Page 86 - MSAM-2-3

Materials Science in Additive Manufacturing Functional graded and hybrid TPMS lattices

gyroid lattices RD45-05 with the relative density 45% in E 58 13. * 121. (XV)
the inner region and the relative density 5% in the outer
region. All three lattices had the same overall 25% relative G 26 93. 127. * (XVI)
density. The 3-node triangular shell (S3R) element was 111.
utilized to mesh the gyroid lattice, where 195,900 elements K 48 08. * (XVII)
were utilized to guarantee the model quality. To investigate Equations XV and XVI show that both the exponent
the stress shielding reduction, the displacement of two values of elastic modulus E, which is equal to 1.21, and
points on the edge of the lattice (point 3 and point 4 as shear modulus G, which is equal to 1.27, of the sheet-based
shown in Figure 2C) and two points in the core of the gyroid lattices are between 1.0 and 2.0, indicating that the
lattice (point 1 and point 2 as shown in Figure 2D) was sheet-based gyroid lattice under uniaxial compression and
extracted for comparison. The stress contour was obtained shear loading has a combined stretching- and bending-
from the simulation to further assist the analysis of gyroid dominated behavior. The exponent value for bulk modulus
lattices as implant infillings. is closer to 1.0, suggesting that the sheet-based gyroid

The elastic modulus, shear modulus, bulk modulus, lattice under triaxial loads has a stretching-dominated
and Poisson’s ratio of the sheet-based gyroid lattices under behavior. As shown in Figure 3D, the relative density has a
different relative densities are presented in Figure 3A-D, limited impact on the Poisson’s ratio.
respectively. As shown in Figure 3A-D, the elastic modulus, The stress contours of the uniform gyroid lattice with
bulk modulus, and shear modulus of the sheet-based a relative density of 25%, the graded gyroid lattice with a
gyroid lattice increase when the relative density increases, relative density of inner 5% and outer 45%, and the graded
whereas the Poisson’s ratio decreases when the relative gyroid lattice with a relative density of inner 45% and outer
[27]
density increases. The Gibson-Ashby model was utilized 5% under a 5% compressive strain are shown in Figure 4. As
to fit the simulation. The dashed lines in Figure 3A-C shown in Figure 4A, the outer region of the uniform sheet-
indicate that the elastic properties from the Gibson-Ashby based gyroid lattice has a higher level of stress, whereas the
model fit well with the simulation results. The relevant stress in the central region of the lattice is at a much lower
Gibson-Ashby model results are illustrated as follows: level. Compared with the uniform case, the central part

A B

C D

Figure 3. Elastic properties of the sheet-based gyroid lattice under different relative density: (A) Elastic modulus E, (B) Shear modulus G, (C) Bulk
modulus K, and (D) Poisson’s ratio ν.

Volume 2 Issue 3 (2023) 5 https://doi.org/10.36922/msam.1753