Cortical bone can exhibit 3-4% nonlinear tensile strain before it ruptures. In the literature, this strain is commonly described as being 'plastic.' However, the two experiments presented here show that bone is not plastic in the classical sense. Instead, bone shows highly time dependent behavior that is dominated by creep effects.
The first experiment is a multiple cycle tensile creep test. It differed from previously reported creep tests in that the hold periods were shorter and the stress levels were higher, approaching the literature's value for 'yield.' The results show that several percent creep strain can be produced when loads are of sufficient magnitude. They also show that the creep process is accompanied by a loss of stiffness and that most of the creep strain is recovered after unloading. These two results, which cannot be explained within the context of classical plasticity, suggest that damage is responsible for the creep behavior.
The second experiment consisted of applying short duration triangular tensile load pulses to bone specimens. Substantial nonlinear strain was produced during both the loading and unloading portions of the pulse. This is consistent with transient creep behavior and verifies that the nonlinear strains produced by loads of physiological duration are also associated with creep. Transverse strain, which was monitored during the loading, showed no significant nonlinearity. This type of behavior, which is inconsistent with slip induced nonlinearity, can be explained by a damage model consisting of an array of aligned cracks.
The experimental results are developed into an internal state variable constitutive model, consisting of a set of differential equations. The equations are integrated and shown to accurately model the deformation of bone. The constitutive model is then applied to the bending of a simple cantilever beam and to the bending of the human femur. The cantilever beam simulations are in good agreement with experimental results. The human femur simulations clearly show the effect of load rate on the stress distribution across the femur.