Bending Mechanics Of Multilayer Van Der Waals Materials

Multilayer van der Waals materials,as a highly representative class of novel thin materials,hold extensive application promise in the fields such as flexible electronic,optoelectronic,and energy-storage devices for their excellent mechanical,optical,electronic,and thermal properties.Due to their inherent atomic scale thickness coupled with weak interlayer van der Waals interactions,multilayer van der Waals materials exhibit nontrivial out-of-plane responses and deformability.Therefore,it is of great significance for the mechanical optimization design of relevant devices to study their out-of-plane deformation,especially bending behavior.However,given the diversity of multilayer van der Waals materials and the variety of their structural dimensions,there remains no comprehensive understanding of how interlayer interactions affect their macroscopic response.Besides,a specific discussion of the nonplanar section effect in multilayered structures is still lacking.There is an urgent need for a general mechanical model to quantify the extraordinary bending characteristics of multilayer van der Waals materials.By introducing the competing mechanisms between intralayer stretching,interlayer shearing,and monolayer bending,we developed a general centerline-based theory for multilayered structures to portray the bending landscape of multilayer van der Waals materials.Combined with large-scale molecular dynamics simulations of three-point bending,it was found 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,we proposed a critical criterion to depict transformation from planar to nonplanar section deformation by introducing a dimensionless characteristic parameter,which reflects the competition mechanism between in-plane deformation and interlayer shear with respect to geometrical dimensions.The effective bending stifness was then systematically explored in the space of characteristic geometries and material properties to reveal the underlying mechanism of the anomalous size effect.We clarified the transition of proportional exponent between bending stiffness and normalized length with the dominant deformation under the competition between structural dimensions and material properties.Interestingly,we identified that the effective bending stiffness follows a unified scaling law regarding the dimensionless characteristic parameter.Furthermore,a series of deformation-mode phase diagrams were 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.The proposed diagrams were validated by several typical van der Waals materials and novel semiconducting two-dimensional materials.Using critical deflection and bending stiffness as important indicators,we proposed an optimization design idea for the deformability and flexibility of multilayer van der Waals materials with different layer numbers,where a softer and more adhesive structure is achieved by selecting a suitable material and regulating its interlayer shear modulus.The theoretical model presented here would not only serve as a valuable starting point for developing and validating more complete continuum-mechanical models for multilayered structures such as plate/shell mechanical behavior,geometric nonlinearity,and post-buckling but also provide guidelines for the design and optimization of multilayer van der Waals material-based devices.