Abstract

In this work, we make use of analytical homogenization methods to develop multiscale models for the macroscopic response and field statistics of elasto-viscoplastic polycrystals in the transient and steady-state regimes.

First, we develop homogenization models for the steady-state response of porous polycrystals composed of large randomly distributed pores in a fine-grained polycrystalline matrix, with grains described by crystal viscoplasticity. The model is then used to estimate the effects of microstructure on the macroscopic response of sea ice. The key finding here is that the brine-air inclusions induce macroscopic compressibility, which is significantly affected by the porosity, pore geometry, and crystallographic texture of polycrystalline ice. Finally, we obtain homogenization estimates for the transient response of polycrystals with Maxwell-type elasto-viscoplastic grains, exhibiting discrete relaxation spectra (short memory). However, their interaction leads to a continuous relaxation spectrum for the macroscopic response (long memory). To capture the elasto-viscoplastic interaction of the grains, and the associated long-memory effects, we develop differential variational estimates for elasto-viscoplastic polycrystals. We find that the long-memory effects increase with the anisotropy and nonlinearity of the viscoplastic response of the grains and that these effects are correlated with rapid changes in the inter- and intra-granular field fluctuations.