Analyzing the bending deformation of van der Waals-layered materials by a semi-discrete layer model

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Van der Waals (vdW)-layered materials, such as graphite, exhibit unique mechanical properties owing to their structural and mechanical anisotropies. This study reports the development of a mechanical model that reproduces the characteristics of the nonlinear and reversible bending deformation of vdW-layered materials, while taking into account the microscopic mechanism of the discrete interlayer slips. The vdW-layered material was modeled as a stack of interacting discrete deformable layers (semi-discrete layer model), and the interlayer interaction was modeled using a cohesive zone model that reproduced the localized interlayer slip. Using the finite-element method, out-of-plane bending deformation analyses were performed on the cantilevers of the highly oriented pyrolytic graphite (HOPG) and MoTe2, and the validity of the model was verified by comparing it with the experimental results. The model accurately reproduced the loading and unloading behaviors in the experiments for the submicron HOPG cantilevers or the large nonlinear and reversible deformation with a hysteresis loop. Furthermore, the model reproduced well the characteristics of the bending experiments for the micro-MoTe2 cantilevers, or the intermittent decrease in stiffness during the loading process and deformation restoration during the unloading process. These results demonstrated that the designed semi-discrete layer model can be universally applied to reproduce the bending deformation characteristics of a variety of vdW-layered materials and can be employed to effectively elucidate the underlying deformation mechanisms.