Explicit and Implicit Integration of Constitutive Equations of Chaboche Isotropic-Kinematic Hardening Material Model

The proper selection of the material model and its parameters in numerical simulations of the material response under loading is a very important task. In the cyclic load one should assume different phenomena, e.g. ratchetting effect, the mean stress relaxation, creep, etc. The Chaboche kinematic hardening model is mainly applied in order to capture the Bauschinger effect due to its good description of the material behaviour under the cyclic loading. The modified Chaboche isotropic-kinematic hardening model is considered in this paper in order to simulate the strain-controlled and stress-controlled uniaxial cyclic tension-compression test. The implicit and explicit integration procedures are tested here, showing advantages and disadvantages of both methods. It is shown that both approaches provide similar results. The implicit integration method of constitutive equations is unconditionally stable and thus less calculation steps are required in comparison to the explicit procedure. The implicit and explicit integration of the Chaboche model including isotropic and kinematic hardening are then implemented for the 3D case in commercial ABAQUS program in the form of the user material procedure. The correctness of results obtained for the user material model is verified by comparison to results for  commercially implemented Chaboche model.