A variational-based homogenization model for plastic shakedown analysis of porous materials with a large range of porosity

Abstract In this paper, a new homogenization model is developed for the determination of macroscopic shakedown limit state for porous media subjected to general cyclic loads. Based on the variational principle over the stabilized cycle, a new macroscopic fatigue criterion is established, beyond which the collapse of material will occur due to fatigue. Unlike the classical Melan’s theory by statical approaches relying on the complex construction of a time-independent residual stress field, the formulation of the new criterion is derived from a variational-based kinematical approach which allows overcoming this difficulty. Dirac’s measure is adopted to simplify the volume integral with the assumption of vanishing plastic strain increment over a stabilized cycle. The established criteria exhibit directly the dependence of the plastic shakedown limit load on the invariants of the macroscopic stress tensor, Poisson’s ratio of the solid matrix and the porosity. The macroscopic safety domain is defined by the intersection of limit surface of this new fatigue criteria and that corresponds to the incremental collapse which is reached monotonically. The theoretical predictions of shakedown limits by the new criterion are compared with the numerical results obtained from non-linear optimization method and with those given by some representative existing criteria. It is shown that the new criterion significantly improves the accuracy of plastic shakedown limit prediction for porous materials with large values of porosity.