Numerical modelling of the deformation behaviour of polymer lattice structures with density gradient based on additive technologies

Authors

  • Nataliya V. Elenskaya Perm National Research Polytechnic University, 29, Komsomolsky pr., Perm, 614990, Russian Federation
  • Mikhail A. Tashkinov Perm National Research Polytechnic University, 29, Komsomolsky pr., Perm, 614990, Russian Federation
  • Vadim V. Silberschmidt Loughborough University, Epinal Way, Loughborough, LE11 3TU, United Kingdom

DOI:

https://doi.org/10.21638/spbu01.2022.410

Abstract

The mechanical behavior of gradient lattice structures whose geometry is based on the analytic definition of three-dimensional triply periodic minimal surfaces (TPMS) is investigated. Several homogeneous and gradient lattice models with different types of representative volume geometry and gradient parameters are considered. The numerical models are validated with data obtained experimentally using the Vic-3D video system. The results of numerical simulation of the deformation behaviour of gradient structures with the Shoen G (gyroid) TPMP geometry under uniaxial compression are presented. The influence of structure parameters and gradient properties on the mechanical behaviour is studied.

Keywords:

triply periodic minimal surfaces, two-phase structures, finite element method, functional gradient, microstructure

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References

Литература

1. Afshar M., Anaraki A.P., Montazerian H., Kadkhodapour J. Additive manufacturing and mechanical characterization of graded porosity scaffolds designed based on triply periodic minimal surface architectures J. Mech. Behav. Biomed. Mater. 62, 481-494 (2016). https://doi.org/10.1016/j.jmbbm.2016.05.027

2. Bracaglia L.G., Smith B., Watson E., Arumugasaamy N., Mikos A.G., Fisher J. 3D printing for the design and fabrication of polymer-based gradient scaffolds. Acta Biomater. 56, 3-13 (2017). https://doi.org/10.1016/j.actbio.2017.03.030

3. Pagani S., Liverani E., Giavaresi G., De Luca A., Belvedere C., Fortunato A., Leardini А., Fini М., Tomesani L., Caravaggi P. Mechanical and in vitro biological properties of uniform and graded Cobalt-chrome lattice structures in orthopedic implants. J. Biomed. Mater. Res. Part B Appl. Biomater. 109 (12), 2091-2103 (2021). https://doi.org/10.1002/jbm.b.34857

4. Wang Y., M¨uller W.D., Rumjahn A., Schmidt F., Schwitalla A.D. Mechanical properties of fused filament fabricated PEEK for biomedical applications depending on additive manufacturing parameters. J. Mech. Behav. Biomed. Mater. 115, 104250 (2021). https://doi.org/10.1016/j.jmbbm.2020.104250

5. Li X., Xiong Y.Z., Zhang H., Gao R.N. Development of functionally graded porous titanium/silk fibroin composite scaffold for bone repair. Mater. Lett. 282, 128670 (2021). https://doi.org/10.1016/j.matlet.2020.128670

6. Zhao M., Liu F., Fu G., Zhang D.Z., Zhang T., Zhou H. Improved mechanical properties and energy absorption of BCC lattice structures with triply periodic minimal surfaces fabricated by SLM. Materials. 11 (12), 2411 (2018). https://doi.org/10.3390/ma11122411

7. Liu F., Mao Z., Zhang P., Zhang D.Z., Jiang J., Ma Z. Functionally graded porous scaffolds in multiple patterns: New design method, physical and mechanical properties. Mater. Des. 160, 849-860 (2018). https://doi.org/10.1016/j.matdes.2018.09.053

8. Shi X., Liao W., Liu T., Zhang C., Li D., Jiang W., Wang C., Ren F. Design optimization of multimorphology surface-based lattice structures with density gradients. Int. J. Adv. Manuf. Technol. 117, 2013-2028 (2021). https://doi.org/10.1007/s00170-021-07175-3

9. Bargmann S., Klusemann B., Markmann J., Schnabel J.E., Schneider K., Soyarslan C., Wilmers J. Generation of 3D representative volume elements for heterogeneous materials: A review. Prog. Mater. Sci. 96, 322-384 (2018). https://doi.org/10.1016/j.pmatsci.2018.02.003

10. Han C., Li Y., Wang Q., Wen S., Wei Q., Yan C., Hao L., Liu J., Shi Y. Continuous functionally graded porous titanium scaffolds manufactured by selective laser melting for bone implants. J. Mech. Behav. Biomed. Mater. 80, 119-127 (2018). https://doi.org/10.1016/j.jmbbm.2018.01.013

11. Ng J.L., Collins C.E., Knothe Tate M.L. Engineering mechanical gradients in next generation biomaterials - Lessons learned from medical textile design. Acta Biomater. 56, 14-24 (2017). https://doi.org/10.1016/j.actbio.2017.03.004

