Fixed scale transformation for fracture growth processes governed by vectorial fields

We use the Fixed Scale Transformation (FST) approach to study the problem of fractal growth in fracture patterns generated by using the Born Model. The application of the method to this model is very complex because of the vectorial nature of the system considered. In particular, the implementation of this scheme requires a careful choice of the fracture path and the identification of the appropriate way to take into account screening effects. The good agreements of our results with computer simulations shows the validity and flexibility of the FST method which represents a general theoretical approach for the study of fractal patterns evolution.