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

Hao Wang, Yongtao Lyu, Jian Jiang, Feihu Zhao Orcid Logo, Sergei Bosiakov, Hanxing Zhu

Frontiers in Bioengineering and Biotechnology, Volume: 13, Start page: 1626104

Swansea University Author: Feihu Zhao Orcid Logo

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    © 2026 Wang, Lyu, Jiang, Zhao, Bosiakov and Zhu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY).

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DOI (Published version): 10.3389/fbioe.2025.1626104

Abstract

Introduction: Bone scaffolds are widely used for repairing bone defects. As a biomimetic structure for bone scaffolds, 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 experimen...

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Published in: Frontiers in Bioengineering and Biotechnology
ISSN: 2296-4185
Published: Frontiers Media S.A. 2026
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URI: https://cronfa.swan.ac.uk/Record/cronfa71269
Abstract: Introduction: Bone scaffolds are widely used for repairing bone defects. As a biomimetic structure for bone scaffolds, 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 method 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 that the calculated mechanical properties of TPMS structures with varying porosity and strut orientation are acceptable. Methods: In this paper, approximate analytical prediction of 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. The ranges for porosity were from 70% to 90%. The ranges for orientation were defined by rotating the scaffold from 0° to 90° along the [100] and [110] directions, and from -30° to 90° along the [111] direction. 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. Results: It was shown from the experimental validation that the results from non-experimental methods were acceptable at certain porosities and orientations. The FE method, which is commonly used and a reliable approach, was utilized to represent the non-experimental methods and was compared with the experimental results. Therefore, the approximate analytical solutions and the results from elasticity theory were indirectly compared with experimental results. When the porosity of the structure was 85%, the approximate analytical solution showed differences of 17.65% relative to the FE result and 39.13% relative to the elasticity theory result. Therefore, the approximate analytical solution was considered acceptable at a higher porosity. The acceptable ranges of the porosity for applying the approximate analytical approach were higher than 85% in the [001] and [110] directions, and higher than 90% in the [111] direction. At the same structural porosity, in the (100) plane, the predicted results were acceptable when the structural orientation was close to 0° or 90°. In the (110) plane, the predicted results were acceptable when the structural orientation was close to 0°. In the (111) plane, whether the predicted results can be accepted or not was basically independent of the structural orientation but was dependent on the porosity of the structure. The planes of (100), (110) and (111) are defined as the planes perpendicular to the directions of [100], [110] and [111], respectively. Discussion: Data in the present study provide valuable guidance on applying the approximate analytical approach to efficiently predict the mechanical properties of TPMS structures prior to performing formal calculations and experiments.
Keywords: triply periodic minimal surface, diamond structure, approximate analytical approach, finite element method, theory of elasticity, effective elastic modulus
College: Faculty of Science and Engineering
Funders: This work was supported by the National Natural Science Foundation of China (12572376, W2521087), the National Science Foundation of Liaoning Province (2025-MS-365), the National Key R&D Program of China (2024YFE0213500), the Fundamental Research Funds for the Central Universities (DUT25YG245), and the State Key Laboratory of Structural Analysis, Optimization, and CAE Software for Industrial Equipment (GZ25110).
Start Page: 1626104

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