This paper deals with a class of rate-independent metal plasticity models which exhibit non-linear isotropic hardening, non-linear kinematic hardening (Chaboche-Marquis model) and ductile damage (Lemaitre-Chaboche model). The backward Euler scheme is used to integrate the rate constitutive relations. The non-linear equations obtained are solved by the Newton method. The consistent tangent operator is obtained by exact linearization of the algorithm. Despite the complexity of the constitutive equations, closed-form expressions are derived, without any approximations. Analytical, numerical and experimental results are presented acid discussed.
Doghri, I. (1995). Numerical Implementation and Analysis of a Class of Metal Plasticity Models Coupled With Ductile Damage. International Journal for Numerical Methods in Engineering, 38(20), 3403-3431. https://doi.org/10.1002/nme.1620382004 (Original work published 1995)