# Mechanical Behavior of Ti6 Al4V Scaffolds Filled with CaSiO\({}_{3}\) for Implant Applications
## 2 Materials and Methods  
Five distinct scaffolds were designed by SolidWorks, as shown in Figure 1 (rectangular, primitive, lattice, gyroid and honeycomb, respectively). The names are chosen according to the shape of the structures. These computer-aided design (CAD) models can be used both in finite element analysis (FEA) for the simulation of mechanical properties and the selective laser melting (SLM) process for the fabrication of the real parts. All the five scaffolds were of the following dimensions: A diameter of 20 mm and a height of 15 mm. The weight range of these samples varied between \(\approx\)3.8 and 5.5 g. Ti6 Al4V powders with size of 10-45 \(\upmu\)m (produced by a gas atomization process) from TLS Technik were used as the raw material for the production of triply periodic minimal surfaces (TPMS)-type scaffolds.  
A Realized SLM50 device with a maximum laser power of 120 W was used for the fabrication of the scaffolds. The following parameters were used for the fabrication of Ti6 Al4V by SLM: Laser current 3000 mA, exposure time 600 \(\upmu\)s, point distance 1 \(\upmu\)m and unit cell size 1.5 mm. These are standard parameters that are observed for the fabrication of the Ti6 Al4V samples. SLM-SPS processes were combined for producing metal-ceramic hybrid composites, which is suggested for chronic osteomyelitisitis, Vancomycin local delivery, and infected bones replacement in the field of tissue engineering [9]. The entire spark plasma sintering (SPS) setup is kept under the glovebox, in order to maintain the consolidation process in an inter atmosphere. This also helps in avoiding oxygen contamination during the SPS consolidation process. Microstructure of the samples were observed using scanning electron microscope (SEM), (Zeiss EVO MA 15, Germany)  
Structural explicit dynamics using the AUTODYN solver and arbitrary Lagrange-Euler (ALE) method via ANSYS Workbench 17.2 is applied for these simulations. A high-quality finite element analysis (FEA) mesh is generated to gain a high-resolution response. The linearized governing motion equation in cylindrical coordinates \((r,\ \theta,\ z)\) can be expressed by [31]:  
\[\frac{\partial\sigma_{r}}{\partial r}+\frac{1}{r}\frac{\partial\sigma_{r\theta }}{\partial\theta}+\frac{\partial\sigma_{rz}}{\partial z}+\frac{1}{r}(\sigma_ {rr}-\sigma_{\theta\theta})+F_{r}=\rho\frac{\partial^{2}u_{r}}{\partial t^{2}} \tag{1}\]  
\[\frac{\partial\sigma_{r\theta}}{\partial r}+\frac{1}{r}\frac{\partial\sigma_ {\theta\theta}}{\partial\theta}+\frac{\partial\sigma_{\theta z}}{\partial z} +\frac{2}{r}\sigma_{r\theta}+F_{\theta}=\rho\frac{\partial^{2}u_{\theta}}{ \partial t^{2}} \tag{2}\]  
\[\frac{\partial\sigma_{rz}}{\partial r}+\frac{1}{r}\frac{\partial\sigma_{ \theta z}}{\partial\theta}+\frac{\partial\sigma_{zz}}{\partial z}+\frac{2}{ r}\sigma_{rz}+F_{z}=\rho\frac{\partial^{2}u_{z}}{\partial t^{2}} \tag{3}\]  
where, \(\sigma_{ij}=\sigma_{ji}\) is the Cauchy stress tensor, \(u_{i}\) is displacement, \(\rho\) is density and \(F_{i}\) is body force (\(F_{r}=F_{\theta}=0\), \(F_{z}=axial compression\)). In the simulation, compressive punches are assumed rigid (unchanged dimension). Bottom punch is the fixed support and the top punch was kept moving until a maximum force of 100 kN (safe loading of machine), or a maximum deformation of 10 mm (with rate of 2 mm/min), is reached. Both the experimental tests and the numerical simulations have identical  
Figure 1: Scaffolds with: (**A**) Rectangular-, (**B**) Primitive-, (**C**) Lattice-, (**D**) Gyroid- and (**E**) Honeycomb-type structures (Dimensions: 20 mm in diameter and with 15 mm height), designed via computer-aided design (CAD) software.  
boundary conditions. An Instron 8500 apparatus was used for measuring the compression tests of these scaffolds.