[1] H. A. Schwarz, Gesammelte Mathematische Abhandlungen. in AMS Chelsea Publishing Series. Chelsea Publishing Company, 1972. [Online]. Available: https://books.google.co.jp/books?id=cKWBJBcM_18C.
[2] T. Poltue, C. Karuna, S. Khrueaduangkham, S. Seehanam, and P. Promoppatum, “Design Exploration of 3D-printed Triply Periodic Minimal Surface Scaffolds for Bone Implants,“ International Journal of Mechanical Sciences, Vol. 211, p. 106762, 2021, doi: https://doi.org/10.1016/j.ijmecsci.2021.106762.
[3] D. W. Abueidda, M. Bakir, R. K. Abu Al-Rub, J. S. Bergström, N. A. Sobh, and I. Jasiuk, “Mechanical Properties of 3D Printed Polymeric Cellular Materials with Triply Periodic Minimal Surface Architectures,“ Materials & Design, Vol. 122, pp. 255–267, 2017, doi: https://doi.org/10.1016/j.matdes.2017.03.018.
[4] M. Rezapourian, N. Kamboj, and I. Hussainova, “Numerical Study on the Effect of Geometry on Mechanical Behavior of Triply Periodic Minimal Surfaces,“ IOP Conference Series: Materials Science and Engineering, Vol. 1140, No. 1, p. 012038, 2021, doi: https://doi.org/10.1088/1757-899X/1140/1/012038.
[5] A. H. Schoen, “Infinite Periodic Minimal Surfaces without Self-intersections,“, Vol. 5541, United States: National Aeronautics and Space Administration, 1970.
[6] S. AlMahri, R. Santiago, D. Lee, H. Ramos, H. Alabdouli, M. Alteneiji, Z. Guan, and M. Alves, “Investigation of the Specific Energy Absorption of Triply Periodic Minimal Surfaces Subjected to Impact Loading,“ EPJ Web of Conferences, Vol. 250, p. 01022, 2021, doi: https://doi.org/10.1051/epjconf/202125001022.
[7] V. Nguyen-Van, P. Tran, C. Peng, L. Pham, G. Zhang, and H. Nguyen-Xuan, “Bioinspired Cellular Cementitious Structures for Prefabricated Construction: Hybrid Design & Performance Evaluations,“ Automation in Construction, Vol. 119, p. 103324, 2020, doi: https://doi.org/10.1016/j.autcon.2020.103324.
[8] R. Asbai-Ghoudan, S. Ruiz de Galarreta, and N. Rodriguez-Florez, “Analytical Model for the Prediction of Permeability of Triply Periodic Minimal Surfaces,“ Journal of the Mechanical Behavior of Biomedical Materials, Vol. 124, p. 104804, 2021, doi: https://doi.org/10.1016/j.jmbbm.2021.104804.
[9] O. Al-Ketan and R. K. Abu Al-Rub, “Multifunctional Mechanical Metamaterials Based on Triply Periodic Minimal Surface Lattices,“ Advanced Engineering Materials, Vol. 21, No. 10, 2019, doi: https://doi.org/10.1002/adem.201900524.
[10] J. M. Ashraf, S. E. Taher, D.-W. Lee, K. Liao, and R. K. Abu Al-Rub, “On the Computational Modeling, Additive Manufacturing, and Testing of Tube-networks TPMS-based Graphene Lattices and Characterizing Their Multifunctional Properties,“ APL Materials, Vol. 10, No. 12, 2022, doi: https://doi.org/10.1063/5.0101412.
[11] C. S. Ha, R. S. Lakes, and M. E. Plesha, “Cubic Negative Stiffness Lattice Structure for Energy Absorption: Numerical and Experimental Studies,“ International Journal of Solids and Structures, Vol. 178–179, pp. 127–135, 2019, doi: https://doi.org/10.1016/j.ijsolstr.2019.06.024.
[12] T. Wang, J. An, H. He, X. Wen, and X. Xi, “A Novel 3D Impact Energy Absorption Structure with Negative Poisson’s Ratio and its Application in Aircraft Crashworthiness,“ Composite Structures, Vol. 262, p. 113663, 2021, doi: https://doi.org/10.1016/j.compstruct.2021.113663.
[13] Y. Du, J. Maassen, W. Wu, Z. Luo, X. Xu, and P. D. Ye, “Auxetic Black Phosphorus: A 2D Material with Negative Poisson’s Ratio,“ Nano Letters, Vol. 16, No. 10, pp. 6701–6708, 2016, doi: https://doi.org/10.1021/acs.nanolett.6b03607.
[14] J. N. Grima-Cornish, J. N. Grima, and D. Attard, “A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility,“ Materials, Vol. 13, No. 1, p. 79, 2019, doi: https://doi.org/10.3390/ma13010079.
[15] W. Yang, J. An, C. K. Chua, and K. Zhou, “Acoustic Absorptions of Multifunctional Polymeric Cellular Structures Based on Triply Periodic Minimal Surfaces Fabricated by Stereolithography,“ Virtual and Physical Prototyping, Vol. 15, No. 2, pp. 242–249, 2020, doi: https://doi.org/10.1080/17452759.2020.1740747.
[16] J. Feng, J. Fu, C. Shang, Z. Lin, and B. Li, “Porous Scaffold Design by Solid T-splines and Triply Periodic Minimal Surfaces,“ Computer Methods in Applied Mechanics and Engineering, Vol. 336, pp. 333–352, 2018, doi: https://doi.org/10.1016/j.cma.2018.03.007.
