Lithium-ion batteries are increasingly employed to meet energy storage needs of all sizes, and are chosen for their high energy and power density. These characteristics depend on the ability of brittle metal-oxide particles in the battery cathode to transfer electrons as they absorb and release charged lithium ions. Compaction during manufacturing results in a highly interconnected matrix of active material particles, but also causes some of the particles to split. This reduces the matrix connectivity and damages the battery's energy storage and release capabilities. Our focus is on employing numerical methods to characterize the inter-particle contacts and particle fracture fundamental to this problem. We propose the fabric tensor formalism to describe the structure and evolution of the electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode. We then shift focus to the development and analysis of fracture models that may be applied to study cathode particle splitting during manufacturing. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials break into a large number of smaller pieces. We implement the Thick Level-Set model to simulate this process as an alternative to existing methods. We find that, in terms of energy dissipated by fracture and mean fragment size, the proposed model reproduces the rate-dependent observations of analytical approaches, numerical models and experimental studies.