Regularly configured structures with polygonal prisms for three-dimensional auxetic behaviour

Area of Science:

• Materials Science
• Solid Mechanics
• Metamaterials

Background:

• Poisson's ratio describes a material's tendency to deform in directions perpendicular to applied force.
• Traditional materials typically exhibit positive Poisson's ratios.
• Auxetic materials, with negative Poisson's ratios, offer unique mechanical properties.

Purpose of the Study:

• To design and analyze structures with negative Poisson's ratios using regular polygonal prisms.
• To identify the geometric constraints for achieving auxetic behavior in these structures.
• To provide a theoretical and numerical basis for these novel materials.

Main Methods:

• Construction of unit cells using regular n-gonal component prisms.
• Mathematical derivation of the Poisson's ratio formula for specific n-gonal structures.
• Analytical and numerical verification of the auxetic properties.

Main Results:

• Identified n=3, 4, and 6 as the only possible values for regular n-gonal prism-based structures.
• Derived specific Poisson's ratio formulas for these three configurations.
• Demonstrated negative Poisson's ratios under defined geometric conditions through analysis and simulation.

Conclusions:

• Regular polygonal prism-based structures can be engineered to exhibit negative Poisson's ratios.
• The geometric parameters of the component prisms are critical for achieving auxetic behavior.
• These findings open avenues for designing advanced metamaterials with tailored mechanical responses.