PSI - Issue 37

Nataliya Elenskaya et al. / Procedia Structural Integrity 37 (2022) 692–697 Nataliya Elenskaya / Structural Integrity Procedia 00 (2019) 000 – 000

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biomedical devices (Smith et al., 2019). For instance, porous scaffolds with a complex structure similar to human bone attract attention because they combine mechanical and biological requirements to better mimic the host tissue. Additive manufacturing is actively developing as a technological method for creating structures with controlled geometry (Montgomery et al., 2020). Fused filament fabrication (FFF/FDM) method allows to utilize biocompatible polymers for manufacturing of biomedical devices. This work is focused on the structures made of polyetheretherketone (PEEK), a high-performance biocompatible thermoplastic that retains mechanical properties, stiffness, and creep resistance at high temperatures and when exposed to aggressive environments. It is often used in 3D printing for highly demanding applications (Su et al., 2020). This work is focused on numerical studying of deformation features of cellular polymeric structures that are used in bone tissue scaffolds, depending on gradient of volume fraction of the porous phase. Three-dimensional geometric models of heterogeneous bicontinuous interpenetrating cellular structures are obtained using the level set method based on gyroid equations with variation of parameters (Liu et al., 2018; Zhang et al., 2020). Numerical models of mechanical behavior of the studied structures are implemented using the finite element analysis. 2. Creation of geometry models To create models of interpenetrating open-cell structures, methods based on analytical definition of three dimensional surfaces separating the two phases were used. Models with periodic structures were considered, for generation of which analytical expressions containing the sum of products of trigonometric functions were used. A common approach for generating ordered bicontinuous microstructures is to use triply periodic minimal surfaces (TPMS). In this study, geometric models of three-dimensional heterogeneous cellular structures were obtained using the gyroid equation (Liu et al., 2018): ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , , cos sin cos sin cos sin 0, G G x y z x z z y y x R y        = + + + = (1) 0 R to obtain the gradient of porosity. The studied models of open-type cellular microstructures with pore volume fraction ranged from 0% to 50%, 0% to 70%, and from 50% to 70% are shown in Fig. 1. Model dimensions are 12 24 12   mm. ( ) 01 , , G x y z  ( ) 02 , , G x y z  ( ) 03 , , G x y z  where , ,    are constants that regulating the size of a unit cell, ( ) 0 G R y ky R = + is y -coordinate function, which varies in a given way with constants k and

a) c) Fig. 1 Models of gradient open-cell structures based on the gyroid equation of different pore volume fraction along the direction of the gradient : а) 0 to 50%, gradient parameters are 0, 0623, k = 0 1,5; R = − b) 0 to 70%, gradient parameters are 0, 087, k = 0 1,5; R = − c) 50 to 70%, gradient parameters are 0, 0245, k = 0 0. R = Discretization of derived geometric regions using tetrahedral elements was performed for finite element analysis, the optimal element s’ maximum size was chosen after performing convergence analysis. b)