By Dusan Krajcinovic, Jan van Mier

The valuable goal of this e-book is to narrate the random distributions of defects and fabric power at the microscopic scale with the deformation and residual power of fabrics at the macroscopic scale. to arrive this aim the authors thought of experimental, analytical and computational types on atomic, microscopic and macroscopic scales.

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**Example text**

Thus, there is a r dependence in both ft and at also. However, while the distribution of currents become broader as the breakdown process evolves, the threshold distribution becomes narrower. The rupture criterion, Eq. (81), becomes in these variables = = min~ -t min(at(r)- a(r)) . (97) We have no way of using this formulation to predict the detailed shape of f(a), since it is merely a rewriting of our starting point in different variables. However, it makes it possible 51 Statistics Toolbox for Damage and Fracture to deduce some powerful statements on what kind of threshold distributions may allow for the evolvement of multifractality in the current distribution.

Roux Multifractality Let us assume that local currents i scale as Iii

As expected from the previous discussion, the absence of length scale imposes that this cluster is also fractal. 6432 as estimated by Grassberger (1999)). From this figure, we can grasp some interesting features of the structure of this backbone. e. clusters of loops, connected by "singly connected bonds", such that the structure would no longer percolate if they are removed. Those singly connected bonds have a fractal dimension, Dscb which has been shown to be related to the correlation length A.