Estimating the Strength of an Elastic Network Using Linear Response

Disordered networks of fragile elastic elements have been proposed as a model for inner porous regions of large bones [Gunaratne et.al., cond-mat/0009221]. In numerical studies, weakening of such networks is seen to be accompanied by reductions in the fraction of load carrying bonds. This observation is used to show that the ratio $\Gamma$ of linear responses of networks to DC and AC driving can be used as a surrogate for their strength. The possibility of using $\Gamma$ as a non-invasive diagnostic of osteoporotic bone is discussed.