Nanoporous materials with a general isotropic plastic matrix: exact limit state under isotropic loadings

In this paper, hydrostatic strength properties of nanoporous materials are investigated by addressing the limit state of a hollow sphere undergoing isotropic loading conditions. Void-size effects are modelled by treating the cavity boundary as a coherent-imperfect homogeneous interface. The hollow sphere is assumed to be comprised of a rigid-ideal- plastic material obeying to a general isotropic yield criterion. The latter is defined by considering a simplified form of the yield function proposed by Bigoni and Piccolroaz in [Int J Solids Struct; 41: 2855e2878], resulting able to account for a broad class of pressure- sensitive materials whose plastic response is also affected by the stress Lode angle. The corresponding support function is consistently derived and discussed. The exact solution of the limit-state problem is fully determined, providing a closed-form description of stress, strain-rate and velocity fields, as well as the macroscopic hydrostatic strength of nanoporous media. Proposed approach allows to consistently generalise available analyt- ical solutions for porous and nanoporous materials, by accounting for a general plastic response of the solid matrix and for void-size effects. Finally, present exact solution, as well as the identification of the support function for the adopted general strength criterion, open towards novel kinematic limit-analysis approaches for describing macroscale strength properties of nanoporous materials under arbitrary triaxial loadings.