Shakedown of porous materials

The paper is devoted to the determination of shakedown limit states of porous ductile materials under cyclically repeated loads by considering the hollow sphere model with von Mises matrix. We adopt Melan's statical approach based on time-independent residual stress fields. First of all, we determine the exact solution for the pure hydrostatic loading. It turns out that the collapse occurs by fatigue. Next, suitable trial stress fields are built with additional terms to capture the shear effects. This theoretical fatigue criterion of porous materials agreed with numerical simulations and experimental results provided in literature according to which, in ductile metals, the strain to fracture under cyclic loading is considerably lower than the one reached monotonically. Finally, the built criterion is compared to numerical simulations derived by both shakedown direct method and incremental simulations.