VELAS: An open-source toolbox for visualization and analysis of elastic anisotropy

Although elastic properties and their anisotropy play a crucial role in materials science and technology, it is not straightforward to visualize how properties such as shear modulus vary with the direction of stress/strain. Here, written in GNU Octave, we have developed an easy-to-use, flexible, and user-friendly open-source toolbox with a graphical user interface, VELAS, which automatically visualizes and analyses the elastic anisotropy of arbitrary crystal systems using second-order elastic constants. Using Voigt-Reuss-Hill averaging scheme, VELAS allows the calculation of more than ten significant mechanical properties such as modulus, hardness, anisotropy index, ductility, and bond type. It also supports the determination of the mechanical stability of crystals at atmospheric and high pressures using the Born mechanical stability criterion. VELAS provides a new easy-to-use tool for detecting and identifying unusual mechanical properties such as negative Poisson's ratio, negative linear compressibility, and negative bulk modulus. VELAS offers several alternative visualization solutions for elastic properties, such as unit spherical projection, and map projection, and supports direct output of high-quality images. Furthermore, VELAS provides users an interface to read data from the Materials Project API in both online and offline modes. After introducing the basic theory, we detail the software framework, technical route, and installation specifications of VELAS. Moreover, the reliability and versatility of VELAS are confirmed by the analysis of the cases of negative linear compressibility, negative Poisson's ratio, hardness, and fracture toughness.尽管弹性性质及其各向异性在材料科学与工程领域发挥着至关重要的作用，但直观呈现剪切模量等力学性能随应力/应变方向的变化规律并非易事。本次研究基于GNU Octave开发了一款易用、灵活且交互友好的开源图形用户界面（Graphical User Interface）工具包VELAS，该工具可利用二阶弹性常数自动可视化并分析任意晶系的弹性各向异性。借助Voigt-Reuss-Hill平均法，VELAS可计算十余种重要的力学性能，包括弹性模量、硬度、各向异性指数、延性以及键型等。该工具还可基于Born力学稳定性判据，判断晶体在常压与高压环境下的力学稳定性。VELAS还为检测与识别负泊松比、负线性压缩率、负体积模量等非常规力学性能提供了全新的易用工具。VELAS针对弹性性质提供了多种可视化方案，例如单位球面投影与地图投影，并支持直接导出高质量图像。此外，VELAS还为用户提供了可在线、离线两种模式读取Materials Project API数据的交互接口。在介绍基本理论之后，本文详细阐述了VELAS的软件架构、技术实现路径与安装规范。此外，通过对负线性压缩率、负泊松比、硬度以及断裂韧性相关案例的分析，验证了VELAS的可靠性与通用性。