Extended overstress model and its implicit stress integration algorithm: Formulations, experiments, and simulations

The extended overstress model is formulated based on the subloading surface model with the smooth elastic‐inelastic transition, which is called the subloading‐overstress model. Therein, the rigorous translation rules of the elastic‐core and the similarity‐center, the limitation in the expansion of the subloading surface, and so forth are incorporated. The model possesses the basic structure capable of describing the monotonic/cyclic loading behaviors at the general rate of deformations from the quasi‐static to the impact loading. The experiments were conducted using the spheroidal graphite cast iron under the various loading conditions. It was verified that the experimental results can be simulated accurately by the subloading‐overstress model. Further, the complete implicit stress integration algorithm based on the return‐mapping projection is formulated for the present subloading‐overstress model and implemented into Abaqus through UMAT. Then, the deformation analyses of the R‐notched cylinder were performed by the present algorithm. Consequently, the performability of the present algorithm is verified by the analyses of the boundary‐value problem under the cyclic loadings.