Current theoretical works on the mechanical behaviors of graphene layered materials are usually limited to the regular staggering. But, more practical staggering modes haven't been paid enough attention. In this work, we extend the deformable tension-shear (DTS) model to non-uniform staggering through two different methods, i.e. eigenvalue method and isolated break method. Then, different staggering modes such as the regular staggering with offset, stair-wise staggering, and non-uniform staggering are studied under the framework of the extended DTS model. An effective shear load transfer length $l_c=\sqrt{D{h}_0/G}$ is defined, where D is the in-plane tension stiffness of graphene, $h_0$ is the interlayer distance, G is the interlayer shear modulus. It is found the ratio of minimum in-plane adjacent break distance to the effective shear load transfer length ${\Delta }_{min}/l_c$ plays an important role in determining the mechanical behaviors of graphene layered materials. For example, when ${\Delta }_{min}<0.5l_{\mathrm{c}}$ the intralayer force distribution in platelet is linear which is the uniform shear strain solution of nacre-like structure, while when ${\Delta }_{min}>8l_c$, the intralayer force has a long plateau away from the break and the plateau value is also the same at different platelets. Therefore, the in-plane interaction of adjacent breaks can be ignored for large size of graphene sheet, based on which the in-plane isolated break solution is derived. Then, the interlayer force concentration factor (IFCF) is analytically obtained for arbitrary N graphene layers with r aligned breaks. Further analysis indicates the in-plane isolated break solution gives the upper bound of IFCF for the uniform stair-wise staggering but may underestimate the IFCF for random staggering. The results presented herein comprehensively explore the staggering effect on mechanical behaviors of graphene layered materials which may guide the design of high-performance nacre-like materials.

当前关于石墨烯层状材料力学行为的理论研究通常仅限于规则的交错。但是，更实用的交错模式还没有得到足够的重视。在这项工作中，我们通过两种不同的方法，即特征值法和孤立断裂法，将可变形拉剪（DTS）模型扩展到非均匀交错。然后，在扩展的DTS模型的框架下研究了不同的交错模式，例如有偏移的规则交错、阶梯交错和非均匀交错。有效剪切载荷传递长度${升}_C=\sqrt{D{H}_0/G}$被定义，其中D是石墨烯的面内拉伸刚度，$H_0$是层间距离，G是层间剪切模量。发现最小平面内相邻断裂距离与有效剪切载荷传递长度的比值${\Delta }_{米\mathrm{一世}n}/{升}_C$在决定石墨烯层状材料的力学行为方面起着重要作用。例如，当${\Delta }_{米\mathrm{一世}n}<0.5{升}_{\mathrm{C}}$ 片层内力分布是线性的，是类珍珠层结构的均匀剪应变解，而当 ${\Delta }_{米\mathrm{一世}n}>8{升}_C$, 层内力距断裂处有很长的平台期，平台值在不同的血小板上也相同。因此，对于大尺寸的石墨烯片，可以忽略相邻断裂的面内相互作用，在此基础上推导出面内孤立断裂解。然后，对于任意的被分析得到的层间力集中系数（IFCF）ñ与石墨烯层ř对齐中断。进一步的分析表明，面内隔离断裂解给出了均匀阶梯交错的 IFCF 上限，但可能低估了随机交错的 IFCF。本文提出的结果全面探讨了石墨烯层状材料对机械行为的惊人影响，这可能会指导高性能类珍珠层材料的设计。