A visco-plastic constitutive model for ratcheting of cyclically stable materials and its finite element implementation

A visco-plastic constitutive model was proposed to simulate the uniaxial/multiaxial ratcheting of cyclically stable materials (such as U71Mn rail steel), and its finite element implementation was also achieved. The kinematic hardening rule used in the proposed model is similar to that developed by Abdel-Karim and Ohno [Int. J. Plast. 16 (2000) 225], except for a modification to the dynamic recovery term. The proposed model is verified by simulating the uniaxial/multiaxial ratcheting of U71Mn rail steel at room temperature. In the finite element implementation of the proposed model, based on radial return method and backward Euler integration, a new implicit stress integration algorithm is proposed by combining the successive substitution method developed by Kobayashi and Ohno [Int. J. Numer. Meth. Engng. 53 (2002) 2217] with Newton–Raphson solving method of non-linear scalar equation. Simultaneously, a new expression of consistent tangent modulus is also derived for rate-dependent plasticity. Numerical examples are given to verify the advantage of the implementation and the capability of the model in simulating ratcheting and cyclic stress relaxation. [Copyright &y& Elsevier]