Local Minima and Gradients of Stiffness and Conductivity as Indicators of Strength Reduction of Brittle-Elastic Materials

It is often suggested in literature to use change in the effective elastic properties (stiffness loss) as an indicator of reduction of strength due to defects such as cracks and pores. We argue that the key parameter is not the reduction of the average (over the specimen) stiffness but its local minimal values caused by formation of defect clusters. These defect clusters can be identified by the emergence of spatial gradients of elastic stiffness on a smaller scale. A convenient tool of detecting these gradients is provided by the elasticity-conductivity connection: the electric conductance gradient is usually easier to measure than the stiffness gradient. This concept is supported by computational and experimental results reported in two accompanying papers published in the present issue (by Sevostianov et al and Caiulo and Kachanov).