Analytical solution and finite element approach to the 3D re-entrant structures of auxetic materials

• We adapt a 2D re-entrant structure for a 3D ones using energy methods.
• This paper contributes to understanding the characteristics of re-entrant structures.
• It contributes to advancement of research in auxetic materials.
• We use both finite element and analytical solution and compare results.
• The findings lay out a good foundation for further research.

One of the methods in understanding the real microstructure of auxetic material is by separating it into several simplified structures that have distinct mechanisms. Among those simplified structures are chiral and re-entrant structures. This paper adapts a 2D re-entrant structure for a 3D auxetic structure. A re-entrant structure is chosen due to its fundamental characteristics underlying the main characteristics of auxetic materials. The energy methods of solid mechanics along with numerical methods are used to study the fundamental concept of auxetic materials. 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.

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