Skip to main content

Modal characterization of additively manufactured TPMS structures: comparison between different modeling methods


The use of lattice structures has received increasing interest in various engineering applications owing to their high strength to weight ratio. Advances in additive manufacturing technologies enabled the manufacturing of highly complex lattice structures such as triply periodic minimal surface (TPMS) models in recent years. The application of simulation tools is expected to enhance the performance of these designs further. Therefore, it is vital to understand their accuracy and computational efficiency. In this paper, modal characterization of additively manufactured TPMS structures is studied using five different modeling methods for a beam, which is composed of primitive, diamond, IWP, and gyroid unit cells. These methods include (1) shell modeling, (2) solid modeling, (3) homogenization, (4) super-element modeling, and (5) voxelization. The modal characterization is performed by using modal analysis, and the aforementioned models are compared in terms of their computational efficiency and accuracy. The results are experimentally validated by performing an experimental modal testing on a test specimen, made of HS188, and manufactured by direct metal laser melting. Finally, the relationship between the modal characteristics and volume fraction is derived by carrying out a parametric study for all types of TMPS structures considered in this paper. The complex modal characteristics of different TPMS types suggest that they can be jointly used to meet the ever-challenging design requirements using the modeling guidelines proposed in this study.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15


  1. Gibson LJ, Ashby MF (1999) Cellular-solids-structure-and-properties-Cambridge-Solid-State-Science-Seri es-.pdf

  2. Khaderi S, Deshpande V, Fleck N (2014) The stiffness and strength of the gyroid lattice. Int J Solids Struct 51(23):3866–3877

    Article  Google Scholar 

  3. Hertzberg RW, Vinci RP, Hertzberg JL (2012) Deformation and fracture mechanics of engineering materials, 4th edn. Wiley, Hoboken

    Google Scholar 

  4. Dalaq AS, Abueidda DW, Abu Al-Rub RK, Jasiuk IM (2016) Finite element prediction of effective elastic properties of interpenetrating phase composites with architectured 3D sheet reinforcements. Int J Solids Struct 83:169–182

    Article  Google Scholar 

  5. Fleck NA, Deshpande VS, Ashby MF (2010) Micro-architectured materials: past, present and future. Proc R Soc A: Math Phys Eng Sci 466(2121):2495–2516

    Article  Google Scholar 

  6. Brennan-Craddock J, Brackett D, Wildman R, Hague R The design of impact absorbing structures for additive manufacture, Journal of Physics: Conference Series 382 (1)

  7. Maskery I, Hussey A, Panesar A, Aremu A, Tuck C, Ashcroft I, Hague R (2017) An investigation into reinforced and functionally graded lattice structures. J Cell Plast 53(2):151–165

    Article  Google Scholar 

  8. Panesar A, Ashcroft I, Brackett D, Wildman R, Hague R (2017) Design framework for multifunctional additive manufacturing: coupled optimization strategy for structures with embedded functional systems. Additive Manufacturing 16:98– 106

    Article  Google Scholar 

  9. Maskery I, Aremu AO, Simonelli M, Tuck C, Wildman RD, Ashcroft IA, Hague R (2015) Mechanical properties of Ti-6Al-4V selectively laser melted parts with body-centred-cubic lattices of varying cell size. Exp Mech 55(7):1261–1272

    Article  Google Scholar 

  10. Wang L, Lau J, Thomas EL, Boyce MC (2011) Co-continuous composite materials for stiffness, strength, and energy dissipation. Adv Mater 23(13):1524–1529

    Article  Google Scholar 

  11. Maskery I, Sturm L, Aremu A, Panesar A, Williams C, Tuck C, Wildman R, Ashcroft I, Hague R (2018) Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing. Polymer 152:62–71. sI: Advanced Polymers for 3DPrinting/Additive Manufacturing

    Article  Google Scholar 

  12. Yan C, Hao L, Hussein A, Young P, Huang J, Zhu W (2015) Microstructure and mechanical properties of aluminium alloy cellular lattice structures manufactured by direct metal laser sintering. Mater Sci Eng A 628:238–246

    Article  Google Scholar 

  13. Yan C, Hao L, Hussein A, Young P, Raymont D (2014) Advanced lightweight 316L stainless steel cellular lattice structures fabricated via selective laser melting. Mater Des 55:533–541

    Article  Google Scholar 

  14. Yan C, Hao L, Hussein A, Bubb SL, Young P, Raymont D (2014) Evaluation of light-weight AlSi10Mg periodic cellular lattice structures fabricated via direct metal laser sintering. J Mater Process Technol 214(4):856–864

    Article  Google Scholar 

  15. Yan C, Hao L, Hussein A, Raymont D (2012) Evaluations of cellular lattice structures manufactured using selective laser melting. Int J Mach Tools Manuf 62:32–38

