## 2 Model Development
### Stress Downscaling to Hydrates via ITZs  
We start with concentrating the macroscopic loading, which is imposed in terms of a homogeneous macroscopic stress state \(\mathbf{\Sigma}\) on the RVE of recycled concrete, down to the stress state prevailing in the six ITZs. Therefore, the macrostresses \(\mathbf{\Sigma}\) are first concentrated to phase stresses of the new natural aggregates (phase stresses denoted as \(\sigma_{na}\)), of old plain aggregates (\(\sigma_{opa}\)), and of old mortar aggregates (\(\sigma_{oma}\)). Within the framework of our continuum micromechanics-based approach, the stress fields inside these aggregates are represented by homogeneous average microstresses, reading as  
\[\sigma_{j}=\mathrm{B}_{j}^{con}:\mathbf{\Sigma}\qquad\forall j\in\{na,\,opa,\,oma \}\,, \tag{3}\]  
whereby \(\mathrm{B}_{j}^{con}\) stands for the fourth-order, concrete scale-related stress concentration tensor which is a function of the elastic phase properties and of the phase volume fractions (see Appendix A for an analytical set of formulas). The stress field of the old cement paste cover around the old covered aggregates, however, cannot be suitably represented by homogeneous microstresses. Rather, microstresses are position-dependent and read as  
\[\sigma_{ocpc}(\underline{x})=\mathrm{B}_{ocpc}^{con}(\underline{x}):\mathbf{ \Sigma}\,, \tag{4}\]  
whereby both the stress state \(\sigma_{ocpc}\) and the stress concentration tensor \(\mathrm{B}_{ocpc}^{con}\) are functions of the position vector \(\underline{x}\) (see Appendix B for more details). Next, the sought ITZ stress states are constructed, based on the phase stresses given in Equations (3) and (4). To obtain the ITZ stresses prevailing in the immediate vicinity around the new virgin aggregates (denoted as \(\sigma_{T_{na}^{nrp}}\)), around the old plain aggregates (\(\sigma_{T_{apa}^{nrp}}\)), and around the old mortar aggregates (\(\sigma_{T_{uma}^{nrp}}\)), respectively, we consider a perfect bond in all interfaces, implying continuity conditions between displacements and tractions across the interfaces. Combining the continuity conditions with the isotropic elasticity law for the aggregate phase and the new cement paste, respectively, provides access to the sought ITZ stresses [18]. This procedure can be formalized by yet another stress concentration relation, reading as  
\[\sigma_{T_{j}^{nrp}}=\mathrm{B}_{j}^{ncp}:\sigma_{j}\qquad\forall j\in\{na,\,opa,\,oma\}\,, \tag{5}\]  
whereby \(\mathrm{B}_{j}^{ncp}\) denotes the ITZ-specific stress concentration tensor. Next, we focus on the ITZ between the old embedded aggregates and the old cement paste matrix, which is located inside the RVE of mortar. First, we consider that the average stresses of the old mortar aggregates, \(\sigma_{oma}\) according to Equation (3), take the role of the homogeneous macroscopic stresses and act at the boundary the RVE of old mortar according to Figure 1b. This allows us to downscale the stress states of the old mortar aggregates to average stresses in the old embedded aggregates \(\sigma_{oa}\), by analogy to stress concentration rule (3), according to  
\[\sigma_{oa}=\mathrm{B}_{oa}^{oma}:\sigma_{oma}\,. \tag{6}\]  
Figure 4: Schematic representation of ITZ-driven failure (cracking) in recycled concrete under uniaxial compressive loading in vertical direction. Considering perfect bond across \(\mathcal{I}_{oa}^{ocp}\) yields, by analogy to interface stress concentration rule (3), the sought old embedded aggregate-related ITZ stresses \(\mathbf{\sigma}_{\mathcal{I}_{oa}^{ocp}}\) as  
\[\mathbf{\sigma}_{\mathcal{I}_{oa}^{ocp}}=\mathrm{B}_{oa}^{ocp}:\mathbf{\sigma}_{oa}\,. \tag{7}\]  
The stress state of the ITZ between the old covered aggregates and the old cement paste, \(\mathbf{\sigma}_{\mathcal{I}_{oa}^{ocp}}\), simply follows from evaluating the stress field of the old cement paste cover according to Equation (4) for the location of the covered aggregate-old paste interface.