Designing Structural Metamaterials ^†

Metamaterials are materials that exhibit properties that are opposite to those normally found in nature. For structural metamaterials, the most studied cases are those showing negative Poisson’s ratio (also known as auxetics), negative coefficient of thermal expansion (NTE), and/or negative linear compressibility (also known as negative bulk modulus).

These properties can be found in nature only for very specific cases and conditions. Cork is known to have a Poisson’s ratio of zero while re-entrant polymer foams and some metallic crystals have a Poisson’s ratio below zero [1]. Water is known to have a negative thermal expansion coefficient between the temperatures of 0 and 4 °C, while ZrW2O8 shows the same behavior between the temperatures of 0.3 and 1050 Kelvin [2]. Furthermore, there are very few materials that naturally present negative linear compressibility, as shown by most research carried out on man-made structures.

Anepectic materials, on the other hand, which simultaneously present both negative Poisson’s ratio and negative thermal expansion, while being potentially advantageous in fields as diverse as those of medicine, defense, sports, automobile, and aeronautics, have only recently come to light, and as such still warrant in-depth studies. The anepectic behavior can be obtained by coupling two or more adequately chosen base materials with specific architectures.

By observing the five categories of known auxetic materials (re-entrant, chiral, rotating, crumpled sheet, and perforated sheet), it is possible to choose which parts of a structure should be replaced with a second material of suitable stiffness and thermal expansion to transform an auxetic structure into an anepectic one. This approach was previously applied for 2D meshes [3], and current work has extended similar results into the third dimension.

The current work reports a series of simulation and experimental results on rotating and re-entrant 3D metamaterials manufactured by the filament deposition method, as well as the underlying theories and state-of-the-art presentation [4].