FRACTAL AND TOPOLOGICAL PROPERTIES OF DIRECTED FRACTURES

We use the Born model for the energy of elastic networks to simulate ' 'directed'' fracture growth. We define directed fractures as crack pat terns showing a preferential evolution direction imposed by the type o f stress and boundary conditions applied. This type of fracture allows a more realistic description of some kinds of experimental cracks and presents several advantages in order to distinguish between the vario us growth regimes. By choosing this growth geometry it is also possibl e to use without ambiguity the box-counting method to obtain the fract al dimension for different subsets of the patterns and for a wide rang e of the internal parameters of the model. We find a continuous depend ence of the fractal dimension of the whole patterns and of their backb ones on the ratio between the central- and noncentral-force contributi ons. For the chemical distance we find a one-dimensional behavior inde pendent of the relevant parameters, which seems to be a common feature for fractal growth processes.