ortiz  M, and Pister  KS (1983), Numerical integration of rate constitutive equations in finite deformation analysis, Comput. Methods Appl. Mech. Eng. 40, 137–158.
Reed  KW and Atluri  SN (1983), Analysis of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm, Comput. Methods Appl. Mech. Eng. 39, 245–295.
Saran  J and Runesson  K (1992), A generalized closest-point-projection method for deformation-neutralized formulation in finite strain plasticity, Eng. Comput. 9, 359–370.
Nishiguchi  I, Sham  T-L, and Krempl  E (1990), A finite deformation theory of viscoplasticity based on overstress: Part I-Constitutive equations, ASME J. Appl. Mech. 57, 548–552.
Hibbitt  HD, Marcal  PB, and Rice  JR (1970), A finite element formulation for problems of large strain and large displacement, Int. J. Solids Struct. 6, 1069–1086.
Key  SW (1974a), A finite element procedure for the large deformation dynamic response of axisymmetric solids, Comput. Methods Appl. Mech. Eng. 4, 195–218.
Key SW (1974b), On an implementation of finite strain plasticity in transient dynamic large-deformation calculations, in Theoretical Foundation for Large-Scale Computations of Nonlinear Material Behavior, S Nemat-Nasser, RJ Assaro, and GA Hegemier (eds), Matrinus Nijhoff Pub, 99–108.
Nagtegaal  JC, Parks  DM, and Rice  JR (1974), On numerically accurate finite element solutions in the fully plastic range, Comput. Methods Appl. Mech. Eng. 4, 153–177.
Krieg RD and Key SW (1976), Implementation of a time independent plasticity theory into structural computer programs, in Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects, Winter Annual Meeting of ASME, NY.
Key  SW and Krieg  RD (1982), On the numerical implementation of inelastic time dependent and time independent, finite strain constitutive equations in structural mechanics, Comput. Methods Appl. Mech. Eng. 33, 439–452.
Reed  KW and Atluri  SN (1984), Hybrid stress finite elements for large deformations of inelastic solids, Comput. Struct. 19(1–2), 175–182.
Flangan  DP and Taylor  LM (1987), An accurate numerical algorithm for stress integration with finite rotations, Comput. Methods Appl. Mech. Eng. 62, 305–320.
Weber  GG, Lush  AM, Zavaliangos  A, and Anand  L (1990), An objective time-integration procedure for isotropic rate-independent and rate dependent elastic-plastic constitutive equations, Int. J. Plast. 6, 701–744.
Nemat-Nasser  S and Li  YF (1992), A new explicit algorithm for finite-deformation elastoplasticity and elastoviscoplasticity: performance evaluation, Comput. Struct. 44, 937–963.
Li  YF and Nemat-Nasser  S (1993), An explicit integration scheme for finite-deformation plasticity in finite element methods, Finite Elem. Anal. Design 15, 93–102.
Wang  LH and Atluri  SN (1994), An analysis of an explicit algorithm and the radial return algorithm, and proposed modification, in finite plasticity, Comput. Mech. 13, 380–389.
Rodriguez-Ferran  A, Pegon  P, and Huerta  A (1997), Two stress update algorithms for large strains: accuracy analysis and numerical implementation, Int. J. Numer. Methods Eng. 40, 4363–4404.
Lush  AM, Weber  G, and Anand  L (1987), An implicit time-integration procedure for a set of internal variable constitutive equations for isotropic elasto/viscoplasticity, Int. J. Plast. 5, 521–549.
Hill  R (1968), On constitutive inequalities for simple materials-I, J. Mech. Phys. Solids 16, 229–242.
Hoger  A (1986), The material time derivative of logarithmic strain, Int. J. Solids Struct. 22, 1019–1032.
Nemat-Nasser  S (1982), On finite deformation elasto-plasticity, Int. J. Solids Struct. 18, 857–872.
Ogden RW (1984), Non-Linear Elastic Deformations, Ellis Horwood, Chichester, England.
