Buckling of van der Waals materials

Unlike common materials, van der Waals (vdW) materials are vulnerable to buckling under basal plane compression regardless of their slenderness. Understanding their post-buckling configurations is fundamental to preparing large-size high-quality samples, modulating physical properties, and revealing the strengthening and toughening mechanism in layered crystalline phases. Nevertheless, due to their unique features, such as layered crystalline lattice, decoupled intralayer and bending deformation mechanisms, and extreme anisotropy, vdW materials exhibit unique post-buckling behaviors that remain poorly understood. In this paper, we propose a general layered model, incorporating both the layered structure and interlayer tension–compression asymmetry, which can well capture the post-buckling evolvement behaviors for both bulk and finite-thickness vdW materials. The analytical expression of initial buckling strain is derived, only depending on two dimensionless parameters, reflecting the competition among intralayer compression, monolayer bending and interlayer shearing modes. For bulk vdW materials, the kink band configuration forms during the post-buckling deformation. Further analysis indicates that it is energetically driven by the release of intralayer and interlayer compression energies, stemming from the extreme anisotropy of layered crystalline structure, while the transformation from a sinusoidal configuration to a kink band configuration is induced by high interlayer pressure during post-buckling. In finite-thickness systems, three distinct post-buckling configurations are identified. i.e., internal kink, internal fold, global buckling, arising from the impaired lateral constraint as the slenderness increases. Phase diagrams for these three post-buckling configurations are presented. This work advances our understanding of the buckling and post-buckling evolvement behaviors in vdW materials, offering valuable insights for high-quality sample preparation and strengthening and toughening design of layered crystalline phases.