A general theory for the bending of multilayer van der Waals materials

ZC Huang and ZZ He and YB Zhu and HA Wu, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 171, 105144 (2023).

DOI: 10.1016/j.jmps.2022.105144

Multilayer van der Waals (vdW) materials exhibit nontrivial out-of-plane responses and deformability due to their inherent atomic scale thickness coupled with weak interlayer vdW interactions, which call for a general mechanical framework to quantify such extraordinary characteristics given the structure and material properties. Here, we demonstrate that by considering the competing mechanisms between intralayer stretching, interlayer shearing, and monolayer bending, a general centerline-based theory for multilayered structures is developed to portray the bending landscape of multilayer vdW materials. Combined with large-scale molecular dynamics simulations of three-point bending, we find that when the slenderness ratio or the interlayer shear rigidity is smaller or the intralayer elasticity is higher, the multilayered structures exhibit pronounced nonplanar section deformation due to the interlayer shear capacity. To elucidate quantitative correlations between deformation distribution and structural dimensions and material properties, a critical criterion is proposed to depict the transformation from planar to nonplanar section deformation through a dimensionless characteristic parameter. The effective bending stiffness is then systematically explored in the space of characteristic geometries and material properties to reveal the underlying mechanism of the anomalous size effect. We identify that the effective bending stiffness follows a unified scaling law regarding the dimensionless characteristic parameter. More importantly, a series of deformation-mode phase diagrams are constructed using two universal characteristic lengths, intuitively illustrating the transition of dominated deformation modes and the synergism of geometries and inherent material properties on the bending responses. Validated by several typical vdW materials and novel semiconducting two-dimensional materials, the proposed diagrams not only deepen the understanding of bending in multilayer vdW materials but also provide guidelines for the design and optimization of vdW material-based devices.

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