Peric  D, Owen  DRJ, and Honnor  ME (1992), A model for finite strain elasto-plasticity based on logarithmic strains: Computational issues, Comput. Methods Appl. Mech. Eng. 94, 35–61.
Hill  R (1970), Constitutive inequalities for isotropic elastic solids under finite strain, Proc. R. Soc. London, Ser. A A314, 457–472.
Atluri  SN (1984), Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational anlyses of finitely deformed solids, with application to plates and shells-I, Comput. Struct. 18, 93–116.
Green  AE and Naghdi  PM (1965), A general theory of an elastic-plastic continuum, Arch. Ration. Mech. Anal. 18, 251–281.
McMeeking  RM and Rice  JR (1975), Finite element formulation for problems of large elastic-plastic deformation, Int. J. Solids Struct. 11, 601–616.
Nagtegaal  JD and Jong  JE De (1981), Some computational aspects of elastic-plastic large strain analysis, Int. J. Numer. Methods Eng. 17, 15–41.
Kim  SJ and Oden  JT (1985), Finite element analysis of a class of problems in finite elastoplasticity based on the thermodynamic theory of materials of type N, Comput. Methods Appl. Mech. Eng. 53, 277–302.
Nagtegaal JC and Veldpaus FE (1984), On the implementation of finite strain plasticity equations in a numerical model, in Numerical Analysis of Forming Processes, JF Pitman, OC Zienkiewicz, RD Wood, and JM Alexander (eds), J Wiley & Sons Ltd, 351–371.
Nemat-Nasser S (1984), Theoretical foundations of plasticity, in Theoretical Foundation for Large-Scale Computations of Nonlinear Material Behavior, S Nemat-Nasser, RJ Assaro, and GA Hegemier (eds), Matrinus Nijhoff Pub, 7–24.
Reed  KW and Atluri  SN (1985), Constitutive modeling and computational implementation for finite strain plasticity, Int. J. Plast. 1, 63–87.
Lee  EH and Liu  DT (1967), Finite strain elastic-plastic theory particularly for plane wave analysis, J. Appl. Phys. 38, 19–28.
Lee  EH (1969), Elastic-Plastic Deformation at Finite Strains, ASME J. Appl. Mech. 36, 1–6.
Hill  R (1966), Generalized constitutive relations for incremental deformation of metal crystals by multislip, J. Mech. Phys. Solids 14, 95–102.
Hill  R and Rice  JR (1972), Constitutive analysis of elastic-plastic crystals at arbitrary strain, J. Mech. Phys. Solids 20, 401–443.
Hill  R and Rice  JR (1973), Elastic potentials and the structure of inelastic constitutive laws, SIAM J. Appl. Mech. 25, 448–461.
Teodosiu  C and Sidorff  F (1976), A finite theory of the elastoviscoplasticity of single crystals, Int. J. Eng. Sci. 14, 713–723.
Asaro  RJ and Rice  JR (1977), Strain localization in ductile single crystals, J. Mech. Phys. Solids 25, 309–338.
Asaro RJ (1983), Micromechanics of crystals and polycrystals, Adv. Appl. Mech. 23.
Lubarda  VA and Lee  EH (1981), A correct definition of elastic and plastic deformation and its computational significance, ASME J. Appl. Mech. 48, 35–40.
Lubarda  VA (1991), Constitutive analysis of large elasto-plastic deformation based on the multiplicative decomposition of deformation gradient, Int. J. Solids Struct. 27, 885–895.
Miehe  C (1994), On the representation of Prandtl-Reuss tensors within the framework of multiplicative elastoplasticity, Int. J. Plast. 10, 609–621.
Peric D and Owen DRJ (1992), A model for large deformations of elasto-viscoplastic solids at finite strain: Computational Issues, in Finite Inelastic Deformations—Theory and Applications, D Besdo and E Stain (eds), Springer-Verlag, Berlin-Heidelberg, 300–309.
Katochvil  J (1973), On a finite strain theory of elastic-inelastic materials, Acta Mech. 16, 127–142.
