Graphene-metal nanolayered composites (GMNCs) are a new generation of nano-structural composites characterized by a very high density of graphene reinforced interfaces (GRI) between metal nanolayers. Compared to traditional graphene flake reinforced composites, GMNCs have much higher strength, toughness and ductility due to the excellent ability of GRI on constraining dislocation motion and crack propagation. Despite numerous experimental and numerical studies on the mechanical behavior of GMNCs, the underlying strengthening mechanism is still not fully understood due to the absence of appropriate theoretical model. This paper proposes a continuum mechanics based theoretical model to explain the strengthening mechanism in GMNCs. In this model, the metal matrix and the GRI are simulated as homogenous elastic medium of infinite extend and inextensible thin membrane of zero thickness, respectively. Using the theoretical model, two boundary value problems namely (i) A circular prismatic dislocation loop approaching to the GRI and (ii) A mixed mode I/II penny-shaped crack near the GRI are formulated to reveal the two key strengthening mechanism: dislocation blocking and crack shielding, respectively. The two problems are solved analytically by the Generalized Kelvin's Solution (GKS) based method for 3D elasticity and Fredholm integral integration technique. Exact closed form solution for the Peach-Koehler (P-K) force on the dislocation loop is obtained. An efficient numerical scheme is developed to solve the Fredholm integral integration for the crack problem with very high accuracy. It is shown that our theoretical model can well capture and explain the strengthening mechanism observed in experiments. Moreover, the dominant role of Poisson's ratio on the strengthening efficiency is also revealed by our model. This finding implies the exciting possibility that the strength of GMNCs can be tailored by controlling the Poisson's ratio of the metal matrix. The present theoretical modeling can provide valuable insights into the mechanics-based design of GMNCs.

石墨烯-金属纳米层复合材料（GMNC）是新一代纳米结构复合材料，其特征是金属纳米层之间具有非常高密度的石墨烯增强界面（GRI）。与传统的石墨烯片增强复合材料相比，由于GRI优异的约束位错运动和裂纹扩展的能力，GMNCs具有更高的强度、韧性和延展性。尽管对 GMNC 的机械行为进行了大量的实验和数值研究，但由于缺乏适当的理论模型，其潜在的强化机制仍然不完全清楚。本文提出了一种基于连续介质力学的理论模型来解释 GMNC 的强化机制。在该模型中，金属基体和 GRI 分别被模拟为无限延伸的均质弹性介质和零厚度的不可延伸薄膜。利用理论模型，提出了两个边值问题，即 (i) 接近 GRI 的圆棱柱形位错环和 (ii) GRI 附近的混合模式 I/II 便士形裂纹，以揭示两个关键的强化机制：位错分别是阻塞和裂纹屏蔽。这两个问题通过基于广义开尔文解 (GKS) 的 3D 弹性方法和 Fredholm 积分积分技术来解析解决。获得了位错环上 Peach-Koehler (PK) 力的精确闭式开发了一种有效的数值方案，以非常高的精度求解裂纹问题的 Fredholm 积分。结果表明，我们的理论模型可以很好地捕捉和解释实验中观察到的强化机制。此外，我们的模型还揭示了泊松比对强化效率的主导作用。这一发现暗示着一种令人兴奋的可能性，即可以通过控制金属基体的泊松比来调整 GMNC 的强度。目前的理论模型可以为基于力学的 GMNC 设计提供有价值的见解。