As society becomes more aware of global warming, it is moving towards more sustainable technologies such as renewable energy sources and electric cars. This transition relies on developing advanced battery materials with improved performance and limited degradation. The inherent mechanisms of battery electrodes involve complex coupled electro-chemo-mechanical processes that are also linked to electrode degradation. Ion intercalation in active materials can induce large volume changes, leading to high stress values and fracture. Cracking and fatigue are among the most critical degradation mechanisms, leading to additional issues such as loss of electrical conductivity, uncontrolled SEI growth, or capacity loss [1]. This work proposes a comprehensive description of different numerical implementations for the analysis of diffusion-assisted fracture in battery materials. First, a stochastic chemo-mechanical model is proposed, encompassing stress-diffusion interaction and a stress-based phase-field fracture model. The heterogeneous nature of some battery materials (e.g., graphite or NMC) is modelled using random fields of tensile strength. This approach allows for capturing non-deterministic cracking patterns in these materials at reduced computational cost, as it does not require resolving the small-scale structure of primary particles. Second, a Finite-Element (FE) implementation is discussed, offering high flexibility for handling complex particle geometries, boundary conditions, and functionally graded material properties [2]. Thirdly, a variational implementation based on the Fast Fourier Transform (FFT) is presented as an efficient and robust alternative to the FE model, enabling the analysis of high-resolution microstructural domains at reduced computational cost [3]. This synthesis of numerical methods provides a robust toolkit for the multi-scale design of fracture-resistant electrode materials, such as graphite and NMC. It analyzes fracture processes considering different chemistries (Li-ion, Dual-graphite batteries, etc.).