Damage Phenomena

  • Sergey G. AbaimovEmail author
Part of the Springer Series in Synergetics book series (SSSYN)


The problem of percolation, studied in the previous chapter, might be called complex. The system was not thermal; and the concept of thermodynamic temperature was absent. The structure of the model allowed the possibility of nonthermal fluctuations which, in turn, lead to the presence of a continuous phase transition and a critical point in the system. We saw many similarities with the thermal systems of statistical physics; however, the completely developed analogy was absent. So, we introduced a set of parameters, such as the order parameter, the field parameter, and the averaged cluster size \(\tilde{S}\); but so far we have not found the counterparts of these quantities in statistical physics. In more detail, we return to this question in Chap. 6, where these analogies will be found. However, at first we need to consider one more complex, nonthermal system whose mapping on the phenomena of statistical physics will be more transparent.

The model considered represents damage phenomena. The thermodynamic temperature is absent in the system; however, the stochastic distribution, as an “input” of the model, generates fluctuations, perfectly described by the laws of statistical physics.

In fact, the analogy with statistical physics will be so complete and the model will be so illustrative that the discussion of the concepts of statistical physics itself in Chap. 2 could be illustrated with the aid of this system instead of the thermodynamic systems.


Partition Function Thermal Fluctuation Fiber Strength Rigid Plate Fiber Failure 
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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Advanced Structures, Processes and Engineered Materials CenterSkolkovo Institute of Science and TechnologySkolkovoRussia

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