Analytical investigation of in-plane and out-of-plane elastic properties of bone-inspired cellular structures

Determining the elastic moduli of materials plays an important role in solving many structural problems, such as vibration and buckling analyses of advanced laminate plates and shells. Bone-inspired cellular structure material (BCS) is a new cellular structure material that has recently attracted the attention of scientists and engineers. However, till now, none of the works in the literature can fully provide the elastic moduli of the BCS. To address these limitations and answer the question of how many elastic constants of BCS are and how to determine all the elastic constants of this material, analytical models are developed in this paper. Here, the analytical models are derived by taking the bending and axial stretching/compression and out-of-plane average normal and shear stress/strain deformation mechanisms in the analysis. We found that the BCS material is orthotropic material with nine independent elastic modulus, including four in-plane elastic constants and five out-of-plane elastic constants. Using the developed analytical models, numerical results are then provided. The accuracy of proposed method is confirmed by the previous obtained results in the literature. Further, in this work we have investigated the influence of the geometry parameters on the elastic properties of the considered bone-inspired cellular structure materials also.