Mechanical properties of trabecular bone. Dependency on strain rate

Abstract

The effect of strain rate (ε) and apparent density (ϱ) on stiffness ( E), strength ( σ u), and ultimate strain ( ε u) was studied in 60 human trabecular bone specimens from the proximal tibia. Testing was performed by uniaxial compression to 5% specimen strain. Six different strain rates were used: 0.0001, 0.001, 0.01, 0.1, 1, and 10 s −1. Apparent density ranged between 0.23 and 0.59 g cm −3. Linear and non-linear regression analyses using strength, stiffness and ultimate strain as dependent variables ( Y) and strain rate and apparent density as independent variables were performed using the following models: Y = aϱ b ε ̇ c , Y = ϱ b(a+c ε ̇ ; Y=(a+bϱ) ε ̇ c , Y=aϱ 2 ε ̇ c , E=aϱ 3 ε ̇ c . The variations of strength and stiffness were explained equally well by the linear and the power function relationship to strain rate. The exponent was 0.07 in the power function relationship between strength and strain rate and 0.05 between stiffness and strain rate. The variation of ultimate strain was explained best using a power function relationship to strain rate (exponent =0.03). The variation of strength and stiffness was explained equally well by the linear, power function and quadratic relationship to apparent density. The cubic relationship between stiffness and apparent density showed a less good fit. Ultimate strain varied independently of apparent density.