In order to study the failure of disordered materials, theensemble evolution of a nonlinear chain model was examined by using astochastic slice sampling method. The following results were obtained.(1) Sample-specific behavior, i.e. evolutions are different from sampleto sample in some cases under the same macroscopic conditions, isobserved for various load-sharing rules except in the globally meanfield theory. The evolution according to the cluster load-sharing rule,which reflects the interaction between broken clusters, cannot bepredicted by a simple criterion from the initial damage pattern and eventhen is most complicated. (2) A binary failure probability, itstransitional region, where globally stable (GS) modes andevolution-induced catastrophic (EIC) modes coexist, and thecorresponding scaling laws are fundamental to the failure. There is asensitive zone in the vicinity of the boundary between the GS and EICregions in phase space, where a slight stochastic increment in damagecan trigger a radical transition from GS to EIC. (3) The distribution ofstrength is obtained from the binary failure probability. This, likesample-specificity, originates from a trans-scale sensitivity linkingmeso-scopic and macroscopic phenomena. (4) Strong fluctuations in stressdistribution different from that of GS modes may be assumed as aprecursor of evolution-induced catastrophe (EIC).
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Xia, M., Ke, F., Wei, Y. et al. Evolution Induced Catastrophe in a Nonlinear Dynamical Model of Material Failure. Nonlinear Dynamics 22, 195–214 (2000). https://doi.org/10.1023/A:1008324329908
- material failure
- evolution-induced catastrophe
- binary failure probability