PSI - Issue 32

Nataliya Elenskaya et al. / Procedia Structural Integrity 32 (2021) 253–260 N. Elenskaya, M. Tashkinov/ Structural Integrity Procedia 00 (2019) 000 – 000

254 2

In recent years, the use of porous functional-gradient materials created on the basis of additive technologies has increased significantly, in particular, in the field of biomedicine (Bracaglia et al., 2017; Han et al., 2018; Liu et al., 2018; Ng et al., 2017; Zhang et al., 2019). Functionally graded porous frameworks (FGPS) are attractive because they combine mechanical and biological requirements with gradient frameworks to better mimic host tissue. Objects and devices with a lattice structure have an architecture formed by an array of elementary cells with a given shape. In such objects, the composition or structure may vary within its dimensions, resulting in the gradient of properties implemented within the same structure. Such mechanical gradients have an important role in distribution of stress. An important aspect of gradient structures is the smoothing of stress gradients to avoid stress concentrations caused by abrupt geometric changes. This paper is devoted to the development of methods for creating three-dimensional finite element models of the geometry of lattice structures with a gradient of the volume fraction of the porous phase as well as modeling the deformation features of polymer structures with such geometry. Geometric models of heterogeneous bicontinuous interpenetrating lattice structures were obtained using the level-set method based on the gyroid and I-WP equations with variation of parameters (Liu et al., 2018; Zhang et al., 2020). Models of mechanical behavior are implemented using the finite element method. The polyether ether ketone (PEEK) is a high-performance biocompatible thermoplastic, which retains mechanical properties, stiffness and creep resistance at high temperatures and when exposed to aggressive environments. It is often used in 3D printing for high-demanding applications and was taken as a model material in this work. 2. Creation of geometry models The methods based on the analytical definition of three-dimensional surfaces that separate the two phases were used for a synthesis of models of bicontinuous open-cell structures. For models with periodic structure, analytical expressions containing the sum of products of periodic functions ( sin and cos ) were used. The common approach for generating the ordered bicontinuous microstructures is to use Triply Periodic Minimal Surfaces (TPMS) such as Schwarz-D (diamond), Schwarz-P (primitive), Schon I-WP (wrapped package) and G (gyroid) surfaces. This paper is focused on Gyroid and I-WP surfaces, the analytical expressions for which are given in the following equations (Scherer, 2013):               , , cos sin cos sin cos sin , G x y z x z z y y x           (1)





(2)

     cos cos 2 cos 2 cos 2 , I WP x y z x z x y z            , , 2 cos 

    cos z y  

    cos y x  

cos

cos























where , ,     are constants or functions varying in a given way along the coordinate axes. The examples of the resulting unit cells are presented in Fig.1.

Fig. 1 Unit cells of triply periodic minimal surface-based bicontinuous composite microstructures: (a) Gyroid; (b) I-WP