Page 211 - IJB-9-4

International Journal of Bioprinting b-Ti21S TPMS FGPs produced by laser powder bed fusion

Table 8. Summary of Young’s modulus obtained by means of cell size on the normal plane in the case of homogenization
homogenization method on the single unit cell for both TPMS analysis, a fully solid FEA of the complete specimen
structures (nTopology software). with 4.0 mm and 2.5 mm unit cell size were performed,

TPMS-FGPSs Relative density ρ r E hom (GPa) E hom (GPa) as shown in Figures 17 and 18, respectively. Thanks to
(−) nom real Equation XII, an elastic modulus of 7.7 GPa and of 3.2 GPa
2.5 mm 0.17 1.15 0.93 was obtained in the case of TPMS-FGPS 4.0 and TPMS-
0.34 4.88 4.16 FGPS 2.5, respectively. The stiffness obtained in case of
TPMS-FGPS 4 is closer to the experimental value (−25%),
0.50 10.83 9.77 confirming that the non-negligible edge effects occur in the
0.66 19.47 18.00 case of a small number of unit cells in the normal area with
0.83 32.5 31.13 respect to the load [64,69,70] . A similar variation with respect
4.0 mm 0.17 1.12 0.86 to experimental results was achieved with TPMS-FGPS 2.5
0.34 4.88 2.79 (−27%). The deviation of approximately 25% between the
0.50 10.84 8.92 experimental and predicted elastic modulus through FEA
may be attributed to the fact that compression testing is not
0.66 19.47 16.73 an ideal quasi-static process, even at low strain rates. As
0.83 32.7 28.67 noted by Yang et al. , the ideal quasi-static compression
[71]
test occurs primarily in the first layers near the applied
load, where the stress is not transmitted to lower parts.
The solid FEA analysis presented here was conducted to
Table 9. Elastic modulus of the two TPMS-FGPSs obtained highlight the limitations of the homogenization method
by experimental analysis and through homogenization using when the minimum required number of unit cell sizes
nominal and real ligament dimensions one. was not used. Further considerations, deriving from more

TPMS-FGPSs E cyclic (GPa) E nom E hom detailed FEA modeling, will be the subject of future works.
hom
real
(GPa) (GPa) Taken together, the measurement of the Gibson–Ashby
2.5 mm 4.1 ± 0.1 4.6 (10%) 3.8 (−8%) constants was carried out in the case of TPMS-FGPS 2.5
since it was characterized by enough unit cell number
4.0 mm 10.7 ± 0.1 4.2 (−61%) 3.1 (−70%) to avoid the edge effects (Figure 19). The plot permits to

Figure 17. Finite element simulation of the complete TPMS-FGPS 4.0. (a) The contour mesh of the as-manufactured samples. (b) Loading condition
resembling the experimental condition, i.e., a fixed constraint on the bottom surface of the specimen and a fixed displacement equal to 0.1 mm in the
vertical direction on the top surface. (c) Results of the simulation analysis.

Volume 9 Issue 4 (2023) 203 https://doi.org/10.18063/ijb.729