标题： 基于墙纸群的机械超材料：包含机械响应的数据集 显示英文标题

标题： Wallpaper Group-Based Mechanical Metamaterials: Dataset Including Mechanical Responses

摘要： 机械超材料通常通过不稳定性表现出图案变换，这使其在软体机器人、声音减少和生物医学等领域具有应用价值。 这些变换及其产生的机械性能与这些超材料的微观结构中的对称性密切相关，而这些对称性仍鲜有研究。 由于设计空间无限，设计此类材料具有挑战性，尽管机器学习提供了有前景的工具，但它们需要大量训练数据。 在此，我们提供了一个包含二维微观结构及其在超弹性、大变形范围内的宏观机械响应的数据集，包括屈曲现象。 微观结构是通过一种新方法生成的，该方法涵盖了所有17种墙纸对称群，并采用贝塞尔曲线以实现丰富的参数空间。 机械响应是通过基于有限元的计算均质化方法获得的。 该数据集包含1020种不同的几何结构，每种结构受到12种加载轨迹，总计12240种轨迹。 我们的数据集支持代理模型的开发和基准测试，促进对对称性-性能关系的研究，并能够对图案变换过程中的对称性破缺进行研究，可能会揭示机械超材料中的涌现行为。 显示英文摘要

摘要： Mechanical metamaterials often exhibit pattern transformations through instabilities, enabling applications in, e.g., soft robotics, sound reduction, and biomedicine. These transformations and their resulting mechanical properties are closely tied to the symmetries in these metamaterials' microstructures, which remain under-explored. Designing such materials is challenging due to the unbounded design space, and while machine learning offers promising tools, they require extensive training data. Here, we present a large dataset of 2D microstructures and their macroscopic mechanical responses in the hyperelastic, finite-strain regime, including buckling. The microstructures are generated using a novel method, which covers all 17 wallpaper symmetry groups and employs B\'ezier curves for a rich parametric space. Mechanical responses are obtained through finite element-based computational homogenization. The dataset includes 1,020 distinct geometries, each subjected to 12 loading trajectories, totaling 12,240 trajectories. Our dataset supports the development and benchmarking of surrogate models, facilitates the study of symmetry-property relationships, and enables investigations into symmetry-breaking during pattern transformations, potentially revealing emergent behavior in mechanical metamaterials.