A diffuse interface model for electro-chemo-mechanical systems

Electro-chemo-mechanics plays a critical role in the performance and longevity of energy storage systems, such as lithium-ion batteries and hydrogen energy storage. These systems involve multi-material composites comprising both liquid and solid phases, with their behavior influenced by processes in the bulk phases and at their interfaces. Traditional multi-phase theoretical and numerical models often adopt a discrete representation of material interfaces, introducing discontinuities in the problem's fields. The numerical implementation is carried out using special interface elements, a methodology that requires conformal meshes and is not always supported by open-source computing platforms. This paper introduces a novel modeling framework that employs a diffuse representation of material interfaces, inspired by the phase-field method. From a modeling perspective, this approach allows for the consistent coupling of bulk and interface electro-chemo-mechanical processes, adhering to thermodynamic principles. Numerically, the proposed model is particularly suited for simulating real material microstructures using regular meshes, facilitating advanced numerical implementations. The methodology is detailed for a generic multi-material electro-chemo-mechanical system and applied specifically to Li-ion batteries. Numerical examples demonstrate the model's effectiveness in simulating coupled interface processes without resorting to interface elements. This work provides a significant advancement in the simulation of electro-chemo-mechanical systems, offering a robust tool for studying the complex interplay of bulk and interface processes.