Auxetic properties and anisotropy of elastic material constants of 2D crystalline media

TL;DR

This paper investigates the anisotropic elastic properties of 2D crystalline media, deriving conditions for auxetic behavior and mapping regions of auxeticity in quadratic symmetry crystals.

Contribution

It provides necessary and sufficient conditions for auxeticity in 2D crystals and characterizes stability regions for quadratic symmetry materials.

Findings

Identified conditions for auxetic, non-auxetic, and auxetic behaviors.

Mapped stability regions for quadratic symmetry crystals.

Presented examples of auxetic properties in various 2D crystal symmetries.

Abstract

Anisotropies of Young's modulus E, the shear modulus G, and Poisson's ratio of all 2D symmetry systems are studied. Simple necessary and sufficient conditions on their elastic compliances are derived to identify if any of these crystals are completely auxetic, non-auxetic and auxetic. Particular attention is paid to 2D crystals of quadratic symmetry. All mechanically stable quadratic crystals are characterized by three parameters belonging to a prism with the stability triangle in the base. Regions in the stability triangle in which quadratic materials are completely auxetic, non-auxetic, and auxetic are established. Examples of all types of auxetic properties of crystals of oblique and rectangular symmetry are presented.