Simo  JC (1988), A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. Part II: computational aspects, Comput. Methods Appl. Mech. Eng. 68, 1–31.
Moran  B, Ortiz  M, and Shih  F (1990), Formulation of implicit finite element methods for multiplicative finite deformation plasticity, Int. J. Numer. Methods Eng. 29, 483–514.
Simo  JC (1992), Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory, Comput. Methods Appl. Mech. Eng. 99, 61–112.
Muller-Hoeppe N and Stein E (1992), Modelling and computation of finite viscoplastic strains, in Finite Inelastic Deformations—Theory and Applications, D Besdo and E Stein (eds), Springer-Verlag, Berlin Heidelberg, 363–372.
Simo  JC and Meschke  G (1993), A new class of algorithms for classical plasticity extended to finite strains. Application to geomaterials, Comp. Mech. 11, 253–278.
Famiglietti  CM and Prevost  JH (1994), Solution of the slump test using a finite deformation elasto-plastic Drucker-Prager model, Int. J. Numer. Methods Eng. 37, 3869–3903.
Kojic M, Slavkovic R, Grujovic N, and Zivkovic M (1995e), A solution procedure for large strain plasticity of the modified Cam-clay material, in Proc. of 4th Greek Natl Congress on Mech, PS Theocaris and EE Gdoutos (eds), 511–518.
Simo  JC and Taylor  RL (1991), Quasi-incompressible finite elasticity in principal stretches: Continuum basis and numerical algorithms, Comput. Methods Appl. Mech. Eng. 85, 273–310.
Jeremic B (1997), Finite deformation hyperelasto-plasticity of geomaterials, PhD thesis, Univ Colorado, Boulder.
Papadopoulos  P and Lu  J (1998), A general framework for the numerical solution of problems in finite elasto-plasticity, Comput. Methods Appl. Mech. Eng. 159, 1–18.
Miehe  C (1998b), A formulation of finite elastoplasticity based on dual co- and contravariant eigenvector triads normalized with respect to a plastic metric, Comput. Methods Appl. Mech. Eng. 159, 223–260.
Bathe KJ, Slavkovic R, and Kojic M (1986), On large strain elasto-plastic and creep analysis, Finite Element Methods for Nonlinear Problems, in P Bergan, KJ Bathe, and W Wunderlich (eds), Springer Verlag, Berlin-Heidelberg, 175–190.
Eterovic  AL and Bathe  KJ (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. Methods Eng. 30, 1099–1114.
Cuitino  A and Ortiz  M (1992), A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics, Eng. Comput. 9, 437–451.
Miehe  C, Stein  E, and Wagner  W (1994), Associative multiplicative elasto-plasticity: formulation and aspects of the numerical implementation including stability analysis, Comput. Struct. 52, 969–978.
Dvorkin  EN, Pantuso  D, and Repetto  EA (1994), A finite element formulation for finite strain elasto-plastic analysis based on mixed interpolation of tensorial components, Comput. Methods Appl. Mech. Eng. 114, 35–54.
Gabriel  G and Bathe  KJ (1995), Some computational issues in large strain elasto-plastic analysis, Comput. Struct. 56, 249–267.
Jeremic B, Runesson K, and Sture S (1998), Large deformation constitutive integration algorithm, Proc of 12th Conf, Eng Mech Div ASCE, La Jolla, CA, 1029–1032.
Jeremic  B, Runesson  K, and Sture  S (1999b), A model for elastic-plastic pressure sensitive materials subjected to large deformations, Int. J. Solids Struct. 36, 4901–4918.
Kojic M, Slavkovic R, Grujovic N, and Zivkovic M (1999), PAK-S—Program for Linear and Nonlinear Structural Analysis, Center for Sci Res Serbian Academy Sci Art and Univ Kraguaguj, Serbia.
Simo  JC and Miehe  C (1992), Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation, Comput. Methods Appl. Mech. Eng. 98, 41–104.
Miehe  C (1995), Entropic thermoelasticity at finite strains. Aspects of the formulation and numerical implementation, Comput. Methods Appl. Mech. Eng. 120, 243–269.
