Foundations of measurement fractal theory for the fracture mechanics

摘要: A wide variety of natural objects can be described mathematically using fractal geometry as, for example, contours clouds, coastlines , turbulence in fluids, fracture surfaces, or rugged surfaces contact, rocks, and so on. None them is a real fractal, characteristics disappear if an object viewed at scale sufficiently small. However, range scales the look very much like fractals, which case they considered fractal. There are no true fractals nature there straight lines circles too. Clearly, models better approximations that circles. If classical Euclidean as first approximation to irregular lines, planes volumes, apparently flat on more rigorous level approximation. Fractal provides new scientific way thinking about phenomena. According Mandelbrot [1], set whose fractional dimension (Hausdorff-Besicovitch dimension) strictly greater than its topological (Euclidean dimension).