A HYPERELASTIC-BASED LARGE STRAIN ELASTO-PLASTIC CONSTITUTIVE FORMULATION WITH COMBINED ISOTROPIC-KINEMATIC HARDENING USING THE LOGARITHMIC STRESS AND STRAIN MEASURES

This paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity. The combined isotropic-kinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions: (i) the formulation is hyperelastic based, (ii) the stress-strain law preserves the elastic constants of the infinitesimal theory but is written in terms of the Hencky strain tensor and its elastic work conjugate stress tensor, and (iii) the multiplicative decomposition of the deformation gradient is adopted. Since no stress rates are present, the formulation is, of course, numerically objective in the time integration. It is shown that the model gives adequate physical behaviour, and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor.

[1]  Satya N. Atluri,et al.  Objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses , 1983 .

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

[3]  En-Jui Lee.  Elastic-Plastic Deformation at Finite Strains , 1969 .

[4]  Jacob Lubliner,et al.  Normality rules in large-deformation plasticity , 1986 .

[5]  K. Bathe,et al.  FINITE ELEMENT FORMULATIONS FOR LARGE DEFORMATION DYNAMIC ANALYSIS , 1975 .

[6]  T. Hughes,et al.  Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis , 1980 .

[7]  G. Strang,et al.  The solution of nonlinear finite element equations , 1979 .

[8]  R. Hill.  The mathematical theory of plasticity , 1950 .

[9]  P. M. Naghdi,et al.  A general theory of an elastic-plastic continuum , 1965 .

[10]  Eduardo N. Dvorkin,et al.  ON THE SOLUTION OF NONLINEAR FINITE ELEMENT EQUATIONS. , 1984 .

[11]  R. F. Kulak,et al.  Accurate Numerical Solutions for Elastic-Plastic Models , 1979 .

[12]  R. Asaro,et al.  Micromechanics of Crystals and Polycrystals , 1983 .

[13]  Rodney Hill,et al.  Aspects of Invariance in Solid Mechanics , 1979 .

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

[15]  S. Atluri,et al.  Constitutive modeling and computational implementation for finite strain plasticity , 1985 .

[16]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multipli , 1988 .

[17]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

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

[19]  J. Mandel.  Thermodynamics and Plasticity , 1973 .

[20]  Milos Kojic,et al.  The ‘effective‐stress‐function’ algorithm for thermo‐elasto‐plasticity and creep , 1987 .

[21]  Milos Kojic,et al.  Thermo-elastic-plastic and creep analysis of shell structures , 1987 .

[22]  E Hinton,et al.  COMPUTATIONAL PLASTICITY Models , Software and Applications , .

[23]  L. Anand,et al.  Finite deformation constitutive equations and a time integrated procedure for isotropic hyperelastic—viscoplastic solids , 1990 .

[24]  Jacob Lubliner,et al.  A maximum-dissipation principle in generalized plasticity , 1984 .

[25]  J. Nagtegaal,et al.  Some computational aspects of elastic-plastic large strain analysis , 1981 .

[26]  Walter Noll,et al.  The thermodynamics of elastic materials with heat conduction and viscosity , 1963 .

[27]  Milos Kojic,et al.  Studies of finite element procedures—Stress solution of a closed elastic strain path with stretching and shearing using the updated Lagrangian Jaumann formulation , 1987 .

[28]  K. Bathe,et al.  A note on the use of the additive decomposition of the strain tensor in finite deformation inelasticity , 1991 .

[29]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. part II: computational aspects , 1988 .