Approximate analytical prediction on elastic properties of Diamond structures with varying porosities and orientations

Hao Wang^1,2Yongtao Lyu^1,3Jian Jiang^2*Feihu Zhao⁴Sergei Bosiakov⁵Hanxing Zhu⁶

• ¹School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian, China
• ²Department of Spinal Surgery, Central Hospital of Dalian University of Technology, Dalian University of Technology, Dalian, China
• ³DUT-BSU Joint Institute, Dalian University of Technology, Dalian, China
• ⁴Department of Biomedical Engineering, Zienkiewicz Institute for Modelling, Data & AI, Faculty of Science and Engineering, Swansea University, Swansea, United Kingdom
• ⁵Faculty of Mechanics and Mathematics, Belarusian State University, Minsk, Belarus
• ⁶School of Engineering, Cardiff University, Cardiff, United Kingdom

Bone scaffolds are widely used for repairing bone defects. As a biomimetic structure for bone scaffold, the triply periodic minimal surface (TPMS) structure is an ideal choice. To evaluate / characterize the mechanical properties of TPMS structures, multiple methods (e.g., via experiment or theoretical analysis) can be used. Each one has its advantages and disadvantages. Using approximate analytical approach, the mechanical properties of structures can be predicted quickly and efficiently. Therefore, it is necessary to determine the applicable range to ensure the computational accuracy of the mechanical properties of TPMS structures with varying porosities and strut orientations. In this paper, approximate analytical prediction on elastic properties of TPMS structures (i.e., Diamond) with varying porosities and strut orientations was investigated, and finite element (FE) method and theory of elasticity were compared with the approximate analytical approach. Due to the cubic symmetry of Diamond structure, these angular ranges ensure that the structure is non-repeating and is comprehensively analyzed in all three directions. Additionally, experimental tests were performed to validate the feasibility of the non-experimental methods. It was shown from the experimental validation that the results from non-experimental methods were acceptable at certain porosities and orientations. FE method, which is commonly used and a convinced approach, was utilized to represent the nonexperimental methods, comparing with experimental results. Therefore, the approximate analytical solutions and the results from elasticity theory were indirectly compared with experimental results. The errors between the approximate analytical solution and the results of the FE and elasticity theory were 17.65% and 39.13%, respectively, when the porosity of the structure was 85%. Therefore, the approximate analytical solution was considered relatively accurate at a higher porosity. At the same structural porosity, in the (100) plane, the closer the orientation of the structure was to 0° or 90°, the more accurate the prediction was. In the (110) plane, the closer the orientation of the structure was to 0°, the more accurate the prediction was. In the (111) plane, the accuracy of the prediction was basically not related to the orientation of the structure, but rather to the porosity of the structure.