    Article  Google Scholar 

  16. Aremu A, Maskery I, Tuck C, Ashcroft I, Wildman R, Hague R (2014) A comparative finite element study of cubic unit cells for selective laser melting. In: Solid freeform fabrication proceedings, pp 1238–1249

  17. Yánez A., Cuadrado A, Martel O, Afonso H, Monopoli D (2018) Gyroid porous titanium structures: A versatile solution to be used as scaffolds in bone defect reconstruction. Materials & Design 140:21–29

    Article  Google Scholar 

  18. Maskery I, Aboulkhair NT, Aremu AO, Tuck CJ, Ashcroft IA (2017) Compressive failure modes and energy absorption in additively manufactured double gyroid lattices. Additive Manufacturing 16:24–29

    Article  Google Scholar 

  19. Abueidda DW, Bakir M, Abu Al-Rub RK, Bergstrȯm J. S., Sobh NA, Jasiuk I (2017) Mechanical properties of 3D printed polymeric cellular materials with triply periodic minimal surface architectures. Mater Des 122:255–267

    Article  Google Scholar 

  20. Al-Ketan O, Rezgui R, Rowshan R, Du H, Fang NX, Abu Al-Rub RK (2018) Microarchitected stretching-dominated mechanical metamaterials with minimal surface topologies. Adv Eng Mater 20 (9):1–15

    Article  Google Scholar 

  21. Abueidda DW, Al-Rub RKA, Dalaq AS, Lee D. -W., Khan KA, Jasiuk I (2016) Effective conductivities and elastic moduli of novel foams with triply periodic minimal surfaces. Mech Mater 95:102–115

    Article  Google Scholar 

  22. Altintas G (2018) Vibration properties of TPMS based structures. International Journal of Scientific and Technological Research 4:27–42

    Google Scholar 

  23. Elmadih W, Syam WP, Maskery I, Chronopoulos D, Leach R (2019) Mechanical vibration bandgaps in surface-based lattices. Additive Manufacturing 25(April 2018):421–429

    Article  Google Scholar 

  24. Abueidda DW, Jasiuk I, Sobh NA (2018) Acoustic band gaps and elastic stiffness of PMMA cellular solids based on triply periodic minimal surfaces. Mater Des 145:20–27

    Article  Google Scholar 

  25. Simsek U, Gayir C, Kavas B, Sendur P (2019) Computational and experimental investigation of vibration characteristics of variable unit-cell gyroid structures. In: II International conference on simulation for additive manufacturing. Springer

  26. Maskery I, Aremu AO, Parry L, Wildman RD, Tuck CJ, Ashcroft IA (2018) Effective design and simulation of surface-based lattice structures featuring volume fraction and cell type grading. Mater Des 155:220–232

    Article  Google Scholar 

  27. Storm J, Ranjbarian M, Mechtcherine V, Scheffler C, Kaliske M (2019) Modelling of fibre-reinforced composites via fibre super-elements. Theoretical and Applied Fracture Mechanics 103:102294

    Article  Google Scholar 

  28. Madenci E, Guven I (2015) The finite element method and applications in engineering using ANSYS®, second edition

  29. Shirazi SFS, Gharehkhani S, Mehrali M, Yarmand H, Metselaar HSC, Adib Kadri N, Osman NAA (2015) A review on powder-based additive manufacturing for tissue engineering: selective laser sintering and inkjet 3D printing. Science and Technology of Advanced Materials 16 (3)

  30. Flodén O., Persson K, Sandberg G (2014) Reduction methods for the dynamic analysis of substructure models of lightweight building structures. Comput Struct 138:49–61

    Article  Google Scholar 

  31. Matweb 2019, Haynes 188 alloy, 0% cold reduction, 3.2 mm thick sheet, data accessed: 20 April 2019

  32. Herzog D, Seyda V, Wycisk E, Emmelmann C (2016) Additive manufacturing of metals. Acta Mater 117:371–392

    Article  Google Scholar 

  33. Mullen L, Stamp RC, Brooks WK, Jones E, Sutcliffe CJ (2009) Selective laser melting: a regular unit cell approach for the manufacture of porous, titanium, bone in-growth constructs, suitable for orthopedic applications. Journal of Biomedical Materials Research Part B: Applied Biomaterials 89B(2):325–334

    Article  Google Scholar 

  34. Bertol LS, Júnior W. K., da Silva FP, Aumund-Kopp C (2010) Medical design: Direct metal laser sintering of ti–6al–4v. Materials & Design 31(8):3982–3988

    Article  Google Scholar 

Download references


This study was carried out under the TUBITAK Technology and Innovation Support Program (grant number: 5158001).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Polat Sendur.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Simsek, U., Akbulut, A., Gayir, C.E. et al. Modal characterization of additively manufactured TPMS structures: comparison between different modeling methods. Int J Adv Manuf Technol 115, 657–674 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Additive manufacturing
  • Sandwich structure
  • Triply periodic minimal surfaces
  • Finite element analysis
  • Modal analysis