Origin of Pseudo-Stability in Stress-Induced Damage Evolution Process.

In this work we demonstrate that during a stress-induced damage evolution process where the stress field depends on the spatial structure of a system, the measured average value is not always representative of the true value of a system parameter. Such behavior originates from the bias of the structure-dependent fluctuation, i.e. at some point of the damage evolution, fluctuations lean towards higher/lower ends and this in turn affects the average value of a system parameter. We first observe this effect in the local-load-sharing fiber bundle model. This simple model of damage evolution exhibits a pseudo-stability around the percolation threshold, when we measure the average force on the system as a function of damage. We explain this pseudo-stability as a result of the statistical bias of the fluctuations which prefer to go towards higher values than the lower values. Our study on 2D, 3D and 4D systems support the conjecture that the pseudo-stability appears around the percolation threshold of the system. We strongly believe that this observation is not limited to any particular model/scenario - rather it is a general nature of damage evolution process: If fluctuations are biased, average values are not reliable.