Analytical relationships for yield stress of five mechanical meta-biomaterials

In this article, five fundamental unit cells namely BCC, hexagonal packing, rhombicuboctahedron, diamond, and truncated octahedron, for which there was a lack of accurate analytical yield stress relationship in the literature, were studied analytically and numerically using the Timoshenko and Euler–Bernoulli beam theories. Two different approaches based on force or displacement methods were considered. The results of the analytical models were validated against finite element models results as well as experimental data from literature. The results demonstrated that the newly developed analytical relationships based on Timoshenko beam theory give more accurate results as compared to Euler–Bernoulli beam theory, especially in higher values of relative densities.