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Design-dependent mechanical performance of additively manufactured hybrid hierarchical TPMS-based auxetic polymer structures

  • Dr. Fatih Huzeyfe Öztürk is an Assistant Professor in the Department of Mechanical Engineering, Karabük University, Türkiye. He obtained his Ph.D. degree in Industrial Design Engineering from Karabük University in 2023. His main research areas include additive manufacturing, adhesive bonding, material modelling, and finite element analysis. He is currently involved in projects focusing on the mechanical characterization and simulation of advanced materials.

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    Assoc. Prof. Dr. Kerim Gökhan Aktaş is an Associate Professor in the Department of Mechanical Engineering, Karabük University, Türkiye. He received his Ph.D. degree in Mechanical Engineering from Karabük University in 2021. His research interests include mechanical vibrations, theory of machines, dynamics of mechanical systems, and solid mechanics.

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    Dr. Muhammet Mevlüt Karaca is an Assistant Professor at the Iron and Steel Institute, Karabük University, Türkiye. He received his Ph.D. degree in Mechanical Engineering from Karabük University in 2024. His research focuses on composite materials, tribology, and wear behavior of engineering materials. He also works on additive manufacturing, functionally graded structures, and advanced material design for industrial and structural applications.

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    Assoc. Prof. Dr. Abdurrahim Temiz is an Associate Professor in the Department of Mechanical Engineering, Karabük University, Türkiye. He earned his Ph.D. degree in Industrial Design Engineering from Karabük University in 2022. His research focuses on additive manufacturing, functionally graded and lattice structures, biodegradable materials, and process optimization using statistical design methods.

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    Assoc. Prof. Dr. Fatih Pehlivan is an Associate Professor in the Department of Mechanical Engineering, Karabük University, Türkiye. He received his Ph.D. degree in Mechanical Engineering from Karabük University in 2020. His research interests include solid mechanics, mechanical vibrations and noise, optimization, and material design. He has published studies on the mechanical behavior and optimization of engineering structures.
Published/Copyright: January 12, 2026
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Materials Testing
From the journal Materials Testing Volume 68 Issue 2

Abstract

Auxetic metamaterials with negative Poisson’s ratios exhibit unusual deformation behavior, making them ideal for energy absorption, biomedical, and protective applications. This study presents hybrid hierarchical polymer structures integrating Triply Periodic Minimal Surface (TPMS) geometries, Diamond (D), Gyroid (G), and Schwarz (S) into the walls of base auxetic lattices. Structures were fabricated using Tough resin via masked stereolithography (MSLA) 3D printing. Mechanical performance was evaluated under uniaxial compression in terms of stiffness, peak force, absorbed energy (AE), and specific absorbed energy (SAE). Additionally, bulk volume and surface area were used to determine the surface-area-to-volume ratio (SA/V). The results demonstrated that hybrid configurations significantly enhanced the SA/V ratio up to eightfold while maintaining auxetic behavior. Among the samples, the hexagonal honeycomb with Schwarz walls (HH–S) achieved the highest first peak force, whereas the square honeycomb rotated with Diamond walls (SHR-D) exhibited the lowest. The triangular honeycomb rotated with Schwarz walls (THR-S) recorded the highest AE, while Gyroid-based designs underperformed. The highest SAE (0.5790 J g−1) was observed in HH-D, while SH-D showed the lowest (0.0236 J g−1), indicating a 184.33 % difference. These findings highlight the effectiveness of TPMS-based hierarchical designs in improving the multifunctionality of auxetic metamaterials without sacrificing their inherent mechanical characteristics.

Keywords: hierarchical auxetic metamaterial; additive manufacturing; mechanical properties; auxetic structures; TPMS lattice structures
Corresponding author: Fatih Huzeyfe Öztürk, Department of Mechanical Engineering, Karabük University, Karabük, Türkiye, E-mail:

About the authors

Fatih Huzeyfe Öztürk

Dr. Fatih Huzeyfe Öztürk is an Assistant Professor in the Department of Mechanical Engineering, Karabük University, Türkiye. He obtained his Ph.D. degree in Industrial Design Engineering from Karabük University in 2023. His main research areas include additive manufacturing, adhesive bonding, material modelling, and finite element analysis. He is currently involved in projects focusing on the mechanical characterization and simulation of advanced materials.

