We study how electrode microstructures in battery materials can be modeled
using probabilistic random sets, and how they can be tailored to represent real materials.
Our focus is on identifying which morphological criteria are sensitive and insensitive to the material’s physical
response. Transport properties (conductivity) and elasticity are considered. Use is made
of “Fourier-based” numerical schemes to predict the local and overall response of
materials presenting a texture at the small scale. These methods are directly applied to 2D
or 3D images of materials, such as micro-tomography or virtual models, and require no
meshing. By principle, the methods rely on a Green operator discretized in the Fourier
domain, where the equations of admissibility and conservation are enforced, and on a
voxel grid where the constitutive laws are evaluated. Fast Fourier transforms are used
to switch from the real space to the frequency domain. Applications related to fuel cell
materials as well as lithium-ion batteries, that present complex morphologies,
are first examined. We show that standard morphological criteria (covariance functions,
granulometry) are in general insufficient to characterize the material’s effective transport
properties whereas linear homogenization theories have limited capabilities for capturing
the material’s physical response, and highlight how percolation (in a sense to
be defined) strongly affects the physical behavior of materials as well as its local
response.