A recent explosion in the application of additive manufacturing (AM) in biomedical engineering has opened the possibility of manufacturing porous meta-implants with arbitrary micro-architecture. AM makes it possible to manufacture open-cell (i.e., permeable) porous materials with precisely designed microstructure both in micro- and macro-scales [9]. Porous implants should satisfy several physical and biological requirements in order to be in an optimal state for biomedical applications: they should have the right levels of stiffness, permeability, and fatigue resistance, in proximity to how much they are in bone tissues. This is especially crucial to avoid the undesired consequences of using highly stiff solid metallic implants that can cause problems such as stress shielding [10]. This can be achieved using designer materials, which can exhibit exotic properties, commonly known as metamaterials. Permeable metamaterials have shown several advantages in multi-functional applications such as biomedical engineering, acoustics, photonics, and thermal management [11]. Metamaterials used to construct implants are made of repeating building blocks known as unit cells. The mechanical, physical, and biological properties of implants are determined by four main characteristics of the unit cell that they are made of: the shape of the cells, their size, their permeability, and their relative density (which is defined as the fraction of space occupied by the solid material). In recent years, several experimental [12; 13; 14; 15; 16; 17; 18; 19], numerical [20; 21; 22; 23; 24; 25], and analytical [26; 27; 28; 29; 30] studies have been dedicated to studying the influence of unit cell shape on the above-mentioned properties. 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. Analytical relationships for a regularly repeated lattice structure have several benefits: they can be used for validation of numerical or experimental results, they can be implemented in Machine Learning or Artificial Intelligence algorithms to construct optimally designed patient-specific porous implants, and they can give a clear and quick indication of what geometrical/material properties have the most contribution in each of the mechanical properties. Previously, analytical relationships for elastic properties (elastic modulus, Poisson's ratio, and yield stress) of different unit cells such as body-centred cubic (BCC) [31], cube [32; 33], diamond [26; 34], hexagonal packing [35], iso-cube [5], octahedral [27], rhombic dodecahedron [28; 29], rhombicuboctahedron [30], truncated cube [32], truncated cuboctahedron [36], and truncated octahedron [37] have been derived. In the literature, relationships for octahedral [27], rhombic dodecahedron [29], and truncated cuboctahedron [36] have been derived based on both Euler-Bernoulli and Timoshenko beam theories. However, for the rest of the above-mentioned geometries, the relationships are derived based on Euler-Bernoulli beam theory only. The question that arises here is whether or not there can be a convenient way to convert the already-existing relationships based on Euler-Bernoulli to relationships based on Timoshenko beam theory without the need to rewrite all the derivations from the starting point. In this study, we try to answer that question by presenting a technique to convert the already-existing analytical relationships based on Euler-Bernoulli beam theory to equivalent Timoshenko ones. This technique can be used to convert Euler-Bernoulli elastic relationships including elastic modulus, Poisson's ratio, and yield stress (\(E\), \(\sigma_{y}\), \(\
u\)) of any porous material. The efficiency of this technique is evaluated for six unit cell types: BCC, hexagonal packing, rhombicuboctahedron, diamond, truncated cube, and truncated octahedron.