Kerim Gökhan Aktaş

Assoc. Prof. Dr. Kerim Gökhan Aktaş is an Associate Professor in the Department of Mechanical Engineering, Karabük University, Türkiye. He received his Ph.D. degree in Mechanical Engineering from Karabük University in 2021. His research interests include mechanical vibrations, theory of machines, dynamics of mechanical systems, and solid mechanics.

Muhammet Mevlüt Karaca

Dr. Muhammet Mevlüt Karaca is an Assistant Professor at the Iron and Steel Institute, Karabük University, Türkiye. He received his Ph.D. degree in Mechanical Engineering from Karabük University in 2024. His research focuses on composite materials, tribology, and wear behavior of engineering materials. He also works on additive manufacturing, functionally graded structures, and advanced material design for industrial and structural applications.

Abdurrahim Temiz

Assoc. Prof. Dr. Abdurrahim Temiz is an Associate Professor in the Department of Mechanical Engineering, Karabük University, Türkiye. He earned his Ph.D. degree in Industrial Design Engineering from Karabük University in 2022. His research focuses on additive manufacturing, functionally graded and lattice structures, biodegradable materials, and process optimization using statistical design methods.

Fatih Pehlivan

Assoc. Prof. Dr. Fatih Pehlivan is an Associate Professor in the Department of Mechanical Engineering, Karabük University, Türkiye. He received his Ph.D. degree in Mechanical Engineering from Karabük University in 2020. His research interests include solid mechanics, mechanical vibrations and noise, optimization, and material design. He has published studies on the mechanical behavior and optimization of engineering structures.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: None declared.

  7. Data availability: Not applicable.

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Published Online: 2026-01-12
Published in Print: 2026-02-24

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/mt-2025-0247
Keywords for this article
hierarchical auxetic metamaterial; additive manufacturing; mechanical properties; auxetic structures; TPMS lattice structures

Articles in the same Issue

  1. Frontmatter
  2. Heat treatment and corrosion resistance of 304 stainless steel metal rubber
  3. Fatigue life and damage behaviors of GFRP pipes under circumferential bend loading
  4. Topology optimization and thickness minimization of a motor plate used in tower cranes
  5. Comparison of the ballistic performance of 6063, 6061, 6082 aluminum alloy louvers under 7.62 mm bullet impact
  6. Improvement of the mechanical properties of Kagome structures using PUR foam matrices
  7. Design-dependent mechanical performance of additively manufactured hybrid hierarchical TPMS-based auxetic polymer structures
  8. Microstructure and wear resistance of in-situ synthesized TiC/TiB2 reinforced iron-based composite laser cladded coating
  9. Fabrication and analysis of 3D printed ABS-iron powder composites for radar absorption
  10. Influence of riveting speed on mechanical performance of self piercing riveted (SPR) aluminum 5182 sheets
  11. Influence of GMAW welding parameters on grain size, precipitates, and hardness in alloy 6063-T5
  12. Tribomechanical properties of direct energy deposited ceramic reinforced coatings on alloy TC4
  13. Adhesive wear performance of NiHard-4, alloyed spherical cast iron compared to high Cr cast irons and tool steels
  14. Mechanical and thermal properties of jute fiber–reinforced composites with rice husk ash filler for structural applications
  15. Analysis of an internal heat exchanger (IHX) for vehicle air conditioning systems
  16. Multi-objective optimization of process parameters in electro discharge machining of Inconel 625 superalloy with different electrode materials
  17. Optimization of 3D printing parameters for thermal conductivity of carbon fiber reinforced PLA components
  18. Effect of rainwater immersion on the wear and friction characteristics of Ni–B and Ni–B–TiO2 coatings
  19. Wear resistivity and ANFIS modeling for hybrid aluminum metal matrix composites at elevated temperatures
  20. In vitro tribological behavior of Mg2Zn1Mn/HA-Al2O3 nano-biocomposites
  21. The mine blast algorithm for the structural optimization of electrical vehicle components
  22. Influence of stitching on the interlaminar fracture toughness energy – modes I and II – of unidirectional GFRP
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