Interlayer-slip-mediated large deflection bending of multilayer two-dimensional structures: theory and application

Multilayer two-dimensional (2D) materials often exhibit bending profiles and nonlinear responses that lie between membranes and large deflection plates, primarily due to significant interlayer slip. However, a comprehensive theoretical model to quantify this phenomenon remains lacking. By employing an energy variational approach based on complex-variable formalism, this work establishes a concise and general set of governing equations for large deflection bending of multilayer 2D structures. Exact and perturbative solutions for one-dimensional (1D) and axisymmetric pressurized bubbles are derived and validated by Finite Element Method (FEM) simulations. The analytical results quantitatively reveal the influence of the shear factor, a dimensionless parameter quantifying interlayer slip resistance, on the system’s bending profiles and responses, as well as the transition from membrane-like to plate-like behavior. This framework not only explains the nonlinear bending behavior measured in previous experiments on multilayer 2D materials, but also enables direct extraction of interlayer shear parameters. Consequently, it offers critical insights for strain engineering, interfacial property characterization, and the design of functional devices based on multilayer 2D systems.