Scaling Effects in the Fatigue Strength of Bones from Different Animals

The bones of vertebrates are all made from the same basic material, despite a huge variation in size from one species to another. This introduces a problem: large structures are more prone to fatigue failure (stress fracture) than smaller structures made of the same material. This implies that bones in larger animals cannot withstand as much stress in daily use as bones in smaller animals. In fact, this is not the case, because all bones experience approximately the same stresses and strains in use. This implies a variation in the underlying material: bone material in large animals must have superior fatigue properties to offset the disadvantages of size. This hypothesis is tested here by reference to fatigue data from the literature, taken from a range of animals from cows to mice. Fatigue strength was plotted as a function of stressed volume and modelled mathematically using a Weibull distribution. This shows a general tendency for fatigue strength to reduce as volume increases. But when the volume effect is taken into account, there remains a tendency for bones from smaller animals to have lower fatigue strength. This can be modelled by a simple variation in one of the parameters in the Weibull equation, which defines the intrinsic fatigue strength of the material. When extrapolated to the size of the whole bone for each animal, all bones were found to have the same fatigue strength. This resolves the anomaly and implies a complex system in which the underlying structure of bone varies with animal size in order to cancel out scaling effects.