## 2 Model Development
### Modeling of Hydrate Failure in Critical ITZs  
We follow [PERSON] and [PERSON] [29] and consider that if the most unfavorably loaded hydrate needle fails, recycled concrete will fail as well (quasi-brittle strength upscaling). Hydrate failure is modeled by means of a Drucker-Prager criterion, reading as [21]  
\[\mathfrak{f}(\overline{\sigma}_{hyd}^{vol},\overline{\sigma}_{hyd}^{lev})= \frac{\overline{\sigma}_{hyd}^{lev}}{\sqrt{2}}-k_{hyd}+\alpha_{hyd}\frac{ \overline{\sigma}_{hyd}^{vol}}{\sqrt{3}}\leq 0, \tag{1}\]  
whereby \(k_{hyd}\) and \(\alpha_{hyd}\) denote the Drucker-Prager constants of the hydrates. Based on nanoindentation tests combined with limit state analysis [37], these parameters were identified for ordinary Portland cement paste as [21]  
\[k_{hyd}=60.68\,\mathrm{MPa}\,,\qquad\alpha_{hyd}=0.2580\,. \tag{2}\]  
In Equation (1), \(\overline{\overline{\sigma}_{hyd}^{vol}}\) and \(\overline{\overline{\sigma}_{hyd}^{lev}}\) denote volumetric and deviatoric stress measures which trigger hydrate failure. As for their determination, we first report on the situation in ordinary concrete. Driven by the stiffness contrast between aggregates and cement paste, the local microstresses states in the ITZs around the aggregates are larger than in the bulk of the cement paste [18; 19]. The cement paste RVEs hosting the most unfavorably loaded hydrates are therefore located within the ITZs of conventional concrete, i.e., in the immediate vicinity of the aggregate surfaces [21]. As for recycled concrete, the situation is more complex. In RVEs of recycled both concrete and old mortar according to Figure 1a,b, respectively, contain ITZs. Six potentially critical ITZs--with six associated failure modes--may be identified (see Figure 4):  
* the ITZ between the new natural aggregates and the new cement paste matrix, herein labeled as \(\mathcal{I}_{na}^{ncp}\), associated with \(\mathcal{I}_{na}^{ncp}\) failure as sketched in Figure 4a;
* the ITZ between the old plain aggregates and the new cement paste matrix, associated with \(\mathcal{I}_{opa}^{ncp}\) failure as sketched in Figure 4b;
* the ITZ between the old mortar aggregates and the new cement paste matrix, associated with \(\mathcal{I}_{oma}^{ncp}\) failure as sketched in Figure 4c;
* the ITZ between the old embedded aggregates and the old cement paste matrix inside the old mortar aggregates, associated with \(\mathcal{I}_{oa}^{ncp}\) failure as sketched in Figure 4d;
* the ITZ between the old covered aggregates and the old cement paste cover, associated with \(\mathcal{I}_{oca}^{ncp}\) failure as sketched in Figure 4e;
* the ITZ between the old cement paste cover and the new cement paste matrix, associated with \(\mathcal{I}_{ocpc}^{ncp}\) failure as sketched in Figure 4f.  
A priori determination of the critical failure mode is impossible. Rather, we have to \"downscale\" the macroscopic loading to microstress states acting in the hydrates of the individual ITZs and feed the Drucker-Prager failure criterion (1). The downscaling procedure involves two steps, (i) stress concentration from the macroscopic loading to microstresses of the aforementioned six ITZs, respectively, and (ii) further stress concentration from ITZ stresses to hydrate stresses, as discussed next.