A macroscopic criterion of shakedown limit for ductile porous materials subjected to general cyclic loadings

In a recent paper (Zhang et al., 2017), we have analytically derived a macroscopic criterion to determine the shakedown domain for ductile porous media with von Mises matrix under repeated loads by the use of Melan's theorem. The proposed criterion in Zhang et al. (2017) concerns only two limit cyclic loading cases: (i) the alternating and (ii) the pulsating loads. In this paper, we generalize this approach for all possible intermediate cyclic loading cases ranging between the tow limit cases. The key idea relies on the choice of a more appropriate trial residual stress field allowing analytical computations and the improvement of the previous model simultaneously. The new analytical criterion depends on the first and second macroscopic stresses invariants and the sign of the third one. A more accurate value for pure shear loading case is obtained. The obtained results are fully discussed and compared to the previous criterion (Zhang et al., 2017) and numerical results derived by both shakedown direct method and incremental elastic plastic simulations.