Saturation and periodic self-stress in geometric auxetics

Area of Science:

• Materials Science
• Mechanical Engineering
• Solid Mechanics

Background:

• Auxetic materials exhibit unique negative Poisson's ratio properties.
• Designing three-dimensional periodic auxetic structures presents geometric and kinematic challenges.
• Low valency graphs are desirable for simplified structural analysis.

Purpose of the Study:

• To develop a methodology for creating auxetic designs from low valency periodic graphs.
• To explore the relationship between graph saturation and auxetic behavior.
• To generate a wide array of distinct auxetic structures with controlled kinematics.

Main Methods:

• Utilized a general methodology to construct an initial periodic bar-and-joint framework.
• Employed a saturation process by adding edge orbits to increase framework valency.
• Analyzed the deformation path and crystallographic symmetry of saturated and desaturated frameworks.

Main Results:

• An initial framework with valency seven and one degree of freedom was produced.
• Saturation increased valency to 16, enhancing crystallographic symmetry and defining the deformation trajectory.
• Reducing saturation yielded numerous distinct auxetic designs sharing the same fundamental kinematics.

Conclusions:

• A systematic approach to designing auxetic structures from low valency periodic graphs is established.
• The saturation process effectively modifies structural symmetry and kinematic description without altering the auxetic deformation path.
• This method provides a versatile route to a vast number of auxetic designs with predictable behavior.