Our Newly Published articles provide view of research, ideas, and discussion in the field of Porous Media.

Origin of Pseudo-Stability in Stress-Induced Damage Evolution Processes

Jonas T. Kjellstadli, Eivind Bering, Srutarshi Pradhan, Alex Hansen

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.

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Mesoscopic Description of the Equal Load Sharing Fiber Bundle Model

Martin Hendrick, Srutarshi Pradhan, Alex Hansen

One aim of the equal load sharing fiber bundle model is to describe the critical behavior of failure events. One way of accomplishing this, is through a discrete recursive dynamics. We introduce a continuous mesoscopic equation catching the critical behavior found through recursive dynamics. It allows us to formulate the model using the unifying framework of absorbing phase transitions traditionally used in the study of non-equilibrium phase transitions. Consequently, this work is a first step towards a field theory for fiber bundle models.

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A Renormalization Group Procedure for Fiber Bundle Models

Srutarshi Pradhan, Alex Hansen, Purusattam Ray

We introduce two versions of a renormalization group scheme for the equal load sharing fiber bundle model. The renormalization group is based on formulating the fiber bundle model in the language of damage mechanics. A central concept is the work performed on the fiber bundle to produce a given damage. The renormalization group conserves this work. In the first version of the renormalization group, we take advantage of ordering the strength of the individual fibers. This procedure, which is the simpler one, gives EXACT results -but cannot be generalized to other fiber bundle models such as the local load sharing one. The second renormalization group scheme based on the physical location of the individual fibers may be generalized to other fiber bundle models.

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