A Mechanical Model for Reinforced, Expanding Spirally-Wound Layered Materials

30 Pages Posted: 29 Aug 2022

See all articles by Robert Timms

Robert Timms

University of Oxford

Steven Psaltis

Queensland University of Technology

Colin Please

University of Oxford

Jon Chapman

University of Oxford

Abstract

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 mayvary 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 thelarge 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 thevery 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 expressionsand 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.

Keywords: Asymptotic analysis, homogenisation, linear elasticity

Suggested Citation

Timms, Robert and Psaltis, Steven and Please, Colin and Chapman, Jon, A Mechanical Model for Reinforced, Expanding Spirally-Wound Layered Materials. Available at SSRN: https://ssrn.com/abstract=4203825

Robert Timms (Contact Author)

University of Oxford ( email )

Mansfield Road
Oxford, OX1 4AU
United Kingdom

Steven Psaltis

Queensland University of Technology ( email )

2 George Street
Brisbane, 4000
Australia

Colin Please

University of Oxford ( email )

Mansfield Road
Oxford, OX1 4AU
United Kingdom

Jon Chapman

University of Oxford ( email )

Mansfield Road
Oxford, OX1 4AU
United Kingdom

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