Additive Manufacturing of Functionally Graded Lattice Structures for Personalized Below-Knee Prosthetic Dampers

Guy O’Keefe; Naser A. Alsaleh; Mahmoud A. El-Sayed; A. Jiménez; Sabbah Ataya; Khamis Essa

doi:10.1007/s10118-025-3460-1

Your Location：

Home >

Browse articles >

Additive Manufacturing of Functionally Graded Lattice Structures for Personalized Below-Knee Prosthetic Dampers

RESEARCH ARTICLE | Updated：2026-01-13

- Additive Manufacturing of Functionally Graded Lattice Structures for Personalized Below-Knee Prosthetic Dampers
- Chinese Journal of Polymer Science Vol. 44, Issue 1, Pages: 173-188(2026)
- Affiliations：
  
  a.Department of Mechanical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
  b.Industrial Engineering Department, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
  c.Department of Industrial and Management Engineering, Arab Academy for Science Technology and Maritime Transport, Alexandria 21599, Egypt
  d.Universidad de Navarra, TECNUN Escuela de Ingeniería, Manuel de Lardizábal 15, San Sebastián 20018, Spain
  e.Mechanical Engineering Department, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
- Author bio：
  
  ajzabaleta@unav.es (A.J.)
  k.e.a.essa@bham.ac.uk (K.E.)
- Funds：
- DOI：10.1007/s10118-025-3460-1
  CLC：
- Received：25 June 2025，
  
  Accepted：18 September 2025，
  
  Published Online：25 December 2025，
  
  Published：15 January 2026
- Accepted：
Scan QR Code
O’Keefe, G.; Alsaleh, N. A.; El-Sayed, M. A.; Jiménez, A.; Ataya, S.; Essa, K. Additive manufacturing of functionally graded lattice structures for personalized below-knee prosthetic dampers. Chinese J. Polym. Sci. 2026, 44, 173–188

Guy O’Keefe, Naser A. Alsaleh, Mahmoud A. El-Sayed, et al. Additive Manufacturing of Functionally Graded Lattice Structures for Personalized Below-Knee Prosthetic Dampers[J]. Chinese Journal of Polymer Science, 2026, 44(1): 173-188.
O’Keefe, G.; Alsaleh, N. A.; El-Sayed, M. A.; Jiménez, A.; Ataya, S.; Essa, K. Additive manufacturing of functionally graded lattice structures for personalized below-knee prosthetic dampers. Chinese J. Polym. Sci. 2026, 44, 173–188 DOI： 10.1007/s10118-025-3460-1.

Guy O’Keefe, Naser A. Alsaleh, Mahmoud A. El-Sayed, et al. Additive Manufacturing of Functionally Graded Lattice Structures for Personalized Below-Knee Prosthetic Dampers[J]. Chinese Journal of Polymer Science, 2026, 44(1): 173-188. DOI： 10.1007/s10118-025-3460-1.

摘要

This study analyzes two

types of functionally graded lattice structures

Schwarz P and BCC

for use in below-knee prosthesis dampers. A 3×3 design of experiments varied wall thickness and cell size. Optimization

via

Response Surface Methodology and finite element analysis identified optimal lattice parmeters for improved prosthetic performance.

Abstract

Functionally graded cellular structures (FGCSs) have a multitude of applications to a wide range of industries. Utilising the ever-progressing technology of additive manufacturing (AM)

FGCSs can be applied to control material grading and achieve the desired mechanical properties. The current study explores the design and optimisation of FGCSs for AM

with a focus on improving the compression and impact performance of below knee (BK) prosthetic limbs made of thermoplastic polyurethane (TPU). A multiscale research methodology integrating topology optimization (TO)

finite element analysis (FEA)

and design of experiments (DoE) was adopted to optimise lattice structures in terms of stiffness and lightweight properties. Two-unit cell designs were considered in the study: Schwarz P gyroid and body-centered cubic (BCC). Response surface methodology (RSM) was implemented to analyse the effect of minimum and maximum cell wall thickness

cell size

and unit cell type on the mechanical performance of TPU FGCS structures. The results indicated that a Schwarz P FGCS structure with cell size

minimum and maximum cell wall thickness of 6

0.9 and 2.8 mm

respectively

could be optimal for a compromise between performance and weight. In this optimized case

stiffness and volume fraction values of 684 N/mm and 0.64 were obtained

respectively. The study also presents a proof-of-concept design for a BK prosthetic damper

highlighting the potential of FGCSs to enhance patient comfort

reduce manufacturing costs

and enable personalised designs through 3D scanning and AM. The obtained results could be a step forward towards the incorporation of AM technologies in prosthetics

offering a pathway to lightweight

cost-effective

and functionally tailored solutions.

