Fully implicit integration and consistent tangent modulus in elasto‐plasticity

Abstract This paper deals with the numerical integration of a class of rate‐independent elasto‐plastic models. 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 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 derived, without any approximations.