TY - JOUR
T1 - Analytical relationships for 2D Re-entrant auxetic metamaterials
T2 - An application to 3D printing flexible implants
AU - Hedayati, Reza
AU - Yousefi, Armin
AU - Dezaki, Mohammadreza Lalegani
AU - Bodaghi, Mahdi
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - 3D printing
KW - Achilles tendon
KW - Analytical solution
KW - Metamaterials
KW - Negative Poisson's ratio
KW - Re-entrant
UR - http://www.scopus.com/inward/record.url?scp=85162776255&partnerID=8YFLogxK
U2 - 10.1016/j.jmbbm.2023.105938
DO - 10.1016/j.jmbbm.2023.105938
M3 - Article
C2 - 37263172
AN - SCOPUS:85162776255
SN - 1751-6161
VL - 143
JO - Journal of the mechanical behavior of biomedical materials
JF - Journal of the mechanical behavior of biomedical materials
M1 - 105938
ER -