  Stochastic models for pore collapse in granular materials are developed.
First, a general fluctuating stress-strain relation for a plastic flow rule is
derived. The fluctuations account for non-associativity in plastic deformations
typically observed in heterogeneous materials. Second, an axisymmetric
spherical shell compaction model is extended to account for fluctuations in the
material microstructure due to granular interactions at the pore scale. This
changes the stress-strain constitutive equation determining the dynamics of
pore collapse. Results show that stochastic differential equations can account
for multiscale interactions in a statistical sense.
