Predictability and strength of a heterogeneous system: The role of system size and disorder

In this paper, I have studied the effect of disorder (δ) and system size (L) in a fiber bundle model with a certain range R 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 decrements changes drastically as disorder strength is tuned. At moderate disorder, σ_{c} scales with the system size as σ_{c}∼1/logL. In low disorder, where the brittle response is highly expected, the strength decreases in a scale-free manner (σ_{c}∼1/L). With increasing L and R, the model approaches the thermodynamic limit and the mean-field limit, respectively. A detailed study shows different limits of the model and the corresponding modes of failure on the plane of the above-mentioned parameters (δ,L, and R).