Multiple scales homogenisation of a porous viscoelastic material with rigid inclusions: application to lithium-ion battery electrodes

TL;DR

This paper develops a multiscale homogenisation model for porous viscoelastic materials with rigid inclusions, specifically applied to lithium-ion battery electrodes, enabling efficient and accurate prediction of their mechanical behaviour.

Contribution

It introduces a systematic multiple scales homogenisation approach for complex battery electrode materials, simplifying the analysis while maintaining accuracy.

Findings

The effective model closely matches detailed simulations.

The homogenised model reduces computational cost significantly.

Practical application to battery design and durability assessment.

Abstract

This paper explores the mechanical behaviour of the composite materials used in modern lithium-ion battery electrodes. These contain relatively high modulus active particle inclusions within a two-component matrix of liquid electrolyte which penetrates the pore space within a viscoelastic polymer binder. Deformations are driven by a combination of (i) swelling/contraction of the electrode particles in response to lithium insertion/extraction, (ii) swelling of the binder as it absorbs electrolyte, (iii) external loading and (iv) flow of the electrolyte within the pores. We derive the macroscale response of the composite using systematic multiple scales homomgenisation by exploiting the disparity in lengthscales associated with the size of an electrode particle and the electrode as a whole. The resulting effective model accurately replicates the behaviour of the original model (as is demonstrated by a series of relevant case studies) but, crucially, is markedly {simpler and hence} cheaper to solve. This is significant practical value because it facilitates low-cost, realistic computations of the mechanical states of battery electrodes, thereby allowing model-assisted development of battery designs that are better able to withstand the mechanical abuse encountered in practice and ultimately paving the way for longer-lasting batteries.