关键词

Keywords

references

Gross, B. C.; Erkal, J. L.; Lockwood, S. Y.; Chen, C. P.; Spence, D. M. Evaluation of 3D printing and its potential impact on biotechnology and the chemical sciences. Anal. Chem. 2014 , 86 , 3240−3253..

[Wang, Y. L.; Alsaleh, N. A.; Djuansjah, J.; Hassanin, H.; El-Sayed, M. A.; Essa, K. Tailoring 3D star-shaped auxetic structures for enhanced mechanical performance. Aerospace 2024 , 11 , 428..

[Hassanin, H.; Ahmed El-Sayed, M.; ElShaer, A.; Essa, K.; Jiang, K. Microfabrication of ne t shape zirconia/alumina nanocomposite micro parts. Nanomaterials 2018 , 8 , 593..

[Li, Y.; Feng, Z. Y.; Hao, L.; Huang, L. J.; Xin, C. X.; Wang, Y. S.; Bilotti, E.; Essa, K.; Zhang, H.; Li, Z.; Yan, F. F.; Peijs, T. A review on functionally graded materials and structures via additive manufacturing: from multi-scale design to versatile functional properties. Adv. Mater. Technol . 2020 , 5 , 1900981..

[El-Sayed, M. A.; Essa, K.; Ghazy, M.; Hassanin, H. Design optimization of additively manufactured titanium lattice structures for biomedical implants. Int . J . Adv . Manuf . Technol . 2020 , 110 , 2257−2268..

[Bogusz, P.; Popławski, A.; Stankiewicz, M.; Kowalski, B. Experimental research of selected lattice structures developed with 3D printing technology. Materials 2022 , 15 , 378..

[Harish, A.; Alsaleh, N. A.; Ahmadein, M.; Elfar, A. A.; Djuansjah, J.; Hassanin, H.; El-Sayed, M. A.; Essa, K. Designing lightweight 3D-printable bioinspired st ructures for enhanced compression and energy absorption properties. Polymers 2024 , 16 , 729..

[Maran, S. B.; Masters, I. G.; Gibbons, G. J. Additive manufacture of 3D auxetic structures by laser powder bed fusion: design influence on manufacturing accuracy and mechanical properties. Appl . Sci . 2020 , 10 , 7738..

[Panesar, A.; Abdi, M.; Hickman, D.; Ashcroft, I. Strategies for functionally graded lattice structures derived using topology optimisation for Additive Manufacturing. Addit . Manuf . 2018 , 19 , 81−94..

[McMillan, M. L.; Jurg, M.; Leary, M.; Brandt, M. Programmatic generation of computationally efficient lattice structures for additive manufacture. Rapid Prototyp . J . 2017 , 23 , 486−494..

[Nguyen, C. H. P.; Choi, Y. Multiscale design of functionally graded cellular structures for additive manufacturing using level-set descriptions. Struct . Multidiscip . Optim . 2021 , 64 , 1983−1995. .

[Hussein, A.; Hao, L.; Yan, C. Z.; Everson, R.; Young, P. Advanced lattice support structures for metal additive manufacturing. J . Mater . Process . Technol . 2013 , 213 , 1019−1026..

[Mohammed, A.; Elshaer, A.; Sareh, P.; Elsayed, M.; Hassanin, H. Additive manufacturing technologies for drug delivery applications. Int. J. Pharm . 2020 , 580 , 119245..

[de la Rosa, S.; Mayuet, P. F.; Silva, C. S.; Sampaio, Á. M.; Rodríguez-Parada, L. Design and characterization of 3D-printed TPU-based lattice structures. Application to methodology for the design of personalized therapeutic products. Rapid Prototyp . J . 2024 , 30 , 72−86..

[Kumar, A.; Verma, S.; Jeng, J. Y. Supportless lattice structures for energy absorption fabricated by fused deposition modeling. 3D Print . Addit . Manuf . 2020 , 7 , 85−96..

[Daynes, S.; Feih, S. Bio-inspired lattice structure optimisation with strain trajectory aligned trusses. Mater. Des . 2022 , 213 , 110320..

