  The mechanical response of isotropic elastoplastic materials containing
random distributions of initially spherical voids is investigated
computationally based on Fast Fourier Transform simulations. Numerical
limit-analysis simulations at constant stress triaxiality allow to determine
the yield surfaces, leading in particular to the determination of a
Representative Volume Element size for the onset of coalescence / inhomogeneous
yielding. Moreover, two different coalescence regimes are observed that differ
by the presence of shearing. The yield surfaces are found to be consistent with
the combination of two models proposed in the literature, a GTN-type model
calibrated for homogeneous yielding of random porous materials and an
inhomogeneous yielding model accounting for both coalescence with or without
shear. Finite strain simulations performed for different hardening moduli and
stress triaxialities under axisymmetric loading conditions confirm the
existence of a RVE up to the onset of inhomogeneous yielding. Coalescence
strains are found to be significantly smaller for random porous materials than
for periodic distribution of voids. A homogenized model is finally proposed
that reproduces quantitatively the behavior of isotropic elastoplastic
materials containing random distributions of voids under finite strains.
