Analytical solution and finite element approach to the dense re-entrant unit cells of auxetic structures

Chiral, star honeycomb, and re-entrant structures are among the most important structures of auxetic materials. In this study, a dense re-entrant unit cell is introduced for making a 3D auxetic structure to be used in high stiffness applications. A re-entrant structure is chosen due to its fundamental characteristics underlying the main characteristics of auxetic structures. The energy methods of solid mechanics along with numerical methods are used to study the fundamental concept of auxetic structures. Understanding the characteristics of the re-entrant structure will lead to the better comprehension of other structures of auxetic materials, which will eventually contribute to the advance of research in this new class of materials.