100 



E. D. Sedlin, L. Sonnerup 



HooKE and Newton body linked in parallel. (Kelvin body). The rationale for 

 eliminating other model types is too lengthy for presentation here. It is not claimed 

 that the model is a complete rheological formulation for the behavior of bone, but it is 



(a) 



^vww- 



(c) 



Fig. 2. A rheological model to explain some mechanical features of bone. Notation is as in Fig. 1, and 

 text, a) The model consisting of a Hooke body linked in series with a Kelvin body. The independent 

 has its E_, as does the spring in the Kelvin element, Ej. The E for the material is a result of the comb 

 of the two separate E's combined with the damping effect of the dash-pot. If a load be applied very 

 or very rapidly, the damping effect of the dash-pot is minimized, and the stress-strain curve is more 

 linear. For intermediate cases, the slope of the curve is determined by relations of the various consta 

 the components. The constitutional equation for the model can be written: 



a+ ao = bf -fcE 

 where „= rate of stress, i = rate of strain, a = j; (E, + E.j), b = Eo and c = ?? E,Eo. The behavior 



model under the condi 



of loading and unloading at a constant rate, 

 in diagrams (b) and (c) 



and under a const 



tram 



in the 

 spring 



slowly 

 nearly 

 nts for 



3f the 

 shown 



the simplest reasonable model that we can formulate on the basis of the information 

 to date. Some of the properties of wet bone that lead to this model, and that can be 

 predicted by the model are: 



If a specimen be loaded to a defined point, and then the strain be maintained 

 constant, stress within the specimen decreases asymptotically to a new level. This 

 phenomenon of stress relaxation under a constant strain has been true for all sizes, 

 rates, and axes of loading. 



If a specimen be progressively deformed at a constant rate, the stress strain dia- 

 gram is a curve with asymptote determined by the rate of loading. If the rate of 

 deformation be made extremely slow or extremely fast, then a more nearly linear 

 relation of stress to strain is obtained. The obvious conclusion is that a straight line 

 on a stress-strain curve does not necessarily mean a perfectly elastic substance. 



If a specimen is loaded up to some predetermined load, and then unloaded at the 

 same rate, then when the load returns to zero, some residual deformation is present. 

 The amount of residual deformation can be altered by changing the rate and size of 

 the load. 



The residual deformation of the unload cycle described above will be recovered, 

 if the load is less than 40'Vo of the ultimate breaking load. If more, some permanent 

 deformation remains. In other words, while being loaded, bone is capable of conserv- 

 ing a certain amount of energy, a limit which can be exceeded. 



