08 Using second-order bounds to parametrize the anisotropic elastic tensor of snow, firn, and ice microstructures
We consider the common problem of deriving accurate approximations for effective elastic properties of anisotropic, heterogeneous microstructures. On the one hand, microstructure-based FEM simulations are accurate but computationally expensive. On the other hand, rigorous approximations such as bounds often lack accuracy when compared to simulations or experiments. It is the purpose of the present work to provide an accurate parameterization based on volume fraction and structural anisotropy by using an empirical adjustment of the well known Hashin Shtrikman bounds. We illustrate this for the example of snow firn and ice, and the prediction of all components of the transversely isotropic elasticity modulus. We demonstrate for 348 microstructures obtained by X-ray tomography that the empirical structure-property parameterization yields a good agreement with simulated effective elastic properties for all naturally occurring porosities and anisotropies. Since the parametrization relies on generic microstructural characterization through a two-point correlation function, a similar approach might be envisaged for other heterogeneous materials. A comparison of our parameterization with an existing Zysset-Curnier (ZC) parameterization for the elasticity tensor of snow based on the fabric tensor, shows an improvement in the coefficient of determination and accuracy in the prediction of elasticity modulus in particular for high and low porosity samples.