  At present, modeling of the plastic response of porous solids is done using
stress-based plastic potentials. To gain understanding of the combined effects
of all invariants for general three-dimensional loadings, a strain-rate based
approach appears more appropriate. In this paper, for the first time strain
rate-based potentials for porous solids with Tresca and von Mises, matrices are
obtained. The dilatational response is investigated for general 3-D conditions
for both compressive and tensile states using rigorous upscaling methods. It is
demonstrated that the presence of voids induces dependence on all invariants,
the noteworthy result being the key role played by the plastic flow of the
matrix on the dilatational response. If the matrix obeys the von Mises
criterion, the shape of the cross-sections of the porous solid with the
octahedral plane deviates slightly from a circle, and changes very little as
the absolute value of the mean strain rate increases. However, if the matrix
behavior is described by Tresca's criterion, the shape of the cross-sections
evolves from a regular hexagon to a smooth triangle with rounded corners.
Furthermore, it is revealed that the couplings between invariants are very
specific and depend strongly on the particularities of the plastic flow of the
matrix.
