The avalanche process of the multilinear fiber bundles model

In order to describe the smooth nonlinear constitutive behavior in the process of fracture of ductile micromechanics structures, the multilinear fiber bundle model was constructed, based on the bilinear fiber bundle model. In the multilinear fiber bundle model, the Young modulus of a fiber is assumed to decay K max times before the final failure occurs. For the large K max region, this model can describe the smooth nonlinear constitutive behavior well. By means of analytical approximation and numerical simulation, we show that the two critical parameters, i.e. the decay ratio of the Young modulus and the maximum number of decays, have substantial effects on the failure process of the bundle. From a macroscopic view, the model can provide various shapes of constitutive curves, which represent diverse kinds of tensile fracture processes. However, at the microscopic scale, the statistical properties of the model are in accord with the classical fiber bundle model.