One-equation integration algorithm of a generalized quadratic yield function with Chaboche non-linear isotropic/kinematic hardening

•Implicit integration algorithm with nonlinear isotropic/kinematic hardening is proposed.•The model includes the quadratics criterion of Hill and J2 plasticity.•One single non-linear scalar equation is solved using the Newton method.•The consistent tangent modulus is obtained by exact linearization of the algorithm.•The proposed algorithm is suitable for plane stress, plane strain and 3D problems.

In this paper, the implicit integration of a quadratic yield criterion exhibiting Chaboche non-linear kinematic and isotropic hardening is presented. A new expression of consistent tangent modulus is derived and implemented in finite element programs. The non-linear global equilibrium equations as well as the one single non-linear local equations obtained by fully implicit integration of the constitutive equations are solved using the Newton method. The consistent local tangent modulus is obtained by exact linearization of the algorithm. The performance of the present algorithm is demonstrated by numerical examples where a quadratic convergence behavior can be observed.