The flexibility of two-dimensional (2D) materials enables static and dynamic ripples that are known to cause lateral contraction, shrinking of the material boundary. However, the limits of 2D materials' lateral expansion are unknown. Therefore, here we discuss the limits of the intrinsic lateral expansion of 2D materials that are modified by compressive line defects. Using thin sheet elasticity theory and sequential multiscale modeling, we find that the lateral expansion is inevitably limited by the onset of rippling. The maximum lateral expansion ${\chi }_{\text{max}}\approx 2.1t^2{\sigma }_d$, governed by the elastic thickness $t$ and the defect density ${\sigma }_d$, remains typically well below 1%. In addition to providing insight to the limits of 2D materials' mechanical limits and applications, the results highlight the potential of line defects in strain engineering, since for graphene they suggest giant pseudomagnetic fields that can exceed 1000 T.

中文翻译：

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具有线缺陷的二维材料的横向膨胀极限

二维 (2D) 材料的灵活性可实现静态和动态波纹，这些波纹已知会导致横向收缩、材料边界的收缩。然而，二维材料横向膨胀的极限是未知的。因此，我们在这里讨论了由压缩线缺陷修改的 2D 材料的固有横向膨胀的限制。使用薄片弹性理论和顺序多尺度建模，我们发现横向扩展不可避免地受到波纹的开始的限制。最大横向膨胀${\chi }_{\text{最大限度}}\approx 2.1{吨}^2{\sigma }_d$, 受弹性厚度控制 $吨$ 和缺陷密度 ${\sigma }_d$, 通常仍远低于 1%。除了提供对 2D 材料机械限制和应用限制的洞察之外，结果还突出了应变工程中线缺陷的潜力，因为对于石墨烯，它们建议了可以超过 1000 T 的巨大伪磁场。