An implicit numerical scheme for cyclic elastoplasticity and ratcheting under plane stress conditions

The paper reports the development of an implicit numerical scheme for plane stress cyclic elasto-plasticity, capable of integrating a wide range of hardening rules, and simulating multi-axial ratcheting in metal structural components. Constitutive relations account for von Mises yielding in combination with mixed hardening. Emphasis is given to the kinematic hardening part, which is described with an advanced multiple back-stress model suitable for multi-axial material ratcheting simulation. The constitutive equations are integrated implicitly, and the accuracy of the algorithm is assessed via iso-error maps. Two main novelties of the algorithm refer to the incremental update of the internal variables through the solution of a single scalar equation, and the explicit formulation of the consistent tangent moduli. The numerical scheme is implemented within the finite element environment as an external material subroutine, and its computational efficiency is demonstrated through the simulation of large-scale experiments on pipe elbows. Using the proposed computational framework, two kinematic hardening rules are employed to simulate the elbow response with emphasis on local strain amplitude and accumulation (“ratcheting”). The good comparison between numerical and experimental results demonstrates the computational efficiency of the numerical scheme and highlights some key issues concerning multi-axial ratcheting simulation.