[17] J. Feng, J. Fu, X. Yao, and Y. He, “Triply Periodic Minimal Surface (TPMS) Porous Structures: from Multi-scale Design, Precise Additive Manufacturing to Multidisciplinary Applications,“ International Journal of Extreme Manufacturing, Vol. 4, No. 2, p. 022001, 2022, doi: https://doi.org/10.1088/2631-7990/ac5be6.
[18] S. Zhang, D. Da, and Y. Wang, “TPMS-infill MMC-based Topology Optimization Considering Overlapped Component Property,“ International Journal of Mechanical Sciences, Vol. 235, p. 107713, 2022, doi: https://doi.org/10.1016/j.ijmecsci.2022.107713.
[19] I. El Khadiri,
M. Abouelmajd, M. Zemzami, N. Hmina, M. Lagache,
B. AlMangour, A. Bahlaoui, I.
Arroub, and S.
Belhouideg, “TPMS Lattice Structure Derived using Topology Optimization for the Design of Additive Manufactured Components,“, in
2022 8th International Conference on Optimization and Applications (ICOA), IEEE, Oct. 2022, pp. 1–4, . doi: https://doi.org/10.1109/ICOA55659.2022.9934649.
[20] C. Yang and Q. M. Li, “Advanced Lattice Material with High Energy Absorption Based on Topology Optimisation,“ Mechanics of Materials, Vol. 148, p. 103536, 2020, doi: https://doi.org/10.1016/j.mechmat.2020.103536.
[21] J. Hu, S. Wang, B. Li, F. Li, Z. Luo, and L. Liu, “Efficient Representation and Optimization for TPMS-based Porous Structures,“ IEEE Transactions on Visualization and Computer Graphics, Vol. 28, No. 7, pp. 2615–2627, 2022, doi: https://doi.org/10.1109/TVCG.2020.3037697.
[22] A. Viswanath, M. Modrek, K. A. Khan, and R. K. A. AL-Rub, “Deep Learning for Topology Optimization of Triply Periodic Minimal Surface Based Gyroid-like Structures,“, in American Society for Composites 2021, Destech Publications, Inc., Sep. 2021. doi: https://doi.org/10.12783/asc36/35824.
[23] N. Strömberg, “Optimal Grading of TPMS-based Lattice Structures with Transversely Isotropic Elastic Bulk Properties,“ Engineering Optimization, Vol. 53, No. 11, pp. 1871–1883, 2021, doi: https://doi.org/10.1080/0305215X.2020.1837790.
[24] M. J. Buehler, B. Bettig, and G. G. Parker, “Topology Optimization of Smart Structures using a Homogenization Approach,“ Journal of Intelligent Material Systems and Structures, Vol. 15, No. 8, pp. 655–667, 2004, doi: https://doi.org/10.1177/1045389X04043944.
[25] L. Zhang,
S. Feih,
S. Daynes, S. Chang,
M.Y. Wang,
J. Wei, and
W.F. Lu “Energy Absorption Characteristics of Metallic Triply Periodic Minimal Surface Sheet Structures under Compressive Loading,“
Additive Manufacturing, Vol. 23pp. 505–515, 2018, doi: https://doi.org/10.1016/j.addma.2018.08.007.
[26] K. Yeranee, Y. Rao, L. Yang, and H. Li, “Improved Thermal Performance of a Serpentine Cooling Channel by Topology Optimization Infilled with Triply Periodic Minimal Surfaces,“ Energies, Vol. 15, No. 23, p. 8924, 2022, doi: https://doi.org/10.3390/en15238924.
[27] N. Novak,
O. Al-Ketan,
L. Krstulović-Opara, R. Rowshan,
R.K.A. Al-Rub, M. Vesenjak, and
Z. Ren, “Quasi-static and Dynamic Compressive Behaviour of Sheet TPMS Cellular Structures,“
Composite Structures, Vol. 266, p. 113801, 2021, doi: https://doi.org/10.1016/j.compstruct.2021.113801.
[28] H. Geramizadeh, S. Dariushi, and S. J. Salami, “Optimal Face Sheet Thickness of 3D Printed Polymeric Hexagonal and Re-entrant honeycomb sandwich beams subjected to three-point bending,“ Composite Structures, vol. 291p. 115618, 2022, doi: https://doi.org/10.1016/j.compstruct.2022.115618.
[29] H. Geramizadeh, S. Dariushi, and S. J. Salami, “Numerical and Experimental Investigation for Enhancing the Energy Absorption Capacity of the Novel Three-dimensional Printed Sandwich Structures,“ Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 2021, doi: https://doi.org/10.1177/1464420721997490.
[30] H. Geramizadeh and S. Jedari Salami, “Theoretical, Numerical, and Experimental Investigations of 3D Printed Sandwich Beams Subjected to Three-point Bending,“ Iranian Journal of Mechanical Engineering Transactions of ISME, Vol. 24, No. 2, pp. 134–159, 2022, doi: https://doi.org/10.30506/IJMEP.2022.548520.1856.
[31] I. Maskery, L. Sturm, A.O. Aremu, A. Panesar, C.B. Williams, C.J. Tuck, R.D. Wildman, I.A. Ashcroft, and R.J.M. Hague, “Insights into the Mechanical Properties of Several Triply Periodic Minimal Surface Lattice Structures Made by Polymer Additive Manufacturing,“ Polymer, Vol. 152, pp. 62–71, 2018, doi: https://doi.org/10.1016/j.polymer.2017.11.049.
