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• The coupling effect of disorder and rigidity on system's failure behaviors is investigated. • Correlation in disorder has an anomalous effect on the cases of low rigid system. • Crossover in the distribution of avalanches is observed with the influence of disorder and rigidity. Mechanical rigidity and disorder are two important parameters that influence the failure process of solid materials. We investigate the nonlinear mechanics under their coupled effect as well as the influence of disorder's spatial correlation with 2-D network model. The strain–stress relations present strong nonlinearity and rigidity regain phenomenon when there is strong disorder and high rigidity. The correlation of disorder would weaken the effect and has a great influence on the peak stress, initial stiffness, and system toughness. The crossover of power-law exponents of avalanches is observed with consideration of disorder and the transitions in the cluster distribution induced by correlated disorder disappear as the system rigidity decrease. We conclude that although the disorder can be seen as a reduction of average coordinated number for small rupture thresholds system, the correlated disorder still has a great influence on the failure behaviors of heterogeneous materials. [ABSTRACT FROM AUTHOR]

The influences of spatially correlated disorder in microstructure strength are systematic studies in both aspects of failure behaviors and mechanical properties. For the same level of disorder, its spatial distribution has a great influence on failure dynamics and results in different stress–strain responses. The power-law distributions for avalanches and clusters no longer hold when there is a strong correlation between microscope element strength. The brittle and ductile transition is also observed with the change in the disorder's spatial correlation. The results address the importance of the internal correlation structure of disorder and the necessity of considering correlated disorder when studying the failure of heterogeneous materials. • Correlated disorder is introduced and its influence on system's failure behaviors is investigated. • Some universal critical features are broken with the introduction of correlation. • Provide a new viewpoint for study disordered system. [ABSTRACT FROM AUTHOR]