applied fracture mechanics

Foundations of Measurement Fractal Theory for the Fracture Mechanics 31DDLln . (15) lnL0where L0is the projected length obtained from the rugged fractal length LFigure 8. Compass method applied on a line noise or a rough self-affine fractal.Several methods for determining the fractal dimension based on the compass method,among them stand out the following methods: the Coastlines Richardson Method, the SlitIsland Method, etc.3.2. Methods of measurement for determining the fractal dimension of a structureThere are basically two ways to recover an object with boxes for fractal dimension measuring.In the first method, boxes of different sizes extending from a minimum size minuntil to amaximum size max, from a fixed origin recovering the whole object at once time. In thesecond case, one side of the recovering box is kept fixed, and with a minimum size ruler, min,then recovers the figure by moving the boundary of that recovering from the minimum minto maximum size maxof the object. The first method is known as a method Box-Countingexemplified in Figure 9 and the second method is known as Sand-box, shown in Figure 10. Theadvantage of the second over the first is that it detects the changes in dimension D with thelength of the object. If the object under consideration has a local dimension for boxes with size 0 , unlike the global dimension, , it is said that the object is self-affine fractal.Otherwise the object is said self-similar. These two main methods of counts of structureswhich may lead to determination of the fractal dimension of an object [38].3.2.1. Box-counting method by static scaling of the elements in a fractal structureThe Box-Counting method, comes from the theory of critical phenomena in statisticalmechanics. In statistical mechanics there is an analogous mathematical method to describing