Generalized elastica theory for multilayered van der Waals materials: Morphological transformations and deformability

Multilayered van der Waals materials (MvMs) are transforming advanced materials and device engineering. However, their mechanical complexity—arising from the interplay of monolayer bending, interlayer interactions, and intralayer elasticity—remains poorly understood. To address this, we develop a generalized elastica model that incorporates geometric nonlinearity, intralayer elasticity, and interlayer sliding, governed by two dimensionless parameters: the normalized shear-lag and shear-bending coefficients. Under specified loading and boundary conditions, such as a prescribed mean curvature, the model predicts four characteristic morphologies: smooth bending, interlayer sliding, local delamination, and kink formation, following a set of morphology diagrams in terms of the two governing parameters. Moreover, we introduce a dimensionless factor to quantify the deformability of MvMs, offering a metric for tailoring their mechanical response. The model is validated against coarse-grained molecular dynamics simulations of an MvM cantilever subjected to midpoint indentation. This work establishes a robust theoretical framework for understanding the fundamental constitutive behaviors of MvMs and provides rational design principles for optimizing MvM-based functional structures.