Nonlinear effect of rigidity and correlated disorder on network fracture

Abstract

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.