Abstract
INTRODUCTION
Porous metallic materials, due to their capability of tailoring their mechanical properties to those of bone, have been suggested to be utilized in prosthesis to avoid the stress shielding phenomenon1, believed to increase the risk of implant loosening2.
The aim of this work is to obtain the most simplified model possible to simulate the mechanical behavior of a Ti6Al4V porous structure. For this purpose, a beam element model was analyzed and the results were then compared to a 3D-solid model.
EXPERIMENTAL METHODS
Two computational models of the porous structure were developed: a 3D solid model, considered as the reference for comparison, and a beam model as a simplified and computationally inexpensive approximation (Fig. 1). CATIA V5R20 (3D modelling) and ANSYS V13 (simulations) were used.
Isotropic elastic material model was used. Strut diameter (ϕb) was set to 450 μm, pore diameter (ϕp) was varied between 600 and 5000 μm, and pore number (np) between 2 and 9. Structures sizes varied from 2.1 × 2.1 × 2.1 mm3 to 49.05 × 49.05 × 49.05 mm3. Apparent elastic modulus (Eap) and its difference between both models (error) were analyzed for the different values of ϕp and slenderness ratio (SR). In addition, the influence of loading direction was analyzed with the beam model for cubic and diamond cell geometries. Eap variations were compared.
RESULTS
For both models, Eap decreases when np increases, trending to an asymptotic value which depends upon SR. Initially, Eap for beam model is greater than for the solid model. When np > 4, the situation is opposite. From this point, differences in Eap between both models increase, trending to a fixed value (Fig. 2).
When np increases by 1 pore, Eap variation is smaller than 1% for np > 5 in the solid model, and for np > 7 in the beam model.
The solution error (between solid and beam models) diminishes from 7% to 2% when SR increases from approximately 50 (ϕp = 900 μm) to 900 (ϕp = 5000 μm).
For loads aligned with the struts, cubic cell geometry showed higher Eap than diamond. As loading direction changes, Eap reduced dramatically for cubic cells while it remained more constant for diamond cells (Fig. 3).
CONCLUSION
Eap is influenced by np and SR. Eap trends to a fixed value as np increases. The minimal np for a solution with 1% of variation in Eap can be set for np >5 (3D solid model) or np >7 (beam model).
Although errors in beam modeling have been justified by overlapping phenomena at vertex3, we have found that the error may be explained by SR.
Beam models may be used as cost-effective models to evaluate the mechanical behavior of porous structures. However, cubic cell structures' mechanical behavior is very sensible to the loading direction. For this reason, isotropic cell structures such as diamonds may be a better choice for prosthesis design.
