Study on the axial compression buckling behaviors of concentric multi-walled cylindrical shells filled with soft materials

Via the energy-based analytical and numerical methods, this paper studies the pre- and post-buckling compression behaviors of concentric multi-walled cylindrical shells filled with low-shear-modulus (or fluid like) materials, which are widely observed in biological composites. It is found that if the bulk modulus of the filled materials is on the same order of (or larger than) the Young's modulus of the shell, the axial compression resistance in the post-buckling stage can be significantly improved. In specific, the tangent stiffness increases quickly with the increase of the compression strain, and finally may become compatible with that for a non-buckled hollow shell. Moreover, it is interesting to note that the compression resistance after buckling is approximately in proportion to the net shell-wall area, and independent of the thickness or the number of shell-walls. These investigations may quantitatively reveal a mechanism adopted by the nature: rolling the flat thin-layered composites into a filled concentric multi-walled cylindrical shell to achieve better compression resistance. The biological concentric shell can also be viewed as a double-leveled hierarchical structure, which is capable to sustain more complex loadings than the bottom leveled structure.