MEAM Seminar: “A Multi-Scale Homogenization Model for the Viscoplastic Response of Polar and Sea Ice”

The rheology of polar ice evolves in response to weather and climate changes, by modifying its microstructure. While the experimental evidence for the dependence of rheological properties on the microstructure is well documented, there are only a few modeling efforts to capture the rheological behavior of polar ice, mostly by fitting continuum models to the existing experimental data. However, for the rapidly changing polar and sea ice, we need a predictive model to forecast the behavior of polar ice in the future, for which we might not have any experimental data. In this work, we put forth a multi-scale homogenization model for the viscoplastic response of polar and sea ice, by incorporating important microstructural features.

In the Arctic, sea water freezes to form a layer of sea ice, a multi-phase composite, up to a few meters thick, with a complex microstructure spanning several length scales. At the smaller length scales, sea ice is a porous polycrystal with columnar grains, with brine-air inclusions embedded inside the grains or dispersed along the grain boundaries. This work presents a multi-scale constitutive response for sea ice by idealizing it as a three-scale composite where the brine-air inclusions are embedded inside a polycrystalline matrix composed of columnar grains. The results from our model match with published experimental data, by, most importantly, capturing the compressibility effects of brine-air inclusions.

In Antarctica ice sheets with a typical thickness of 1-3km, as the snow accumulates on the surface of the ice sheet, the snow beneath the top layer is densified and is eventually transformed into the ice with trapped air bubbles—bubbly ice. The size, shape and volume fraction of these air bubbles have a profound impact on the rheological response of the ice. In addition, bubble shape could also be used as strain-indicators in glaciers. We develop a multi-scale homogenization model for the constitutive response of bubbly-ice by treating it as a three-phase polycrystalline composite, where pressurized bubbles are embedded inside the polycrystalline matrix. The model predicts that microstructural textures developed in response to different loading conditions significantly influence the macroscopic response.