HOMOGENIZATION OF SPIRALLY WOUND HIGH-CONTRAST LAYERED MATERIALS

Asymptotic homogenization is used to systematically derive reduced-order macroscopic models of conductive behavior 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 behavior 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.

Automated summary

Asymptotic homogenization was used to derive reduced-order macroscopic models of conductive behavior in spirally wound layered materials with varying conductivities. Two composite models were described to provide a uniform approximation spanning two distinguished limits, and the accuracy of the approximations was compared with calculations of the full model on a detailed geometry.