Predictability and Strength of a Heterogeneous System : The Role of System Size and Disorder

Abstract: In this work I have studied the effect of disorder and system size in fiber bundle model with a certain range of stress redistribution. The strength of the bundle as well as the failure abruptness is observed with varying disorder, stress release range and system sizes. With a local stress concentration, the strength of the bundle is observed to decrease with system size. The behavior of such decrement changes drastically as disorder strength is tuned. At moderate disorder, the critical stress scales with system size in an inverse logarithmic manner. In low disorder, where the brittle response is highly expected, the strength decreases in a scale free manner. With increasing system size and stress release range the model approaches thermodynamic limit and the mean field limit respectively. A detail study expresses different limit in the model and the corresponding modes of failure on the plane of above mentioned parameters.