A viscoelastic, viscoplastic model of cortical bone valid at low and high strain rates

The stress-strain behavior of cortical bone is well known to be strain-rate dependent, exhibiting both viscoelastic and viscoplastic behavior. Viscoelasticity has been demonstrated in literature data with initial modulus increasing by more than a factor of 2 as applied strain rate is increased from 0.001 to 1500 s(-1). A strong dependence of yield on strain rate has also been reported in the literature, with the yield stress at 250 s(-1) having been observed to be more than twice that at 0.001 s(-1), demonstrating the material viscoplasticity. Constitutive models which capture this rate-dependent behavior from very low to very high strain rates are required in order to model and simulate the full range of loading conditions which may be experienced in vivo; particularly those involving impact, ballistic and blast events. This paper proposes a new viscoelastic, viscoplastic constitutive model which has been developed to meet these requirements. The model is fitted to three sets of stress-strain measurements from the literature and shown to be valid at strain rates ranging over seven orders of magnitude.