Dataset accompanying:

O'Hare, T.J., Gourgiotis, P.A., Coombs, W.M. and Augarde, C.E. (2026)

"Evolving shear bands in a nonlinear micropolar continuum"

Proceedings of the Royal Society A

DOI: https://doi.org/10.1098/rspa.2026.0151

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OVERVIEW
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This repository contains the numerical data used to generate the figures presented in the manuscript. The dataset is organised into two directories corresponding to the numerical examples discussed in Sections 4.1 and 4.2 of the paper.

Visualisations of field quantities were produced using ParaView. Line plots and post-processing of shear-band centrelines were carried out in MATLAB.

All data were generated numerically. Coordinates are provided in SI units (metres). Variable names referenced below correspond exactly to the field names stored within the VTK/VTU files.

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DIRECTORY STRUCTURE
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4.1 Plane strain compression (biaxial) test
    8.vtu
    12.vtu
    16.vtu
    20.vtu
    classical.vtk
    8poly.csv
    12poly.csv
    16poly.csv
    20poly.csv
    plotSpline.m

4.2 Plane strain column collapse
    A.vtk
    B.vtk
    C.vtk
    D.vtk
    E.vtk
    force-displacement.csv

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FIGURE-TO-DATA LOOKUP
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Figure 3:
    8.vtu, 12.vtu, 16.vtu, 20.vtu

Figure 4:
    8poly.csv, 12poly.csv, 16poly.csv, 20poly.csv
    plotSpline.m

Figure 5a:
    20.vtu

Figure 5b:
    20.vtu

Figure 6a:
    20.vtu

Figure 6b:
    classical.vtk

Figure 8:
    force-displacement.csv

Figure 9:
    A.vtk, B.vtk, C.vtk, D.vtk, E.vtk

Figure 10:
    A.vtk, B.vtk, C.vtk, D.vtk, E.vtk

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4.1 PLANE STRAIN COMPRESSION (BIAXIAL) TEST
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This directory contains simulation results at four levels of axial strain:

8.vtu   : 8% axial strain
12.vtu  : 12% axial strain
16.vtu  : 16% axial strain
20.vtu  : 20% axial strain

Figures 3 and 6a

These figures were produced by visualising the scalar field

    internal hardening

in ParaView.

Figure 5a

This figure was produced by visualising the y-component of the vector field

    rotation

after conversion from radians to degrees.

Figure 5b

This figure shows the curvature measure k associated with the evolving shear band. The field was computed in ParaView from the final simulation state (20.vtu) using the following procedure:

1. Generate a 2D Delaunay triangulation.
2. Compute the spatial gradient of:
       a) internal hardening
       b) rotation angle
3. Normalise the gradient of internal hardening to define the unit vector n.
4. Compute

       k = n · grad(theta)

where theta denotes the rotation angle.

Figure 4

The files

    8poly.csv
    12poly.csv
    16poly.csv
    20poly.csv

contain manually sampled shear-band centreline coordinates obtained from an isocontour of n.

Each file contains Cartesian coordinates

    x, y, z

in metres.

The MATLAB script

    plotSpline.m

applies a Savitzky-Golay filter to the sampled centreline coordinates and generates the orientation plots shown in Figure 4.

A filter window size of 5 points was used in all cases.

Classical plasticity comparison

The file

    classical.vtk

contains the simulation result used to generate Figure 6b.

The equivalent plastic strain corresponds to the scalar field

    alpha

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4.2 PLANE STRAIN COLUMN COLLAPSE
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Figure 8

The file

    force-displacement.csv

contains the data used to generate Figure 8.

Columns:

    Column 1: displacement (m)
    Column 2: specific weight (kN/m^3)

Figures 9 and 10

The files

    A.vtk
    B.vtk
    C.vtk
    D.vtk
    E.vtk

contain five snapshots of the column collapse simulation corresponding to the states shown in the manuscript.

Figure 9

The accumulated plastic multiplier corresponds to the scalar field

    alpha

and was visualised directly in ParaView.

Figure 10

The curvature measure shown in Figure 10 was obtained using the same procedure described for Figure 5b:

1. Generate a 2D Delaunay triangulation.
2. Compute spatial gradients.
3. Replace:
       internal hardening -> alpha
       rotation angle -> phi_y
4. Normalise the gradient of alpha to define the unit vector n.
5. Compute

       k = n · grad(phi_y)

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SOFTWARE
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The dataset was processed using:

    ParaView 5.10
    MATLAB R2025a

The supplied VTK and VTU files can be opened directly in ParaView.

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CONTACT
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Questions regarding this dataset may be directed to the corresponding author, Professor Will Coombs.

Email: w.m.coombs@durham.ac.uk