三重周期极小曲面结构形态对力学响应影响的数值分析。
Numerical analysis of the influence of triply periodic minimal surface structures morphometry on the mechanical response.
机构信息
Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avda. de la Universidad 30, Leganés, 28911, Madrid, Spain; Institute of Mechanical and Biomechanical Engineering - I2MB, Department of Mechanical Engineering and Materials, Universitat Politècnica de València, Camino de Vera, Valencia 46022, Spain.
Institute of Mechanical and Biomechanical Engineering - I2MB, Department of Mechanical Engineering and Materials, Universitat Politècnica de València, Camino de Vera, Valencia 46022, Spain.
出版信息
Comput Methods Programs Biomed. 2023 Mar;230:107342. doi: 10.1016/j.cmpb.2023.107342. Epub 2023 Jan 16.
BACKGROUND AND OBJECTIVE
Design of bone scaffolds requires a combination of material and geometry to fulfil requirements of mechanical properties, porosity and pore size. Triply Periodic Minimal Surface (TPMS) structures have gained attention due to their similarities to cancellous bone. In this work, we aim at exploring relationships between morphometry and mechanical properties for TPMS configurations.
METHODS
Eight TPMS structures are defined considering six porosity levels and their morphometry is characterized. The stiffness matrix of each structure is assessed and related to morphometry through a statistical analysis.
RESULTS
An orthotropic mechanical behavior has been derived from the numerical homogenization. Properties decay exponentially for decreasing volume fraction. Through volume fraction variation, TPMS mechanical properties can be selected to match bone properties in a range of 0.2% to 70% of the bulk material properties.
CONCLUSIONS
The comparison between cancellous bone and TPMS morphometry, considering a unit cell size of 1.5 mm, reveals that the configurations analyzed in this work match the requirements of volume fraction, mean thickness and pore size. However, the TPMS studied in this work differ from cancellous bone anisotropy. The results in this paper provide a framework to select the proper TPMS configuration and its geometry for patient-specific applications.
背景与目的
设计骨支架需要将材料和几何形状相结合，以满足机械性能、孔隙率和孔径的要求。由于与松质骨具有相似性，三重周期性极小曲面（TPMS）结构引起了人们的关注。在这项工作中，我们旨在探索 TPMS 结构的形态计量学和机械性能之间的关系。
方法
考虑到六种孔隙率水平，定义了八种 TPMS 结构，并对其形态计量学进行了表征。通过统计分析，评估了每个结构的刚度矩阵，并将其与形态计量学相关联。
结果
从数值均匀化得出了各向异性的力学行为。随着体积分数的降低，性能呈指数衰减。通过体积分数的变化，可以选择 TPMS 的机械性能，使其在 0.2%至 70%的整体材料性能范围内与骨骼性能相匹配。
结论
在考虑 1.5mm 单元尺寸的情况下，将松质骨与 TPMS 形态计量学进行比较，结果表明，在这项工作中分析的配置满足体积分数、平均厚度和孔径的要求。然而，在这项工作中研究的 TPMS 与松质骨的各向异性不同。本文的研究结果为选择合适的 TPMS 配置及其用于特定患者的几何形状提供了框架。
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