[Claybrook, F. R.; Southee, D. J.; Mohammed, M. Mechanical evaluation of elastomeric thermoplastic polyurethane additively manufactured triply periodic minimal surface area lattice structures for adjustable cushioning properties. Rapid Prototyp . J . 2024 , 30 , 1070−1086..

[Sathishkumar, N.; Kumar, K. M.; Selvam, R.; Udayakumar, A. S. M. Optimization of energy absorption and vibration behaviour of TPMS Schwarz P and Schoen Gyroid lattice structures using Taguchi L9 orthogonal array. J . Elastomers Plast . 2024 , 56 , 539−576..

[Zhang, M.; Roberts, C. Comparison of computational analysis with clinical measurement of stresses on below-knee residual limb in a prosthetic socket. Med . Eng . Phys . 2000 , 22 , 607−612..

[Bhatt, S.; Joshi, D.; Rakesh, P. K.; Godiyal, A. K. Advances in additive manufacturing processes and their use for the fabrication of lower limb prosthetic devices. Expert Rev . Med . Devices 2023 , 20 , 17−27..

[Quintero-Quiroz, C.; Pérez, V. Z. Materials for lower limb prosthetic and orthotic interfaces and sockets: evolution and associated skin problems. Rev . Fac . Med . 2019 , 67 , 117−125..

[Stephens-Fripp, B.; Walker, M. J.; Goddard, E.; Alici, G. A survey on what Australians with upper limb difference want in a prosthesis: justification for using soft robotics and additive manufacturing for customized prosthetic hands. Disabil . Rehabil . Assist . Technol . 2020 , 15 , 342−349..

[Biddiss, E.; Chau, T. Upper limb prosthesis use and abandonment: a survey of the last 25 years. Prosthet . Orthot . Int . 2022 , 31 , 236−257..

[Banga, H. K.; Kalra, P.; Belokar, R. M.; Kumar, R. D esign and fabrication of prosthetic and orthotic product by 3D printing, P&O DOI: 10.5772/intechopen.94846.

[Manero, A.; Smith, P.; Sparkman, J.; Dombrowski, M.; Courbin, D.; Kester, A.; Womack, I.; Chi, A. Implementation of 3D printing technology in the field of prosthetics: past, present, and future. Int . J . Environ . Res . Public Health 2019 , 16 , 1641..

[Asif, M.; Tiwana, M. I.; Khan, U. S.; Qureshi, W. S.; Iqbal, J.; Rashid, N.; Naseer, N. Advancements, trends and future prospects of lower limb prosthesis. IEEE Access 2021 , 9 , 85956−85977..

[, Osama, M. Design of lower prosthetic limb using additive manufacturing processes. J . Stud . Sci . Eng . 2021 , 1 , 36−49..

[Faustini, M. C.; Crawford, R. H.; Neptune, R. R.; Rogers, W. E.; Bosker, G. Design and analysis of orthogonally compliant features for local contact pressure relief in transtibial prostheses. J . Biomech . Eng . 2005 , 127 , 946−951..

[Sengeh, D. M.; Herr, H. A variable-impedance prosthetic socket for a transtibial amputee designed from magnetic resonance imaging data. J . Prosthet . Orthot . 2013 , 25 , 129−137..

[Sing, S. L.; Wiria, F. E.; Yeong, W. Y. Selective laser melting of lattice structures: A statistical approach to manufacturability and mechanical behavior. Robot . Comput . Integr . Manuf . 2018 , 49 , 170−180..

[Hassanin, H.; El-Sayed, M. A.; Ahmadein, M.; Alsaleh, N. A.; Ataya, S.; Ahmed, M. M. Z.; Essa, K. Optimising surface roughness and density in titanium fabrication via laser powder bed fusion. Micromachines 2023 , 14 , 1642..

[El-Sayed, M.A.; El-Nakeeb, N.; Shyha, I.; Ghazy, M.J.I.J.o.M.; Technology, P. Response surface method for optimisation of SLA processing parameters. Int. J. Mater. Prod. Technol. 2022 , 64 , 222−241..

[Kechagias, J. D.; Vidakis, N. Parametric optimization of material extrusion 3D printing process: An assessment of Box-Behnken vs . full-factorial experimental approach. Int . J . Adv . Manuf . Technol . 2022 , 121 , 3163−3172..

