PSI - Issue 49

Nataliya Elenskaya et al. / Procedia Structural Integrity 49 (2023) 43–50 Author name / Structural Integrity Procedia 00 (2023) 000–000

45

3

VD

volume degradation

2. Methodology 2.1. Scaffolds Degradation

This study proposes two methods to model the degradation process: (i) bulk degradation modelling, which assumes a change in the elastic material properties over the entire volume of the structure, and (ii) surface degradation, with a uniform material shrinkage over the entire surface of the structure. In the former case, the elastic modulus of the material gradual decreases according to the degradation factor shown in Table 1.

Table 1 Changes in Young’s modulus of scaffold with time after its implantation (Shi et al. 2018b)

Time (day) Degradation (%)

0 0

5

10

15

20

25

30

35

40

45

50

8.5

19.0

28.3

40.1

48.3

60.2

68.1

75.0

80.4

84.6

In the second approach, it is proposed to simulate a proportional thinning of the structure, starting from its surface, which reduces the volume of the material. The degradation step was chosen according to the experimentally obtained change of the effective modulus of PLA in days (Shi et al. 2020) and was taken as 12.5%. The effect of the chosen degradation model on the effective properties of TPMS-based scaffolds under compressive loading was investigated. 2.2. TPMS-based Scaffolds Methods based on the analytical definition of three-dimensional surfaces separating the two phases were used to synthesise models of interpenetrating open-lattice structures. The TPMS divides the domain, considered as a unit cell, into two different spaces. In the present work, the degradation processes are studied for the scaffolds based on three most widely used TPMS unit cells (Table 2).

Table 2. TPMS equation and parameters. Type

TPMS equation

Surface

(

)

(

)

( ) ( ) ( ) sin sin x y z α γ β

( ) ( ) cos y z γ β

( ) ( ) ( ) sin cos x y z α γ β

( ) ( ) sin y z γ β

sin

cos

cos

cos

0

+

+

+

=

D

( ) ( ) sin x z α β

( ) ( ) sin z y β γ

( ) ( ) sin y x γ α

cos

cos

cos

0

G

+

+

=

(

)

(

)

(

)

(

)

(

)

( ) ( ) cos x z α β

( ) ( ) cos z y β γ

( ) ( ) cos y x γ α

0.5

cos 2 cos 2 cos 2 x z α β + +

cos

cos

cos

0

y

γ

−

+

+

=

I-WP

In Tab. 2 2 k A α β γ π = = = are the parameters controlling the characteristic unit-cell size of the periodic structure; 1 k = is a number of cells along the side of the scaffold, 5 A = mm is the scaffold size. There are two ways to generate the TPMS-based structures: the first based on thickening of the minimal surface in a selected region, yielding a sheet TPMS-based structure; the second considers the volume, encompassed by the minimal surface as a solid, yielding a skeletal structure. This paper investigates the degradation of sheet cells based on the G and D surfaces and a skeletal cell based on the I-WP surface. The initial porosity of all the studied