Two material models for cyclic plasticity: nonlinear kinematic hardening and generalized plasticity

Abstract We present a comparative study between a nonlinear kinematic hardening model and a generalized plasticity model. The two models are reviewed and discussed from both continuous and discrete time points of view. The integration of the discrete models based on a return map algorithm is also addressed. The form of the elastoplastic tangent tensors consistent with both the continuous and the discrete versions is discussed; in particular, the latter guarantees quadratic convergence for a Newton method, frequently adopted in an incremental solution scheme. Finally, numerical examples for uniaxial and multiaxial cyclic loading conditions are presented.

[1]  M. Eisenberg,et al.  A Generalization of Plastic Flow Theory With Application to Cyclic Hardening and Softening Phenomena , 1976 .

[2]  K. Valanis,et al.  FUNDAMENTAL CONSEQUENCES OF A NEW INTRINSIC TIME MEASURE-PLASTICITY AS A LIMIT OF THE ENDOCHRONIC THEORY , 1980 .

[3]  D. McDowell.  An Experimental Study of the Structure of Constitutive Equations for Nonproportional Cyclic Plasticity , 1985 .

[4]  D. C. Drucker,et al.  On Stress-Strain Relations Suitable for Cyclic and Other Loading , 1981 .

[5]  Martin A. Eisenberg,et al.  On nonlinear kinematic hardening , 1968 .

[6]  David L. McDowell,et al.  A nonlinear kinematic hardening theory for cyclic thermoplasticity and thermoviscoplasticity , 1992 .

[7]  J. Chaboche,et al.  Modeling of the cylic response and ratchetting effects on inconel-718 alloy , 1991 .

[8]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

[9]  Zenon Mróz,et al.  On the description of anisotropic workhardening , 1967 .

[10]  Nobutada Ohno,et al.  Recent Topics in Constitutive Modeling of Cyclic Plasticity and Viscoplasticity , 1990 .

[11]  Sanjay Govindjee,et al.  Non‐linear B‐stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity , 1991 .

[12]  S. Kyriakides,et al.  Ratcheting in cyclic plasticity, part II: Multiaxial behavior , 1992 .

[13]  J. Chaboche.  Constitutive equations for cyclic plasticity and cyclic viscoplasticity , 1989 .

[14]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[15]  J. Nagtegaal.  On the implementation of inelastic constitutive equations with special reference to large deformation problems , 1982 .

[16]  J. Chaboche,et al.  Constitutive Modeling of Ratchetting Effects—Part II: Possibilities of Some Additional Kinematic Rules , 1989 .

[17]  N. Ohno,et al.  Kinematic hardening rules with critical state of dynamic recovery, part I: formulation and basic features for ratchetting behavior , 1993 .

[18]  J. Z. Zhu,et al.  The finite element method , 1977 .

[19]  Yannis F. Dafalias,et al.  Plastic Internal Variables Formalism of Cyclic Plasticity , 1976 .

[20]  J. Chaboche.  Time-independent constitutive theories for cyclic plasticity , 1986 .

[21]  Issam Doghri,et al.  Fully implicit integration and consistent tangent modulus in elasto‐plasticity , 1993 .

[22]  A. Phillips,et al.  The effect of repeated loading on the yield surface , 1968 .

[23]  Stefan Hartmann,et al.  Stress computation and consistent tangent operator using non-linear kinematic hardening models , 1993 .

[24]  Z. Mroz.  An attempt to describe the behavior of metals under cyclic loads using a more general workhardening model , 1969 .

[25]  K. Valanis.  A THEORY OF VISCO-PLASTICITY WITH OUT A YIELD SURFACE, PART I: GENERAL THEORY , 1971 .

[26]  Jean-Louis Chaboche,et al.  On some modifications of kinematic hardening to improve the description of ratchetting effects , 1991 .

[27]  J. Gillis,et al.  Methods in Computational Physics , 1964 .

[28]  Jacob Lubliner,et al.  A simple model of generalized plasticity , 1991 .

[29]  Egor P. Popov,et al.  A model of nonlinearly hardening materials for complex loading , 1975 .

[30]  H. P. Shrivastava,et al.  A non-linear hardening model and its application to cyclic loading , 1976 .

[31]  D. McDowell.  An Evaluation of Recent Developments in Hardening and Flow Rules for Rate-Independent, Nonproportional Cyclic Plasticity , 1987 .

[32]  Martin A. Eisenberg,et al.  A theory of plasticity with non-coincident yield and loading surfaces , 1971 .

[33]  Robert L. Taylor,et al.  A new model of generalized plasticity and its numerical implementation , 1993 .

[34]  M. Wilkins.  Calculation of Elastic-Plastic Flow , 1963 .

[35]  A. Phillips,et al.  On the concept of the yield surface , 1965 .

[36]  Yannis F. Dafalias,et al.  BOUNDING SURFACE PLASTICITY, I: MATHEMATICAL FOUNDATION AND HYPOPLASTICITY , 1986 .

[37]  R. D. Krieg,et al.  Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model , 1977 .

[38]  S. Atluri,et al.  Constitutive modeling of cyclic plasticity and creep, using an internal time concept , 1986 .

[39]  Calculations for Uniaxial Stress and Strain Cycling in Plasticity , 1984 .

[40]  G. Maenchen,et al.  The Tensor Code , 1963 .

[41]  Jean-Louis Chaboche,et al.  Constitutive Modeling of Ratchetting Effects—Part I: Experimental Facts and Properties of the Classical Models , 1989 .

[42]  Nobutada Ohno,et al.  Kinematic hardening rules with critical state of dynamic recovery, part II: Application to experiments of ratchetting behavior , 1993 .

[43]  Satya N. Atluri,et al.  Internal time, general internal variable, and multi-yield-surface theories of plasticity and creep: A unification of concepts , 1986 .

[44]  J. C. Simo,et al.  Variational and projection methods for the volume constraint in finite deformation elasto-plasticity , 1985 .