[Petousis, M.; Spiridaki, M.; Mountakis, N.; Moutsopoulou, A.; Maravelakis, E.; Vidakis, N. Box-Behnken modeling to optimize the engineering response and the energy expenditure in material extrusion additive manufacturing of short carbon fiber reinforced polyamide 6. Int . J . Adv . Manuf . Technol . 2024 , 132, 4399−4415..

[Vidakis, N.; Petousis, M.; Korlos, A.; Velidakis, E.; Mountakis, N.; Charou, C.; Myftari, A. Strain rate sensitivity of polycarbonate and thermoplastic polyurethane for various 3D printing temperatures and layer heights. Polymers 2021 , 13 , 2752..

[Groen, J. P.; Thomsen, C. R.; Sigmund, O. Multi-scale topology optimization for stiffness and de-homogenizationusing implicit geometry modeling. Struct . Multidiscip . Optim . 2021 , 63 , 2919−2934..

[Mermillod-Blondin, M.; Olechowski, A.; McComb, C. Benchmarking the current state of lattice design software for additive manufacturing. SFF 2024 ..

[Donnici, G.; Freddi, M.; Liverani, A. RSM applied to lattice patterns for stiffness optimization. Rapid Prototyp . J . 2024 , 30 , 345−356..

[El Magri, A.; El Mabrouk, K.; Vaudreuil, S.; Touhami, M. E. Experimental investigation and optimization of printing parameters of 3D printed polyphenylene sulfide through response surface methodology. J. Appl. Polym. Sci . 2021 , 138 , 49625..

[Hassanin, H.; Modica, F.; El-Sayed, M. A.; Liu, J.; Essa, K. Manufacturing of Ti–6Al–4V micro-implantable parts using hybrid selective laser melting and micro-electrical discharge machining. Adv . Eng . Mater . 2016 , 18 , 1544−1549..

[Neubauer, M.; Pohl, M.; Kucher, M.; Böhm, R.; Höschler, K.; Modler, N. DMA of TPU films and the modelling of their viscoelastic properties for noise reduction in jet engines. Polymers 2022 , 14 , 5285..

[Stoker, P.; Tian, G.; Kim, J. Y. Basic quantitative research methods for urban planners. Routledge, 2020 .

[Montgomery, D. C. Design and analysis of experiments, John Wiley & Sons, 2017 .

[Myers, R. H.; Montgomery, D. C.; Anderson-Cook, C. M. Response surface methodology: process and product optimization using designed experiments, Wiley, 2016 .

[Niknam, H.; Akbarzadeh, A. H. Graded lattice structures: Simultaneous enhancement in stiffness and energy absorption. Mater. Des . 2020 , 196 , 109129..

[Tyagi, S. A.; Manjaiah, M. Additive manufacturing of titanium-based lat tice structures for medical applications–a review. Bioprinting 2023 , 30 , e00267..

[Banga, H. K.; Kalra, P.; Belokar, R. M.; Kumar, R. Customized design and additive manufacturing of kids’ ankle foot orthosis. Rapid Prototyp . J . 2020 , 26 , 1677−1685..

[Gibson, I.; Rosen, D.; Stucker, B.; Khorasani, M.; Rosen, D.; Stucker, B.; Khorasani, M. Additive manufacturing technologies, Springer, 2021 .

[Petousis, M.; Ntintakis, I.; David, C.; Sagris, D.; Nasikas, N. K.; Korlos, A.; Moutsopoulou, A.; Vidakis, N. A coherent assessment of the compressive strain rate response of PC, PETG, PMMA, and TPU thermoplastics in MEX additive manufacturing. Polymers 2023 , 15 , 3926..

[Schwarz, D.; Pagáč, M.; Petruš, J.; Polzer, S. Effect of water-induced and physical aging on mechanical properties of 3D printed elastomeric polyurethane. Polymers 2022 , 14 , 5496..

[Boubakri, A.; Haddar, N.; Elleuch, K.; Bienvenu, Y. Influence of thermal aging on tensile and creep behavior of thermoplastic polyurethane. Comptes Rendus Mécanique 2011 , 339 , 666−673..

[Xu, T.; Shen, W.; Lin, X.; Xie, Y. M. Mechanical properties of additively manufactured thermoplastic polyurethane (TPU) material affected by various processing parameters. Polym ers 2020 , 12 , 3010..

