Mechanical anisotropy of two-dimensional metamaterials: a computational study

Area of Science:

• Materials Science and Engineering
• Computational Materials Science
• Mechanics of Materials

Background:

• Metamaterials offer unique properties like negative Poisson's ratio, driven by their structure and constituent materials.
• Two-dimensional (2D) materials (e.g., graphene, phosphorene) are promising for metamaterials due to their tunability.
• The relationship between nanostructure, composition, and properties, especially mechanical anisotropy, in 2D material metamaterials is underexplored.

Purpose of the Study:

• To investigate the deformation mechanisms of 2D material-based metamaterials with sinusoidally curved ligaments.
• To explore the influence of mechanical anisotropy on the mechanical properties, particularly the negative Poisson's ratio.
• To provide design guidelines for auxetic 2D lattice structures with tunable negative Poisson's ratio.

Main Methods:

• Classical molecular dynamics simulations using a generic coarse-grained model.
• Analysis of deformation under axial tensile load, distinguishing bending-dominated and stretching-dominated stages.
• Parametric study on the effects of amplitude/wavelength ratio and stiffness ratio on auxetic behavior.

Main Results:

• Auxetic behavior arises from junction rotation in the bending-dominated deformation stage.
• Negative Poisson's ratio is significantly influenced by the amplitude/wavelength ratio and axial/transverse stiffness ratio.
• Tunable negative Poisson's ratio values (0 to 0.87) were achieved by varying geometric and material parameters.

Conclusions:

• The study elucidates the deformation mechanism governing auxetic behavior in 2D material metamaterials.
• Mechanical anisotropy and ligament geometry are critical for tailoring the negative Poisson's ratio.
• Findings offer practical guidelines for designing advanced 2D metamaterials with predictable auxetic responses.