Evolution induced catastrophe in a nonlinear dynamical model of material failure

In order to study the failure of disordered materials, the ensemble evoluti on of a nonlinear chain model was examined by using a stochastic slice samp ling method. The following results were obtained. (1) Sample-specific behav ior, i.e. evolutions are different from sample to sample in some cases unde r the same macroscopic conditions, is observed for various load-sharing rul es except in the globally mean field theory. The evolution according to the cluster load-sharing rule, which reflects the interaction between broken c lusters, cannot be predicted by a simple criterion from the initial damage pattern and even then is most complicated. (2) A binary failure probability , its transitional region, where globally stable (GS) modes and evolution-i nduced catastrophic (EIC) modes coexist, and the corresponding scaling laws are fundamental to the failure. There is a sensitive zone in the vicinity of the boundary between the GS and EIC regions in phase space, where a slig ht stochastic increment in damage can trigger a radical transition from GS to EIC. (3) The distribution of strength is obtained from the binary failur e probability. This, like sample-specificity, originates from a trans-scale sensitivity linking meso-scopic and macroscopic phenomena. (4) Strong fluc tuations in stress distribution different from that of GS modes may be assu med as a precursor of evolution-induced catastrophe (EIC).