Micromechanical modeling in determining the transverse elastic moduli and stress distributions of bamboo

In order to enhance the understanding of the microstructural characteristics of bamboo culm within transverse directions, two micromechanics models, Halpin-Tsai (H-T) equations and Mori-Tanaka (M-T) model, are introduced to generate the homogenized moduli in the transverse direction, which cannot be easily predicted using the traditional rule of mixtures that was mostly adopted in the previous literatures. A multi-scale framework is then created by connecting the micromechanics models with structural analysis of bamboo culm cross section, which is treated as concentric composite cylinders composed of fiber vascular bundles and ground tissue with different volume fractions that usually increase from inner periphery to outer periphery. Finally, several numerical examples are illustrated to prove the availability of the present micromechanics models in calculating homogenized moduli and practicing bamboo structural analysis. It has been found that the H-T equations and M-T model usually predict well-matched homogenized moduli, leading to similar stress distributions along the radial direction under symmetric loading boundary conditions. In general, both micromechanics models provide easy predictions of homogenized moduli for future numerical and experimental research of bamboo cross sections.