Homogenisation of spirally-wound high-contrast layered materials

TL;DR

This paper applies asymptotic homogenisation to develop simplified models for electrical and thermal conduction in spirally-wound layered materials with high contrast in layer conductivities, relevant for lithium-ion batteries.

Contribution

It introduces two composite homogenised models that accurately approximate the full detailed model across different conductivity regimes.

Findings

The models effectively capture the conductive behaviour in high-contrast layered structures.

Comparison shows the homogenised models closely match detailed numerical simulations.

The approach provides a systematic way to simplify complex layered material analysis.

Abstract

Asymptotic homogenisation is used to systematically derive reduced-order macroscopic models of conductive behaviour in spirally-wound layered materials in which the layers have very different conductivities. The problem is motivated by the need for simplified models of the electrical and thermal behaviour of lithium-ion cells, accounting for the highly conductive metallic current collectors and relatively poorly conductive electrodes. We identify and study three distinguished limits, and then describe two composite models which each provide a uniform approximation spanning two distinguished limits. We compare the results of the various reduced-order models with calculations of the full model on a detailed geometry to give a guide to the accuracy of the approximations.