I. Doghri, FULLY IMPLICIT INTEGRATION AND CONSISTENT TANGENT MODULUS IN ELASTOPLASTICITY, International journal for numerical methods in engineering, 36(22), 1993, pp. 3915-3932
This paper deals with the numerical integration of a class of rate-ind
ependent elasto-plastic models. The backward Euler scheme is used to i
ntegrate the rate constitutive relations. The non-linear equations obt
ained are solved by the Newton method. The consistent tangent modulus
is obtained by exact linearization of the algorithm. In the case of J2
elasto-plasticity with non-linear isotropic hardening and non-linear
kinematic hardening (Chaboche-Marquis model), explicit formulas are de
rived, without any approximations.