Distribution and propagation of stress and strain in cube honeycombs as trabecular bone substitutes: Finite element model analysis

Abstract

For designing trabecular (Tb) bone substitutes suffering from osteoporosis, finite element model (FEM) simulations were conducted on honeycombs (HCs) of 8 × 8 × 1 (2D) and 8 × 8 × 8 (3D) assemblies of cube cellular units consisting of 0.9 mm long Nylon® 66 (PA, Young's modulus E: 2.83 GPa) and polyethylene (PE, E: 1.1 GPa) right square prisms. Osteoporotic damage to the Tb bone was simulated by removing the inner vertical struts (pillars; the number of removed pillars: Δn ≤ 300) and by thinning the strut (thickness, d: 0.4-0.1 mm), while the six facade lattices were kept flawless. Uniform and uniaxial compressive loads on the HCs induced elastic deformation of the struts. The pillars held almost all the load, while the horizontal struts (beams) shared little. E for PA 3D HCs of all d smoothly decreased with Δn. PA 3D HCs of 0.2 mm struts deserved to be the substitutes for Tb bone, while PE 3D HCs of 0.05 mm struts were only for the Tb bone of the poorest bone quality. For the PA 3D HCs, the maximum von Mises stress (σ_M) first rapidly increased with Δn and showed a break at Δñ50, then gradually approached the yield stress of PA (50 MPa). Moreover, small portions of the stress were transferred from the façade pillars to the adjacent inner beams, especially those near the lost-pillar sites, denoted as X defects. The floor beams of thinner struts associated with the X-defects were lifted, and similar lifting effects in smaller amounts were propagated to the other floors. The 3DHCs of the thicker struts showed no such flexural deformations. The concept of force percolation through the remaining struts was proposed to interpret those mechanical behaviors of the HCs.

Keywords: Cube honeycomb; FEM simulation; Percolation; Strut removal; Trabecular bone.