Estudo computacional de fraturas em meios desordenados

Abstract

In this work, we apply the fuse network model through computer simulations to represent quenched disordered systems, i.e., systems that present random variables that do not depend on time. One of the applications of this model is to simulate fracture processes in heterogeneous materials in order to understand how possible failures spread in man-made structures or in those found in nature. Such knowledge may help to prevent that such failures could compromise the structure. From a technological point of view, such study cover many areas of applied research, such as, materials sciences, materials strength, engineering, physics, etc. The resistor network model presents an analogy between the electrical systems related to Ohm law, I = GV, with the elastics deformations of a material that is described by Hooke’s law, σ = Eε, where the voltage σ is replaced by the electric current I, the modulus of elasticity E by the electrical conductance G and the elastic deformation ε by the electric potential V. Thus, we apply this model to study fracture morphology in disordered media. This computational model was realized in a square lattice with a global current Ig applied to the system and we assign random values of electrical conductance to each resistor, in order to calculate the potentials at each node using Kirchhoff’s law. With this, we defined a criterion for the damage of the resistors, removing them from the lattice, and repeating the same process until we found the fractured aggregate. In addition, we determine the fractal dimension φ, which is related to microscopic flaws stread out on the medium, how and we also analyze the global conductance Gg of the system.