Print Email Facebook Twitter Improving the accuracy of analytical relationships for mechanical properties of permeable metamaterials Title Improving the accuracy of analytical relationships for mechanical properties of permeable metamaterials Author Hedayati, R. (TU Delft Novel Aerospace Materials) Ghavidelnia, Naeim (Amirkabir University of Technology) Sadighi, Mojtaba (Amirkabir University of Technology) Bodaghi, Mahdi (Nottingham Trent University) Date 2021 Abstract Permeable porous implants must satisfy several physical and biological requirements in order to be promising materials for orthopaedic application: they should have the proper levels of stiffness, permeability, and fatigue resistance approximately matching the corresponding levels in bone tissues. This can be achieved using designer materials, which exhibit exotic properties, commonly known as metamaterials. In recent years, several experimental, numerical, and analytical studies have been carried out on the influence of unit cell micro-architecture on the mechanical and physical properties of metamaterials. Even though experimental and numerical approaches can study and predict the behaviour of different micro-structures effectively, they lack the ease and quickness provided by analytical relationships in predicting the answer. Although it is well known that Timoshenko beam theory is much more accurate in predicting the deformation of a beam (and as a result lattice structures), many of the already-existing relationships in the literature have been derived based on Euler–Bernoulli beam theory. The question that arises here is whether or not there exists a convenient way to convert the already-existing analytical relationships based on Euler–Bernoulli theory to relationships based on Timoshenko beam theory without the need to rewrite all the derivations from the start point. In this paper, this question is addressed and answered, and a handy and easy-to-use approach is presented. This technique is applied to six unit cell types (body-centred cubic (BCC), hexagonal packing, rhombicuboctahedron, diamond, truncated cube, and truncated octahedron) for which Euler–Bernoulli analytical relationships already exist in the literature while Timoshenko theory-based relationships could not be found. The results of this study demonstrated that converting analytical relationships based on Euler–Bernoulli to equivalent Timoshenko ones can decrease the difference between the analytical and numerical values for one order of magnitude, which is a significant improvement in accuracy of the analytical formulas. The methodology presented in this study is not only beneficial for improving the already-existing analytical relationships, but it also facilitates derivation of accurate analytical relationships for other, yet unexplored, unit cell types. Subject Analytical relationshipEuler–Bernoulli beam theoryFinite element methodMechanical propertiesTimoshenko beam theory To reference this document use: http://resolver.tudelft.nl/uuid:904b4f4e-1ed1-4786-9129-83d122fecc56 DOI https://doi.org/10.3390/app11031332 ISSN 2076-3417 Source Applied Sciences, 11 (3), 1-38 Part of collection Institutional Repository Document type journal article Rights © 2021 R. Hedayati, Naeim Ghavidelnia, Mojtaba Sadighi, Mahdi Bodaghi Files PDF applsci_11_01332_v2.pdf 4.85 MB Close viewer /islandora/object/uuid:904b4f4e-1ed1-4786-9129-83d122fecc56/datastream/OBJ/view