A homogenized macroscopic criterion for shakedown analysis of ductile porous media with kinematical hardening matrix

Abstract

This paper aims at analytically determining the limit states of ductile porous media with kinematical hardening solid matrix subjected to cyclic loads. Based on the statical approach, a macroscopic shakedown criterion is established with the hollow sphere model by using the homogenization theory. The approach proposed in the present study does not require the construction of the so-called time-independent self-equilibrium residual stress field, which is the most important point in the classical statical shakedown approaches. This feature leads to a significant simplification of the computation. The final closed-form macroscopic criterion depends on the invariants of the macroscopic stress tensor, the porosity, as well as Poisson's ratio of the solid matrix. It is remarked that the shakedown limit load is not affected by the kinematical hardening law by comparison of different hardening cases. The obtained safety domain is bounded by the limit surface of the proposed criterion and the limit analysis issued yield surface, indicating the mechanism of incremental collapse at the first cycle. Finally, original numerical simulations, inspired from the two-surface model, have been performed for different hardening conditions and porosities to verify the accuracy of the established criterion.