Crandall S, Dahl N, and Lardner T (1972), An introduction to Mechanics of Solids, Second Edition, McGraw-Hill Book Co., NY.
Anand  L (1979), On H. Hencky’s approximate strain-energy function for moderate deformations, ASME J. Appl. Mech. 46, 78–82.
Bazant ZP (1997), Recent advances in brittle-plastic compression failure: Damage localization, scaling and finite strain, in Computational Plasticity, DRJ Owen, E Onate, and E Hinton (eds), CIMNE, Barcelona, 3–19.
de Souza  EA Neto, Peric  D, and Owen  DRJ (1994), A model for elastoplastic damage at finite strains: algorithmic issues and applications, Eng. Comput. 11, 257–281.
Borja  RI and Alarcon  E (1995), A mathematical framework for finite strain elastoplastic consolidation. Part 1: Balance laws, variational formulation, and linearization, Comput. Methods Appl. Mech. Eng. 122, 145–171.
Gelin JC and Boisse P (1992), Finite inelastic deformations of three-dimensional shells with applications to sheet metal forming processes, in Finite Inelastic Deformations—Theory and Applications, D Besdo and E Stein (eds), Springer-Verlag, Berlin Heidelberg, 373–387.
Ibrahimbegovic  A (1994), Finite elastoplastic deformations of space-curved membranes, Comput. Methods Appl. Mech. Eng. 119, 371–394.
Batoz JL and Guo YQ (1997), Analysis and design of sheet forming parts using a simplified inverse approach, in Computational Plasticity, DRJ Owen, E Onate, and E Hinton (eds), CIMNE, Barcelona, 178–195.
Miehe  C (1998a), A theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains, Comput. Methods Appl. Mech. Eng. 155, 193–233.
Kojic  M (2002), An extension of 3-D procedure to large strain analysis of shells, Comput. Methods Appl. Mech. Eng. 191, 2447–2462.
Dafalias  YF (1984), The plastic spin concept and a simple illustration of its role in finite deformations, Mech. Mater. 3, 323–333.
Dafalias  YF (1985), The plastic spin, ASME J. Appl. Mech. 52, 865–871.
Aravas  N (1994), Finite strain anisotropic plasticity and plastic spin, Modell. Simul. Mater. Sci. Eng. 2, 483–504.
Biot MA (1965), Mechanics of Incremental Deformations, Wiley, New York.
Pereda  JJ, Aravas  N, and Bassani  JL (1993), Finite deformation of anisotropic polymers, Mech. Mater. 15, 3–20.
Bathe  KJ and Dvorkin  EN (1984), A formulation of general shell elements—The use of mixed interpolation of tensorial components, Int. J. Numer. Methods Eng. 22, 697–722.
Simo  JC and Armero  F (1992a), Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes, Int. J. Numer. Methods Eng. 33, 1413–1449.
Wilkins  M and Guinan  MW (1973), Impact of cylinders on a rigid boundary, J. Appl. Phys. 44, 1200–1206.
Slavkovic  R, Zivkovic  M, and Kojic  M (1994), Enhanced 8-node three-dimensional solid and 4-node shell elements with incompatible generalized displacements, Comm Numer Method Eng 10, 699–709.
Simo  JC, Armero  F, and Taylor  RL (1993), Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems, Comput. Methods Appl. Mech. Eng. 110, 359–386.
Sun  DZ, Siegele  D, Vos  B, and Schmitt  W (1989), Application of local damage models to the numerical analysis of ductile rupture, Fatigue Fract. Eng. Mater. Struct. 12, 201–212.
Simo JC and Armero F (1992b), Recent advances in the numerical analysis of thermoplasticity at finite strains, in Finite Inelastic Deformations—Theory and Applications, D Besdo and E Stein (eds), Springer-Verlag, Berlin Heidelberg, 259–272.
Armero F (1997), Localized anisotropic damage of brittle materials, in Computational Plasticity, DRJ Owen, E Onate, and E Hinton (eds), CIMNE, Barcelona, 635–640.