[Mishra, A. K.; Chavan, H.; Kumar, A. Effect of cell size and wall thickness on the compression performance of triply periodic minimal surface based AlSi 10 Mg lattice structures. Thin Walled Struct . 2023 , 193 , 111214..

[Wu, Y.; Yang, L. The effect of unit cell size and topology on tensile failure behavior of 2D lattice structures. Int. J. Mech. Sci . 2020 , 170 , 105342..

[Chen, Y. M.; Das, R.; Battley, M. Effects of cell size and cell wall thickness variations on the stiffness of closed-cell foams. Int . J . Solids Struct . 2015 , 52 , 150−164..

[de la Rosa, S.; Mayuet, P. F.; Méndez Salgueiro, J. R.; Rodríguez-Parada, L. Design of customized TPU lattice structures for additive manufacturing: influence on the functional properties in elastic products. Polymers 2021 , 13 , 4341..

[Top, N.; Şahin, İ.; Gökçe, H. The mechanical properties of functionally graded lattice structures derived using computer-aided design for additive manufacturing. Appl. Sci . 2023 , 13 , 11667..

[Geyer, S.; Hölzl, C. Comparison of CAD software for designing cellular structures for additive manufacturing. Appl . Sci . 2024 , 14 , 3306..

[Maskery, I.; Sturm, L.; Aremu, A. O.; Panesar, A.; Williams, C. B.; Tuck, C. J.; Wildman, R. D.; Ashcroft, I. A.; Hague, R. J. M. Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing. Polymer 2018 , 152 , 62−71..

[Jafari Chashmi, M.; Fathi, A.; Shirzad, M.; Jafari-Talookolaei, R. A.; Bodaghi, M.; Rabiee, S. M. Design and analysis of porous functionally graded femoral prostheses with improved stress shielding. Designs 2020 , 4 , 12..

[Ursini, C.; Collini, L. FDM layering deposition effects on mechanical response of TPU lattice structures. Materials 2021 , 14 , 5645..

[Cameron, H.; Josef, C.; Nahal, A.; Changki, M.; Amir, A. 3D printed thermoplastic polyurethane with isotropic material properties. Proc. SPIE , 2017 ..

[Doshi, M.; Mahale, A.; Kumar Singh, S.; Deshmukh, S. Printing parameters and materials affecting mechanical properties of FDM-3D printed Parts: Perspective and prospects. Mater . Today Proc . 2022 , 50 , 2269−2275..

[Khan, S.; Joshi, K.; Deshmukh, S. A comprehensive review on effect of printing parameters on mechanical properties of FDM printed parts. Mater . Today Proc . 2022 , 50 , 2119−2127..

[Gu, S. J.; Ma, J.; Kang, L. H.; Wei, H. T.; Jiang, L.; Wang, L. X. Effect of heat treatment on the performance of 3D printed thermoplastic polyurethane flexible substrates. J. Appl. Polym. Sci . 2023 , 140 , e53741..

[Jiang, J. C.; Xu, X.; Stringer, J. Support structures for additive manufacturing: a review. J . Manuf . Mater . Process . 2018 , 2 , 64..

[El-Sayed, M. A.; El-Nakeeb, N.; Shyha, I.; Ghazy, M. Response surface method for optimisation of SLA processing parameters. Int. J. Mater. Prod. Tech. 2022 , 64 , 222−241..

[Foot finder: vari-flex prosthetic feet. [2025-12-15]. https://www.ossur.com/en-us/prosthetics/products/feet.

[Turner, A. T.; Halsne, E. G.; Caputo, J. M.; Curran, C. S.; Hansen, A. H.; Hafner, B. J.; Morgenroth, D. C. Prosthetic forefoot and heel stiffness across consecutive foot stiffness categories and sizes. PLoS One 2022 , 17 , e0268136..

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

High Speed Sintering: Assessing the Influence of Energy Input on Microstructure and Mechanical Properties of Polyether Block Amide (PEBA) Parts

Related Author

Jiang-Tao Sun

Zhi-Yong Fan

Yi-Wei Mao

Wei Li

Wei Zhu

Dao-Sheng Cai

Qing-Song Wei

Related Institution

State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology

State Key Laboratory of Refractories and Metallurgy, Wuhan University of Science and Technology

National Engineering Research Centre for High Efficiency Grinding, Hunan University

Wuhan EasyMFG Technology CO., LTD

⁰