Uncovering a high-performance bio-mimetic cellular structure from trabecular bone

Abstract

The complex cellular structure of trabecular bone possesses lightweight and superior energy absorption capabilities. By mimicking this novel high-performance structure, engineered cellular structures can be advanced into a new generation of protective systems. The goal of this research is to develop an analytical framework for predicting the critical buckling load, Young's modulus and energy absorption of a 3D printed bone-like cellular structure. This is achieved by conducting extensive analytical simulations of the bone-inspired unit cell in parallel to traverse every possible combination of its key design parameters. The analytical framework is validated using experimental data and used to evolve the most optimal cellular structure, with the maximum energy absorption as the key performance criterion. The design charts developed in this work can be used to guide the development of a futuristic engineered cellular structure with superior performance and protective capabilities against extreme loads.

Figure 1

(a) Trabecular bone; (b) Closed cell plate-likestructure of trabecular bone, which is composed of concave (CCV), convex (CVX) and hybrid (HYB), both concave and convex cells; (c) Voronoi diagram for mimicking trabecular bone; (d) Unit cell extracted from the Voronoi diagram; (e) Bone-like structure generated from the unit cell; (f) 3D printed bone-like scaffold; (g) Force–displacement curve of a 3D printed bone-like structure; h) Parallel execution of structural analysis equations to obtain the optimal bone-like cellular structure; (i) Optimised bone-like unit cell.

Figure 2

Bio-inspired structure and unit cell with the design parameters and nodes A–J labelled.

Figure 3

Compressive force–displacement curves for the 3D printed bone-like cellular structure. The deformations in the linear-elastic, plastic and densification regions are also illustrated.

Figure 4

Influence of the sub-cell angles (a) and tie lengths (b) on the stiffness. The unit cell corresponding to the peak stiffness is also illustrated.

Figure 5

Influence of the sub-cell angles (a) and tie lengths (b) on the Euler buckling stress. The unit cell corresponding to the peak Euler buckling stress is also illustrated.

Figure 6

Influence of the sub-cell angles (a) and tie lengths (b) on the energy absorption. The unit cell corresponding to the peak strain energy density is also illustrated.

Figure 7

Influence of combined design parameters on the stiffness of the biomimetic unit cell: (a) $\alpha ,\beta$; (b) $\alpha ,\gamma$; (c) $\beta ,\gamma$; and (d) $l_{\mathit{ut}},l_{\mathit{lt}}$. The unit cell corresponding to the peak stiffness is also illustrated.

Figure 8

Influence of combined design parameters on the Euler buckling stress of the biomimetic unit cell: (a) $\alpha ,\beta$; (b) $\alpha ,\gamma$; (c) $\beta ,\gamma$; and (d) $l_{\mathit{ut}},l_{\mathit{lt}}$. The unit cell corresponding to the peak buckling stress is also illustrated.

Figure 9

Influence of combined design parameters on the energy absorption of the biomimetic unit cell: (a) $\alpha ,\beta$; (b) $\alpha ,\gamma$; (c) $\beta ,\gamma$; and (d) $l_{\mathit{ut}},l_{\mathit{lt}}$. The unit cell corresponding to the peak strain energy density (SED) is also illustrated.