# On Plastic Dislocation Density Tensor

## TL;DR

This paper clarifies the relationships among different definitions of plastic dislocation density tensors and proposes a modified version of Kondo's tensor to resolve existing inconsistencies.

## Contribution

It demonstrates the equivalence of Ortiz's and Berdichevsky's tensors and introduces a modified Kondo tensor for better consistency.

## Key findings

- Ortiz's and Berdichevsky's tensors are equivalent.
- Kondo's tensor differs from the others.
- A modified Kondo tensor is proposed to address discrepancies.

## Abstract

This article attempts to clarify an issue regarding the proper definition of plastic dislocation density tensor. This study shows that the Ortiz's and Berdichevsky's plastic dislocation density tensors are equivalent with each other, but not with Kondo's one. To fix the problem, we propose a modified version of Kondo's plastic dislocation density tensor.