MATLAB Script for the Closed-Form Analysis of Springback due to Inelastic Bending of Beams Based on Eigenstrain Theory

Description

This repository contains MATLAB scripts developed for the analytical modeling of chemo-mechanical stress and residual eigenstrain formation in lithium-ion battery electrodes during lithiation and delithiation. The scripts implement a one-dimensional diffusion–mechanics framework that couples Fick's lithium transport with an elastic–perfectly plastic constitutive model, enabling the prediction of lithium concentration profiles, stress evolution, and plastic strain distribution throughout the electrode thickness. The framework also includes a fracture-aware capping scheme that simulates microcrack-induced stress relaxation by proportionally reducing plastic eigenstrain in overstressed regions. Users can modify key parameters such as electrode thickness, lithium diffusivity, yield strength, and Vegard’s coefficient to perform parametric studies or extend the analysis to other electrode materials. All plots and results presented in the associated manuscript are fully reproducible using the provided MATLAB code. This resource supports further research on chemo-mechanical degradation mechanisms, residual stress modeling, and eigenstrain-based analysis of battery electrode integrity.

Steps to reproduce

1. Download the MATLAB script file (analysis_sections.m) provided in this repository. 2. Open the scripts in MATLAB R2024b or a compatible version. 3. Run the script or execute specific sections to reproduce: Total, plastic, and elastic strain distributions during and after bending. Residual elastic strain profiles for different beam geometries. Springback curves across beam height. Moment–curvature diagrams for rectangular, circular, and I-beam cross-sections. 4. All scripts have been tested using MATLAB R2024b on an Apple Silicon (M-series) Mac to ensure compatibility and performance. No additional toolboxes or dependencies are required beyond base MATLAB functionality.

Institutions

• University of Oxford

  England, Oxford

Categories

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