Analytical relationships for 2D Re-entrant auxetic metamaterials: An application to 3D printing flexible implants

Hedayati, R.; Yousefi, Armin; Dezaki, Mohammadreza Lalegani; Bodaghi, Mahdi

doi:10.1016/j.jmbbm.2023.105938

Analytical relationships for 2D Re-entrant auxetic metamaterials

Title

Analytical relationships for 2D Re-entrant auxetic metamaterials: An application to 3D printing flexible implants

Author

Hedayati, R. (TU Delft Novel Aerospace Materials)
Yousefi, Armin (Nottingham Trent University)
Dezaki, Mohammadreza Lalegani (Nottingham Trent University)
Bodaghi, Mahdi (Nottingham Trent University)

Date

2023

Abstract

Both 2D and 3D re-entrant designs are among the well-known prevalent auxetic structures exhibiting negative Poisson's ratio. The present study introduces novel analytical relationships for 2D re-entrant hexagonal honeycombs for both negative and positive ranges of the cell interior angle θ (θ<0 showing a negative Poisson's ratio). The derived analytical solutions are validated against finite element method (FEM) and experimental results. The results show that, compared to the analytical solutions available in the literature, the analytical relationships presented in this study provide the most accurate results for elastic modulus, Poisson's ratio, and yield stress. The analytical/computational tools are then implemented for designing Kinesio taping (KT) structures applicable to treatment of Achilles tendon injuries. One of the main features of the Achilles tendon is a natural auxetic behavior. Poisson's ratio distribution of an Achilles tendon is obtained using longitudinal and transverse strains and are then used to design and 3D print thermoplastic polyurethane (TPU) KT structures with non-uniform distribution of auxetic unit cells. The presented novel KT shows that it is capable of replicating the deformation and global and local Poisson's ratio distributions, similar to those of the Achilles tendon. Due to the absence of similar formulations and procedures in the literature, the results are expected to be instrumental for designing and 3D printing of flexible implants with unusual auxeticity.

Subject

3D printing
Achilles tendon
Analytical solution
Metamaterials
Negative Poisson's ratio
Re-entrant

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http://resolver.tudelft.nl/uuid:03f66adf-794b-4db6-a2b2-ec429d038ab0

DOI

https://doi.org/10.1016/j.jmbbm.2023.105938

ISSN

1751-6161

Source

Journal of the Mechanical Behavior of Biomedical Materials, 143

Part of collection

Institutional Repository