Department of Engineering Mechanics, Dalian University of Technology, No. 2 Linggong Road, 116024, Dalian, China; State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, No. 2 Linggong Road, 116024, Dalian, China.
Department of Engineering Mechanics, Dalian University of Technology, No. 2 Linggong Road, 116024, Dalian, China.
J Mech Behav Biomed Mater. 2019 Nov;99:56-65. doi: 10.1016/j.jmbbm.2019.07.012. Epub 2019 Jul 19.
The Triple Periodic Minimal Surface (TPMS) has emerged as a new approach for producing open cell porous scaffolds for biomedical applications. However, different from the traditional scaffolds, the TPMS scaffolds always exhibit anisotropic elastic behaviors and consequently the simple mechanical testing is not capable to provide a full characterization of their mechanical behaviors. Additionally, it is still unclear if the TPMS scaffolds possess the similar anisotropic behaviors as the natural bones. The aim of the present study was to analyze the anisotropic elastic behaviors of TPMS based scaffolds using the numerical homogenization method and the analytical analysis approach. Five widely-used TPMS scaffold topologies (Diamond, Gyroid, Fischer-Koch S, Schwarz P and F-RD) were investigated. The independent elastic constants were determined from the analytical analysis and then, the values for these independent constants were determined using the finite element (FE) unit cell models of the scaffolds combined with the periodic boundary condition. The analytical analysis revealed that the Diamond, Gyroid and Fischer-Koch S topologies are threefold rotational symmetric and consequently have seven independent elastic constants. The Schwarz P and F-RD topologies are cubic symmetric and have three independent elastic constants. The FE analysis showed that the Diamond, Gyroid and Fischer-Koch S based scaffolds have only three non-zero independent elastic constants, implying the cubic symmetric property of these scaffolds. All the independent elastic constants decreased quadratically with the increase of scaffold porosity. The absolute difference between the Zener anisotropic factor and one increased the most for the Gyroid based scaffold, while the value for the Fischer-Koch S based scaffold increased the least. The present study revealed that all the five TPMS scaffolds possess cubic symmetry, limiting their anisotropic behaviors. The information on the Zener anisotropic factor and the relationship between the scaffold elastic constants and the porosity can facilitate the selection and design of scaffolds in biomedicine and relevant fields.
三重周期性极小曲面（TPMS）已成为用于生物医学应用的开孔多孔支架的一种新方法。然而，与传统支架不同，TPMS 支架通常表现出各向异性弹性行为，因此简单的机械测试无法全面描述其力学行为。此外，TPMS 支架是否具有与天然骨骼相似的各向异性行为尚不清楚。本研究旨在使用数值均匀化方法和分析分析方法分析基于 TPMS 的支架的各向异性弹性行为。研究了五种广泛使用的 TPMS 支架拓扑结构（菱形、胞状、Fischer-Koch S、Schwarz P 和 F-RD）。从分析分析中确定了独立弹性常数，然后，使用结合周期性边界条件的支架的有限元（FE）单元模型确定了这些独立常数的值。分析分析表明，菱形、胞状和 Fischer-Koch S 拓扑结构是三重旋转对称的，因此具有七个独立的弹性常数。Schwarz P 和 F-RD 拓扑结构是立方对称的，具有三个独立的弹性常数。FE 分析表明，基于菱形、胞状和 Fischer-Koch S 的支架仅具有三个非零独立弹性常数，表明这些支架具有立方对称特性。所有独立弹性常数随支架孔隙率的增加呈二次减小。Zener 各向异性因子的绝对值与 1 的差值对于基于胞状的支架增加最大，而基于 Fischer-Koch S 的支架增加最小。本研究表明，所有五种 TPMS 支架都具有立方对称性，限制了它们的各向异性行为。关于 Zener 各向异性因子的信息以及支架弹性常数与孔隙率之间的关系有助于在生物医学和相关领域选择和设计支架。
