Strength Reduction in Electrical and Elastic Networks

TL;DR

This paper derives an expression for the mean breakdown strength of electrical and elastic networks, analyzing how fractures and element removal affect network strength, with potential applications in medical diagnostics like osteoporosis.

Contribution

It introduces a method to evaluate current redistribution after element removal and demonstrates the similarity in breakdown reduction for electrical and elastic networks.

Findings

Breakdown strength reduction follows a similar pattern in electrical and elastic networks.

Numerical analysis confirms the effect of random element removal on network strength.

Application to bone density suggests diagnostic potential for osteoporosis.

Abstract

Particular aspects of problems ranging from dielectric breakdown to metal insu- lator transition can be studied using electrical o elastic networks. We present an expression for the mean breakdown strength of such networks.First, we intro- duce a method to evaluate the redistribution of current due to the removal of a finite number of elements from a hyper-cubic network of conducatances.It is used to determine the reduction of breakdown strength due to a fracture of size $\kappa$.Numerical analysis is used to show that the analogous reduction due to random removal of elements from electrical and elastic networks follow a similar form.One possible application, namely the use of bone density as a diagnostic tools for osteorosporosis,is discussed.