Table 1.
Equations proposed by Keyak, Carter, Keller, and Keller for vertebra
| Young’s modulus (E: MPa) | Yield stress (σ: MPa) | |
|---|---|---|
| Keyak | E = 0.001 (ρ = 0) | σ = 1.0 × 1020 (ρ ≦ 0.2) |
|
E = 33,900 ρ2.20 (0 < ρ ≦ 0.27) E = 5307 ρ + 469 (0.27 < ρ < 0.6) E = 10,200 ρ2.01 (0.6 ≦ ρ) |
σ = 137 ρ1.88 (0.2 < ρ < 0.317), σ = 114ρ1.72 (0.317 ≦ ρ) | |
| Carter | E = 0.001 (ρ = 0) | σ = 1.0 × 1020 (ρ ≦ 0.2) |
| E = 3790(0.01)0.05 ρ (ρ < 0) | σ = 68(0.01)0.06 ρ2 (0.2 < ρ) | |
| Keller | E = 0.001 (ρ = 0) | σ = 1.0 × 1020 (ρ ≦ 0.2) |
| E = 10,500 ρ2.51 (ρ < 0) | σ = 117 ρ1.93 (0.2 < ρ) | |
| Keller for vertebra | E = 0.001 (ρ = 0) | σ = 1.0 × 1020 (ρ ≦ 0.2) |
| E = 1890 ρ1.92 (ρ < 0) | σ = 284 ρ2.27 (0.2 < ρ) |
E Young’s modulus (MPa), σ yield stress (MPa), ρ ash density (g/cm3)