An integration scheme for Prandtl‐Reuss elastoplastic constitutive equations

We investigate the generalized midpoint rule for the time integration of elastoplastic constitutive equations for pressure-independent yield criteria. The incremental equations are divided into one scalar hydrostatic pressure/dilation rate equation, and a stress deviator/strain rate deviator tensorial equation.This formulation is applied to two classical problems: bulging of a tube under internal pressure and tension test on a notched specimen.

[1]  Pierre Montmitonnet,et al.  Finite element analysis of elastoplastic indentation with a deformable indenter , 1993 .

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

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

[4]  O. C. Zienkiewicz,et al.  Elasto‐plastic solutions of engineering problems ‘initial stress’, finite element approach , 1969 .

[5]  R. G. Whirley,et al.  On the Numerical Implementation of Elastoplastic Models , 1984 .

[6]  J. C. Rice,et al.  On numerically accurate finite element solutions in the fully plastic range , 1990 .

[7]  Rodney Hill,et al.  Some basic principles in the mechanics of solids without a natural time , 1959 .

[8]  Michael Ortiz,et al.  An analysis of a new class of integration algorithms for elastoplastic constitutive relations , 1986 .

[9]  Jean-Loup Chenot,et al.  A plane-strain elastoplastic finite-element model for cold rolling of thin strip , 1992 .

[10]  E. P. Popov,et al.  Accuracy and stability of integration algorithms for elastoplastic constitutive relations , 1985 .

[11]  T. H. H. Pian,et al.  Notes on finite elements for nearly incompressible materials , 1976 .

[12]  L. Herrmann.  Elasticity Equations for Incompressible and Nearly Incompressible Materials by a Variational Theorem , 1965 .

[13]  D. Malkus,et al.  Mixed finite element methods—reduced and selective integration techniques: a unification of concepts , 1990 .

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

[15]  W. Prager,et al.  Theory of perfectly plastic solids , 1968 .

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

[17]  M. Abouaf,et al.  An implicit and incremental formulation for the solution of elastoplastic problems by the finite element method , 1986 .