12. Zhang X.Y., Fang G., Leeflang S., Zadpoor A.A., Zhou J. Topological design, permeability and mechanical behavior of additively manufactured functionally graded porous metallic biomaterials. Acta Biomater. 84, 437-452 (2019). https://doi.org/10.1016/j.actbio.2018.12.013

13. Moetazedian A., Gleadall A., Han X., Silberschmidt V.V. Effect of environment on mechanical properties of 3D printed polylactide for biomedical applications. J. Mech. Behav. Biomed. Mater. 102, 103510 (2020). https://doi.org/10.1016/j.jmbbm.2019.103510

14. Ruiz-Cantu L., Gleadall A., Faris C., Segal J., Shakesheff K., Yang J. Multi-material 3D bioprinting of porous constructs for cartilage regeneration. Mater. Sci. Eng. C, Mater. Bio. Appl. 109, 110578 (2020). https://doi.org/10.1016/j.msec.2019.110578

15. Wang X., Xu S., Zhou S., Xu W., Leary M., Choong P., Qian M., Brandt M., Xie Y.M. Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review. Biomaterials 83, 127-141 (2016). https://doi.org/10.1016/j.biomaterials.2016.01.012

16. Wang Z., Wang Y., Yan J., Zhang K., Lin F., Xiang L., Deng L., Guan Z., Cui W., Zhang H. Pharmaceutical electrospinning and 3D printing scaffold design for bone regeneration. Adv. Drug Deliv. Rev. 174, 504-534 (2021). https://doi.org/10.1016/j.addr.2021.05.007

17. Shah R., Gashi B., Hoque S., Marian M., Rosenkranz A. Enhancing mechanical and biomedical properties of protheses - Surface and material design. Surfaces and Interfaces 27, 101498 (2021). https://doi.org/10.1016/j.surfin.2021.101498

18. Entezari A., Zhang Z., Sue A., Sun G., Huo X., Chang C. C., Zhou S., Swain M.V., Li Q. Nondestructive characterization of bone tissue scaffolds for clinical scenarios. J. Mech. Behav. Biomed. Mater. 89, 150-161 (2019). https://doi.org/10.1016/j.jmbbm.2018.08.034

19. Razi H., Checa S., Schaser K.D., Duda G.N. Shaping scaffold structures in rapid manufacturing implants: A modeling approach toward mechano-biologically optimized configurations for large bone defect. J. Biomed. Mater. Res. Part B Appl. Biomater. 100 В, 1736-1745 (2012). https://doi.org/10.1002/jbm.b.32740

20. Zhang L., Song B., Yang L., Shi Y. Tailored mechanical response and mass transport characteristic of selective laser melted porous metallic biomaterials for bone scaffolds. Acta Biomater. 112, 298-315 (2020). https://doi.org/10.1016/j.actbio.2020.05.038

21. Tashkinov M.A. Multipoint stochastic approach to localization of microscale elastic behavior of random heterogeneous media. Comput. Struct. 249, 106474 (2021). https://doi.org/10.1016/j.compstruc.2020.106474

References

1. Afshar M., Anaraki A.P., Montazerian H., Kadkhodapour J. Additive manufacturing and mechanical characterization of graded porosity scaffolds designed based on triply periodic minimal surface architectures J. Mech. Behav. Biomed. Mater. 62, 481-494 (2016). https://doi.org/10.1016/j.jmbbm.2016.05.027

2. Bracaglia L.G., Smith B., Watson E., Arumugasaamy N., Mikos A.G., Fisher J. 3D printing for the design and fabrication of polymer-based gradient scaffolds. Acta Biomater. 56, 3-13 (2017). https://doi.org/10.1016/j.actbio.2017.03.030

3. Pagani S., Liverani E., Giavaresi G., De Luca A., Belvedere C., Fortunato A., Leardini А., Fini М., Tomesani L., Caravaggi P. Mechanical and in vitro biological properties of uniform and graded Cobalt-chrome lattice structures in orthopedic implants. J. Biomed. Mater. Res. Part B Appl. Biomater. 109 (12), 2091-2103 (2021). https://doi.org/10.1002/jbm.b.34857

4. Wang Y., M¨uller W.D., Rumjahn A., Schmidt F., Schwitalla A.D. Mechanical properties of fused filament fabricated PEEK for biomedical applications depending on additive manufacturing parameters. J. Mech. Behav. Biomed. Mater. 115, 104250 (2021). https://doi.org/10.1016/j.jmbbm.2020.104250

5. Li X., Xiong Y.Z., Zhang H., Gao R.N. Development of functionally graded porous titanium/silk fibroin composite scaffold for bone repair. Mater. Lett. 282, 128670 (2021). https://doi.org/10.1016/j.matlet.2020.128670

6. Zhao M., Liu F., Fu G., Zhang D.Z., Zhang T., Zhou H. Improved mechanical properties and energy absorption of BCC lattice structures with triply periodic minimal surfaces fabricated by SLM. Materials. 11 (12), 2411 (2018). https://doi.org/10.3390/ma11122411

