Extended deformable tension-shear model for graphene layered materials with non-uniform staggering

Abstract

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 lc=Dh0/G is defined, where D is the in-plane tension stiffness of graphene, h0 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 Δmin/lc plays an important role in determining the mechanical behaviors of graphene layered materials. For example, when Δmin<0.5lc the intralayer force distribution in platelet is linear which is the uniform shear strain solution of nacre-like structure, while when Δmin>8lc, 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.