initial stiffness, and the failure strain $\epsilon_f$ and failure stress $\sigma_f$ as the strain and stress for which the system becomes disconnected along the y-direction. For every data point 50 simulations are performed, errorbars represent standard deviation.

\[sec:ResultsDiscussion\] Results & discussion
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![Failure strain, $\epsilon_f$, versus the average failure threshold $\langle \lambda_S \rangle$ in systems with $\delta\lambda=0.250$. Results are shown for the RSN model (solid lines) and the MS model (dashed lines) for stiffness ratios $\mu_M/\mu_S =$ 0.10 (purple), 0.50 (green) and 1.00 (yellow)).[]{data-label="fig:FailureStrain"}](figure3.eps)

![Typical failure response of double networks obtained via the RSN model. (a) The four distinct stress-strain responses: brittle (B), quasibrittle (QB), the first ductile regime (D1), and the second ductile regime (D2). (b)-(e) Corresponding failure patterns. Every line represents a broken sacrificial bond, color-coded according to the strain at which it failed (see color bar above).[]{data-label="fig:StressStrain"}](figure4.eps)

\[sec:FailureRegimes\] Failure regimes of double networks
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The aim of this paper is to systematically explore the effect of disorder and stress heterogeneity on the failure of double networks, focusing especially on the role of the network. To do this in a systematic fashion, we will extensively compare the results of the random spring network (RSN) model with the 1D 