7. Liu F., Mao Z., Zhang P., Zhang D.Z., Jiang J., Ma Z. Functionally graded porous scaffolds in multiple patterns: New design method, physical and mechanical properties. Mater. Des. 160, 849-860 (2018). https://doi.org/10.1016/j.matdes.2018.09.053

8. Shi X., Liao W., Liu T., Zhang C., Li D., Jiang W., Wang C., Ren F. Design optimization of multimorphology surface-based lattice structures with density gradients. Int. J. Adv. Manuf. Technol. 117, 2013-2028 (2021). https://doi.org/10.1007/s00170-021-07175-3

9. Bargmann S., Klusemann B., Markmann J., Schnabel J.E., Schneider K., Soyarslan C., Wilmers J. Generation of 3D representative volume elements for heterogeneous materials: A review. Prog. Mater. Sci. 96, 322-384 (2018). https://doi.org/10.1016/j.pmatsci.2018.02.003

10. Han C., Li Y., Wang Q., Wen S., Wei Q., Yan C., Hao L., Liu J., Shi Y. Continuous functionally graded porous titanium scaffolds manufactured by selective laser melting for bone implants. J. Mech. Behav. Biomed. Mater. 80, 119-127 (2018). https://doi.org/10.1016/j.jmbbm.2018.01.013

11. Ng J.L., Collins C.E., Knothe Tate M.L. Engineering mechanical gradients in next generation biomaterials - Lessons learned from medical textile design. Acta Biomater. 56, 14-24 (2017). https://doi.org/10.1016/j.actbio.2017.03.004

12. Zhang X.Y., Fang G., Leeflang S., Zadpoor A.A., Zhou J. Topological design, permeability and mechanical behavior of additively manufactured functionally graded porous metallic biomaterials. Acta Biomater. 84, 437-452 (2019). https://doi.org/10.1016/j.actbio.2018.12.013

13. Moetazedian A., Gleadall A., Han X., Silberschmidt V.V. Effect of environment on mechanical properties of 3D printed polylactide for biomedical applications. J. Mech. Behav. Biomed. Mater. 102, 103510 (2020). https://doi.org/10.1016/j.jmbbm.2019.103510

14. Ruiz-Cantu L., Gleadall A., Faris C., Segal J., Shakesheff K., Yang J. Multi-material 3D bioprinting of porous constructs for cartilage regeneration. Mater. Sci. Eng. C, Mater. Bio. Appl. 109, 110578 (2020). https://doi.org/10.1016/j.msec.2019.110578

15. Wang X., Xu S., Zhou S., Xu W., Leary M., Choong P., Qian M., Brandt M., Xie Y.M. Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review. Biomaterials 83, 127-141 (2016). https://doi.org/10.1016/j.biomaterials.2016.01.012

16. Wang Z., Wang Y., Yan J., Zhang K., Lin F., Xiang L., Deng L., Guan Z., Cui W., Zhang H. Pharmaceutical electrospinning and 3D printing scaffold design for bone regeneration. Adv. Drug Deliv. Rev. 174, 504-534 (2021). https://doi.org/10.1016/j.addr.2021.05.007

17. Shah R., Gashi B., Hoque S., Marian M., Rosenkranz A. Enhancing mechanical and biomedical properties of protheses - Surface and material design. Surfaces and Interfaces 27, 101498 (2021). https://doi.org/10.1016/j.surfin.2021.101498

18. Entezari A., Zhang Z., Sue A., Sun G., Huo X., Chang C. C., Zhou S., Swain M.V., Li Q. Nondestructive characterization of bone tissue scaffolds for clinical scenarios. J. Mech. Behav. Biomed. Mater. 89, 150-161 (2019). https://doi.org/10.1016/j.jmbbm.2018.08.034

19. Razi H., Checa S., Schaser K.D., Duda G.N. Shaping scaffold structures in rapid manufacturing implants: A modeling approach toward mechano-biologically optimized configurations for large bone defect. J. Biomed. Mater. Res. Part B Appl. Biomater. 100 В, 1736-1745 (2012). https://doi.org/10.1002/jbm.b.32740

20. Zhang L., Song B., Yang L., Shi Y. Tailored mechanical response and mass transport characteristic of selective laser melted porous metallic biomaterials for bone scaffolds. Acta Biomater. 112, 298-315 (2020). https://doi.org/10.1016/j.actbio.2020.05.038

21. Tashkinov M.A. Multipoint stochastic approach to localization of microscale elastic behavior of random heterogeneous media. Comput. Struct. 249, 106474 (2021). https://doi.org/10.1016/j.compstruc.2020.106474

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Published

2022-12-26

How to Cite

Elenskaya, N. V., Tashkinov, M. A., & Silberschmidt, V. V. (2022). Numerical modelling of the deformation behaviour of polymer lattice structures with density gradient based on additive technologies. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(4), 679–692. https://doi.org/10.21638/spbu01.2022.410

Issue

Vol. 9 No. 4 (2022)

Section

Mechanics

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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.