Filipovic N, Kojic M, and Zivkovic M (2000), Viscous flow in collapsible tube solved as a fluid solid interaction problem, IASS-IACM 2000 4th Int Coll Comput Shell Spat Struct, June 5–7 2000, Chania-Crete, Greece.
Makinouchi A, Nakamachi E, Onate E, and Wagoner RH (eds), (1993), NUMISHEET 93, Proc of 2nd Int Conf, Isehara, Japan, 31 Aug–2 Sept.
Lee JK, Kinzel GL, and Wagoner RH, (eds) (1996), NUMISHEET 96, Proc of 3rd Int Conf, Dearborn, MI, Sept 39–Oct 3.
Pastor  M, Zienkiewicz  OC, and Chan  AHC (1990), Generalized plasticity and the modelling of soil behavior, Int. J Numer. Anal. Method Geomech. 14, 151–190.
Jeremic  B, Runesson  K, and Sture  S (1999a), Object oriented approach to hyperelasticity, Int. J. Eng. Comput. 15, 2–12.

Figures

Grahic Jump Location
Graphical representation of the tangent stiffness-radial return method (von Mises perfect plasticity)
Grahic Jump Location
Graphical representation of the secant stiffness method (von Mises perfect plasticity)
Grahic Jump Location
Stress relaxation in the case of viscoplastic deformation of von Mises material
Grahic Jump Location
A general scheme of return mapping in plasticity
Grahic Jump Location
Schematic representation of generalized return mapping algorithms (associated plasticity): a) Generalized trapezoidal rule, b) generalized midpoint rule
Grahic Jump Location
Residual stresses as functions of elongation and shear measures Ū and S̄, plastic material, ULJ analytical solution 107
Grahic Jump Location
Stress solution for pure shear in case of isotropic and kinematic hardening; use of the spin W and a modified spin W * 110
Grahic Jump Location
Representation of multiplicative decomposition of deformation gradient
Grahic Jump Location
Perforated strip, perfect plasticity. Finite element mesh and elastic-plastic interface for Steps 3, 4, and 8 41
Grahic Jump Location
Isoerror maps for the generalized trapezoidal and midpoint rule, perfectly plastic von Mises model, plane strain deformation 42
Grahic Jump Location
Solution of thermoplastic deformation of plane strain element, perfect plasticity 82
Grahic Jump Location
Solution of thermoplastic deformation of plane stress element, kinematic hardening 82
Grahic Jump Location
Creep of beam subjected to bending 83
Grahic Jump Location
Cauchy stresses in terms of shear strain γ (see Fig. 7) for simple shearing of von Mises material 168: a) Isotropic and kinematic hardening, b) Isotropic hardening, c) Kinematic hardening
Grahic Jump Location
Large strain shear deformation of sand, MRS-Lade model for cohesionless granular material 174: a) Numerical setup of a Directional Shear Cell (DSC) test, b) Shear stress–shear deformation dependence, c) Volumetric strain–shear deformation dependence
Grahic Jump Location
Necking of a circular bar 194: a) Final deformed configuration with field of effective plastic strain, b) Force-displacement dependence
Grahic Jump Location
Impact of an aluminum bar on a rigid wall; deformed configurations at t=30 ms 165
Grahic Jump Location
Buckling of a cruciform beam; effect of plastic deformation in the reduction of the critical load 165
Grahic Jump Location
Necking of a thin sheet 98184187: a) Final configuration and field of effective plastic strain, b) Force-displacement of the specimen end dependence
Grahic Jump Location
Deep drawing of a cylindrical cup 183: a) Initial geometry, b) Punch load versus punch displacement
Grahic Jump Location
Elastic-plastic deformation of the soil specimen, Cam-clay model 160: a) Geometry of the specimen, b) Deformed mesh and field of volumetric plastic strain
Grahic Jump Location
Perfect plasticity coupled to damage 58: a) Load versus average strain, b) Displacement patterns (top row) and accumulated plastic strain (bottom row)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In