Page 84 - MSAM-2-3

Materials Science in Additive Manufacturing Functional graded and hybrid TPMS lattices

A B

C

D E

Figure 1. (A) Generation of sheet-based and solid-network-based triply periodic minimal surfaces (TPMS) lattice. (B) TPMS unit cell candidates.
(C) Sheet-based gyroid lattices with different relative densities. (D) Graded sheet-based gyroid lattices. (E) Hybridization of solid-network-based TPMS
lattices.

As shown in Figure 1B, the geometric features of gyroid at the relevant regions. For hybridization, different types of
and primitive TPMS lattices are described by the following solid-network-based TPMS lattices can be combined with
functions: the following function:
)
f gyroid cos( w x)sin( w y cos( w y)sin( w z) gyroid (1 ) primitive , (VI)
y
y
z
x
cos( wz)sin( wx),, (III)
x
z
where gyroid f gyroid c and primitive f primitive c are
)
)cos(
f primitive cos( w x w y cos( w z ) generated based on Equation I to represent solid-network-

z
y
x
cos(wx )cos(wy based TPMS lattices, and µ (x, y, z) is a spatial weighting
)
x
y

)
0..51 cos(wy )cos(wz , (IV) function ranging from 0 to 1, where 0 indicates primitive
z

y
cos(wx )cos(wz ) and 1 indicates gyroid. According to the approach proposed
x z by Yang et al. , the smooth connections between different
[23]
TPMS lattices can be facilitated by applying the sigmoid
where x, y and z are spatial Cartesian coordinates in the 3D function to the µ (x, y, z) function, which is expressed as
space, w is the parameter to manipulate the periodicities of follows:
the TPMS function, which is defined by: 1
n (, ,)xy z , (VII)
,
w 2 L i i for i x yz,, (V) 1 exp kG ( ,, )xy z
i
where n indicates the number of unit cells along x-, y-, where G represents the connection region between gyroid
i
and z-directions, and L controls the lattice size in the and primitive lattices, and k is utilized to represent the
i
corresponding directions. As shown in Figure 1C, by transition width. For the radial hybridization as shown
manipulating the isovalue offset, the solid region can be in Figure 1E, the boundary function can be expressed as
tuned to control the relative density. Therefore, the graded follows:
2
2
TPMS lattices can be facilitated by assigning graded c values Gx yz(, ,) x y R . (VIII)
2
Volume 2 Issue 3 (2023) 3 https://doi.org/10.36922/msam.1753