A mechanical model for reinforced, expanding spirally-wound layered materials

Mechanical deformations induced by expansion within an elastic material which is spirally -wound in layers with a thin inextensible reinforcing material are considered. The motivation is to understand behaviour of spirally-wound batteries where both the active material and the metal current collectors expand due to changes in lithiation and/or temperature. This paper considers a spiral made from a single reinforcing layer with a matrix layer of linear elastic material, whose properties may vary through the layer. The layers undergo prescribed isotropic expansion, where the matrix expansion may depend on the macroscopic radial coordinate. Asymptotic homogenisation, exploiting the small scale of the layer thickness relative to the large scale of the overall spiral structure, reveals the bulk of the spiral has an unexpected simple behaviour while there are boundary layers in a surface region near the inner and outer windings. There are further finer-structure boundary layers at the very beginning and very end of the spiral. In all these regions analytical solutions are found providing simple expressions for the deformations and in particular the tension in the inextensible layer. Comparisons are shown between these expressions and detailed finite-element solutions of the problem. These reduced-order models provide a simple way of accounting for stresses induced by expansion of the spiral structure.

Automated summary

This paper investigates the mechanical deformations of a spirally-wound elastic material with a thin inextensible reinforcing material, considering its application in batteries. The study reveals simple behaviors in the bulk of the spiral, but identifies boundary layers near the inner and outer windings, as well as finer-structure boundary layers at the beginning and end of the spiral. The paper provides analytical solutions for the deformations and tension in the inextensible layer, and compares them with finite-element solutions.