Negative extensibility metamaterials: Occurrence and design-space topology

Area of Science:

• Materials Science and Engineering
• Solid Mechanics
• Metamaterials Design

Background:

• Negative extensibility is an unusual material property where structures contract when subjected to tensile loads beyond a critical point.
• Understanding the underlying mechanics and design principles is crucial for harnessing this property in advanced materials.

Purpose of the Study:

• To mathematically characterize the nonlinear strain energy function governing negative extensibility.
• To develop a comprehensive phase diagram for a unit cell structure to visualize nonlinear mechanical behaviors.
• To identify the design parameter space for achieving negative extensibility.

Main Methods:

• Mathematical analysis of the nonlinear strain energy function.
• Systematic exploration of design parameters for a simple unit cell.
• Development of a phase diagram illustrating mechanical behaviors.

Main Results:

• A clear negative extensibility region was identified within the phase diagram.
• The property is confirmed to be rare, occurring within a narrow range of design parameters.
• Simple bistable cells with specific linearly elastic link properties can exhibit negative extensibility.

Conclusions:

• Negative extensibility, though rare, is achievable in simple bistable unit cells.
• The findings suggest this property may be more prevalent than previously assumed.
• These unit cells offer potential for designing novel periodic mechanical metamaterials and architectural metastructures.