纳米尺度微观结构在显著提高材料强度的同时，也极大地限制了材料的延展性，其强度和韧性已成为先进材料研究关注重点。同时，以格里菲斯准则为代表的宏观断裂力学理论逐渐发展成熟，如何将其应用至原子尺度的微纳材料也引起了广泛的研究兴趣。目前，已有不少研究用原子尺度的J积分描述二维材料的断裂韧性，但一方面缺少验证的细节讨论；另一方面，对J积分的临界条件的描述相对模糊。因此，本文实现了原子尺度J积分计算的三种方法，并通过分子动力学模拟，基于带中心裂纹的石墨烯体系验证了其稳定性和等价性。结合第一性原理计算，对六种常见二维材料的边缘能和J积分进行了表征和分析，在原子尺度探索了格里菲斯准则，讨论并分析了不同二维材料的断裂韧性和行为。在此基础上，提出了三种J积分的临界判断机制，探讨了其适用性和局限性；同时，发现J积分可以定性反映结构中的相变、裂纹尖端条件差异等。此外，基于第一性原理的计算和弹性理论的预测，对单层富勒烯 (mC60) 的各向异性力学特性、破坏模式等进行了研究，为原子尺度断裂韧性分析方法推广至团簇二维材料做准备。

Significantly improving the strength of materials, microstructures of nanoscale also greatly limit the ductility of materials, which leads the strength and toughness of materials to become a focus of advanced materials research. Meanwhile, macroscopic fracture mechanics theories, such as the Griffith criterion, have gradually been developed and become matured. The application of these theories to the atomic scale of micro/nano materials has also aroused huge research interest. Currently, there are many studies using the atomic-scale J-integral to describe the fracture toughness of two-dimensional (2D) materials. However, on the one hand, there is a lack of detailed discussion and validation. On the other hand, the description of the critical condition for the J-integral is relatively vague. Therefore, this paper realizes three methods for calculating the J-integral at the atomic scale, and verifies their stability and equivalence based on molecular dynamics simulations of graphene systems with a central crack. Combined with first-principles calculations, the edge energies and J-integrals of six common 2D materials are characterized and analyzed. The Griffith criterion is explored at the atomic scale, and the fracture toughness and behaviors of different 2D materials are discussed and analyzed. Based on this, three critical criteria for the J-integral are proposed, whose applicability and limitations are explored. In addition, it is found that the J-integral can qualitatively reflect the structural phase transitions and differences in crack tip conditions. Furthermore, based on first-principles calculations and predictions of elastic theory, the anisotropic mechanical properties and failure modes of monolayer fullerenes (mC60) are studied, preparing for the extension of atomic-scale fracture toughness analysis methods to cluster 2D materials.