Idealized 3D Auxetic Mechanical Metamaterial: An Analytical, Numerical, and Experimental Study

Area of Science:

• Materials Science
• Mechanical Engineering
• Solid Mechanics

Background:

• Mechanical metamaterials exhibit unique properties not found in nature.
• Auxetic metamaterials, characterized by negative Poisson's ratio (NPR), offer significant industrial potential.
• The 3D re-entrant structure is a key auxetic metamaterial design.

Purpose of the Study:

• To analytically, numerically, and experimentally investigate the mechanical properties of an idealized 3D re-entrant auxetic metamaterial.
• To derive analytical relationships for elastic modulus, yield stress, and Poisson's ratio.
• To explore the influence of geometric parameters on the auxetic behavior.

Main Methods:

• Analytical modeling using Euler-Bernoulli and Timoshenko beam theories.
• Numerical simulations employing beam and volumetric finite element approaches.
• Experimental validation through additive manufacturing (3D printing) and compression testing.

Main Results:

• Analytical and volumetric finite element models showed good agreement with experimental data.
• Geometric parameter θ significantly impacts the sign and magnitude of Poisson's ratio.
• Compression-dominated struts (angle φ) enhance structural strength and stiffness, enabling zero Poisson's ratio designs.

Conclusions:

• The study validates the analytical and numerical models for 3D re-entrant structures.
• Geometric parameters critically control auxetic behavior, offering tunable properties.
• A lightened 3D re-entrant structure was introduced and compared, showing potential for optimized performance.