Biot-Savart law in the geometrical theory of dislocations

Universal mechanical principles may exist behind seemingly unrelated physical phenomena, providing novel insights into these phenomena. This study sheds light on the geometrical theory of dislocations through an analogy with electromagnetics. In this theory, solving Cartan's first structure equation is essential for connecting the dislocation density to the plastic deformation field of the dislocations. The additional constraint of a divergence-free condition, derived from the Helmholtz decomposition, forms the governing equations that mirror Ampère's and Gauss' law in electromagnetics. This allows for the analytical integration of the equations using the Biot-Savart law. The plastic deformation fields of screw and edge dislocations obtained through this process form both a vortex and an orthogonal coordinate system on the cross-section perpendicular to the dislocation line. This orthogonality is rooted in the conformal property of the corresponding complex function that satisfies the C..., , , # Data from: Biot-Savart law in the geometrical theory of dislocations

## Description of the data and file structure

This dataset contains the plastic and elastic field formed by dislocations in the VTK XML format, which can usually be imported by ParaView.

### Files and variables

#### File: data.zip

**Description:** 
The folder contains the raw source data in the VTK XML format to plot the plastic deformation field, complex potential, and stress fields of an edge and screw dislocations.
We used ParaView to import and visualize the source data.
The description of each files are as follows:

* fig1/edge, fig1/screw: raw data for plotting the plastic deformation field of a straight edge and screw dislocations. `edge.vtr`, `screw.vtr` contains the plastic deformation field, while `edge_circuit.vtu` and `screw_circuit.vtu` includes the data to schematically illustrate the Burgers circuits.
* fig2/imaginarypart, fig2/realpart: raw data for plotting plastic deformation potential of dislo...