On the influence of interfacial properties to the bending rigidity of layered structures

Layered structures are ubiquitous, from one-atom thick layers in two-dimensional materials, to nanoscale lipid bi-layers, and to micro and millimeter thick layers in composites. The mechanical behavior of layered structures heavily depends on the interfacial properties and is of great interest in engineering practice. In this work, we give an analytical solution of the bending rigidity of bilayered structures as a function of the interfacial shear strength. Our results show that while the critical bending stiffness when the interface starts to slide plastically is proportional to the interfacial shear strength, there is a strong nonlinearity between the rigidity and the applied bending after interfacial plastic shearing. We further give semi-analytical solutions to the bending of bilayers when both interfacial shearing and pre-existing crack are present in the interface of rectangular and circular bilayers. The analytical solutions are validated by using finite element simulations. Our analysis suggests that interfacial shearing resistance, interfacial stiffness and preexisting cracks dramatically influence the bending rigidity of bilayers. The results can be utilized to understand the significant stiffness difference in typical biostructures and novel materials, and may also be used for non-destructive detection of interfacial crack in composites when stiffness can be probed through vibration techniques.