manner with significant softening and plastic deformation (leading to ‘necking’) prior to failure (yellow curve) [@Matsuda2016; @Millereau2018]. This macroscopic softening is believed to be due to the progressive breaking of bonds in the stiff network (which is also called the sacrificial network), while the soft matrix formed by the second network stays intact. To obtain tough materials, it is thus crucial that the rupture of the first network occurs without leading to macroscopic cracks in the material.

One way to go forward is to include molecular details, for example using molecular dynamics simulations [@Jang2007; @Wang2017; @Higuchi2018]. However, given the computational costs it is difficult to do this for large system sizes and to explore a large range of parameters. Alternatively, statistical models, such as the fiber bundle model, can give insight into the role of disorder on network failure [@Kovacs2013; @Roy2017]. In such models, however, a priori assumptions must be made about the (re)distribution of stress among the different elements, so that they cannot explain the spatial evolution of damage in the materials and its relation to the structure of the networks.

Here, we develop a random double spring network model, which explicitly takes into account disorder and the resulting 