Fracture-Failure Phenomena in Disordered Media: Critical Behavior and Scaling Properties

The fracture-failure phenomena in heterogeneous material has attracted much scientific attention sence several decades. Despite many partial successes, a complete analytic formulation of this phenomena is still lacking. Among the model studies, the Fiber Bundle Models (FBM) and the Random Fuse Models (RFM) are two most successful and well studied models. We will study the critical behavior and scaling properties of fracture-failure phenomena in disordered systems using both, FBM and RFM. First, we want to study how a lower cut off in fiber threshold distributions affect the failure properties of equal load sharing (ELS) and local load sharing (LLS) FBM. In case of ELS model, we will use the recursive formulation of the failure dynamics, developed by us. O ur next goal is to study the fatigue-failure in heterogeneous materials using ELS and LLS models. Here, we will use the noise-activated failure probability assumed in our earlier work to incorporate `fatigue' in FBM. Recently, we have developed a mixed-mo de load sharing (MMLS) scheme to investigate failure behavior of materials in between ELS and LLS. We are looking for an analytic formulation of MMLS model to explain the numerically observed cross over from mean-field to short-range behavior. Next, using RFM we want to establish that there exist two regimes in fracture morphology: Self-similar regime and self-affine regime depending upon the nature of disordered in the system. Therefore, we expect the crossover region of these two regimes should exhibit typical scaling behavior. We intend to study the fluid-flow in porous media through numerical as well as analytic methods.