Revisiting Volterra defects: Geometrical relation between edge dislocations and wedge disclinations

This study presents a comprehensive mathematical model for Volterra defects and explores their relations using differential geometry on Riemann–Cartan manifolds. Following the standard Volterra process, we derived the Cartan moving frame, a geometric representation of plastic fields, and the associated Riemannian metric using exterior algebra. Although the analysis naturally defines the geometry of three types of dislocations and the wedge disclination, it fails to classify twist disclinations owing to the persistent torsion component, suggesting the need for modifications to the Volterra process. By leveraging the interchangeability of the Weitzenböck and Levi-Civita connections and applying an analytical solution for plasticity derived from the Biot–Savart law, we provide a rigorous mathematical proof of the long-standing phenomenological relationship between edge dislocations and wedge disclinations. Additionally, we showcase the effectiveness of novel mathematical tools, including R..., , , # Data from: Revisiting Volterra defects: Geometrical relation between edge dislocations and wedge disclinations

## Description of the data and file structure

This dataset contains the source data in the VTK XML format. They can be used to plot the complex potential of the disclination dipole and monopole on the Riemann sphere and the complex plane.

**Files and variables**

**File: data.zip**

**Description:** 
The folder contains the raw source data in the VTK XML format for the complex potential of the disclination dipole and monopole plotted on Riemann sphere, and compelx plane as well.
We used [ParaView](https://www.paraview.org/) to import and visualize the source data.
The description of each files are as follows:

* `fig3ab`: Raw data for plotting the complex potential of the disclination dipole in VTK XML format.
* `riemann_sphere_left.vts` and `riemann_sphere_right.vts` are the Riemann sphere subdivided into two hemispheres. They include the real and imaginary part of the ...,