Universidad de Navarra, TECNUN Escuela de Ingenieros, Paseo Manuel de Lardizabal, 13, 20018, San Sebastin, Spain.
Universidad de Navarra, TECNUN Escuela de Ingenieros, Paseo Manuel de Lardizabal, 13, 20018, San Sebastin, Spain.
J Mech Behav Biomed Mater. 2019 Oct;98:357-368. doi: 10.1016/j.jmbbm.2019.05.043. Epub 2019 Jun 22.
As result of the advances made in additive manufacturing in recent years, the design of porous materials with controlled mechanical properties has gained importance due to their capability to offer case-specific solutions in multiple applications. In terms of biomaterials, the use of lattice structures provides a considerable variety of mechanical and geometric properties that can enhance osseointegration and reduce stress shielding. In this paper, the elastic response of a modified face-centered cubic (FCC) unit cell was studied, and analytical expressions for macroscopic effective Young's moduli, shear moduli and Poisson's ratios were obtained, thus providing the necessary parameters for the homogenization of the unit cell. The analytical expressions of the homogenization parameters open the possibility for implementation in other research fields, such as topology optimization. Timoshenko beam theory was used to model the struts of the modified FCC unit cell and a finite element analysis using shear flexible beam elements was performed to assess the accuracy of the analytical expressions. In addition to modelling the bending of the beams, axial and torsional displacements were also considered for a more detailed analysis. It can be concluded that the expressions obtained represent the elastic behavior of the modified FCC unit cell with high accuracy. Finally, the elastic response was further analyzed by introducing variability in the aspect ratio in order to enable the design of unit cells with controlled anisotropy.
由于近年来增材制造技术的进步，具有可控机械性能的多孔材料的设计变得越来越重要，因为它们能够为多种应用提供特定于病例的解决方案。在生物材料方面，晶格结构的使用提供了大量的机械和几何性能，可以增强骨整合并减少应力屏蔽。本文研究了改进的面心立方（FCC）单元的弹性响应，并获得了宏观有效杨氏模量、剪切模量和泊松比的解析表达式，从而为单元的均匀化提供了必要的参数。均匀化参数的解析表达式为在其他研究领域（如拓扑优化）的应用开辟了可能性。本文采用铁木辛柯梁理论来模拟改进的 FCC 单元的支杆，并使用剪切柔性梁单元进行有限元分析，以评估解析表达式的准确性。除了对梁的弯曲进行建模外，还考虑了轴向和扭转位移，以进行更详细的分析。可以得出结论，所得到的表达式能够高精度地表示改进的 FCC 单元的弹性行为。最后，通过引入纵横比的可变性进一步分析了弹性响应，以便能够设计具有可控各向异性的单元。
