heterogeneous stress distributions. Rather than making assumptions about the distribution of strain and stress in the material, this distribution emerges naturally from the condition of mechanical equilibrium between the different networks. Because a network is included explicitly, the model provides information on the failure process both at the macroscopic and the microscopic level. We show how this model predicts a simple criterion for the BDT and we show how the nature of this transition is influenced by disorder and the resulting stress localization. We also compare our network model to a simple 1D multi-spring model, which can be solved analytically.

\[sec:Models\] Models and Methods
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The BDT is the universal mechanical feature of double network materials. In a brittle material, a small microcrack in the sacrifial network directly leads to macroscopic failure. On the contrary, a ductile material remains intact when microcracks develop. To describe this transition, we first present a simple 1D multi-spring model, which is an extension of a previously used two-spring model [@Ahmed2014; @Okumura2004] and which can be solved analytically (Fig. \[fig:ModelOverview\](a)). While heterogeneity can be included in this 1D model, it does not take into account the network structure of the material and therefore cannot give 