## Appendix A Mathematical Expressions for Stiffness Homogenization and Stress Concentration
Herein, we construct an analytical expression for the recycled concrete stiffness tensor \(\mathbb{C}_{con}\) based on strain concentration tensors \(\mathbb{A}_{\infty,i}\), which refer to Eshelby-type matrix inclusion problems [51], resulting in  
\[\mathbb{C}_{con}=\sum_{i}f_{i}^{con}\mathbb{C}_{i}:\mathbb{A}_{\infty,i}:\left( \sum_{i}f_{i}^{con}\mathbb{A}_{\infty,i}\right)^{-1}\forall i\in\{na,opa,oma, ncp,oca,ocp\}\,. \tag{12}\]  
Note that \(\mathbb{C}_{na}=\mathbb{C}_{opa}=\mathbb{C}_{oca}=\mathbb{C}_{a}\), given that the stiffness of all aggregates is considered to be identical. The concentration tensors related to natural aggregates, to old plain aggregates, to old mortar aggregates, and to the new cement paste matrix follow from  
\[\mathbb{A}_{\infty,i}=\left[\mathbb{I}+\mathbb{P}_{sph}^{ncp}:\left(\mathbb{C} _{i}-\mathbb{C}_{ncp}\right)\right]^{-1}\forall i\in\{na,opa,oma,ncp\}\,, \tag{13}\]  
and the two remaining strain concentration tensors, which are related to an Eshelby problem with a covered inclusion, are discussed in Appendix B. As for downscaling of macrostresses (12) to ITZ stress states, access to phase stress concentration tensors \(\mathbb{B}_{na}^{con}\), \(\mathbb{B}_{opa}^{con}\), \(\mathbb{B}_{oma}^{con}\), \(\mathbb{B}_{ocpc}^{con}\), and \(\mathbb{B}_{oeu}^{oma}\), according to Equations (3), (4), and (6), respectively, as well as to ITZ stress concentration tensors \(\mathbb{B}_{na}^{ncp}\), \(\mathbb{B}_{opa}^{ncp}\), \(\mathbb{B}_{oma}^{ncp}\), \(\mathbb{B}_{oeu}^{ocp}\), and \(\mathbb{B}_{ocpc}^{ncp}\), according to Equations (5), (7) and (9), respectively, is required. The stress concentration tensors which relate macrostresses \(\mathbf{\Sigma}\) to average phase stresses of the spherical phases natural aggregates, old plain aggregates, and old mortar aggregates, respectively, read as [18]  
\[\mathbb{B}_{i}^{con}=\mathbb{C}_{i}:\mathbb{A}_{\infty,i}:\left(\sum_{j}f_{j}^ {con}\mathbb{A}_{\infty,i}\right)^{-1}:\left(\mathbb{C}_{con}\right)^{-1}\qquad \forall i\in\{na,opa,oma\}\quad\text{and}\quad\forall j\in\{i,ncp,oca,ocp\}. \tag{14}\]  
As for the stress concentration tensor \(\mathbb{B}_{ocpc}^{con}\), we refer to Appendix B. By analogy to Equation (14), the stress concentration tensor which relates mortar stresses \(\mathbf{\sigma}_{oma}\) to average stresses of the old embedded aggregate phase reads as  
\[\mathbb{B}_{oeu}^{oma}=\mathbb{C}_{a}:\mathbb{A}_{\infty,opa}:\left[\left(1-f_{ oeu}^{oma}\right)\mathbb{I}+f_{oeu}^{oma}\mathbb{A}_{\infty,opa}\right]^{-1}: \left(\mathbb{C}_{oma}\right)^{-1}, \tag{15}\]whereby the strain concentration tensor \(\Lambda_{\infty,oea}\) reads as  
\[\Lambda_{\infty,oea}=\left[\mathbb{I}+\mathbb{P}_{sph}^{\alpha cp}:\left(\mathbb{C }_{a}-\mathbb{C}_{ocp}\right)\right]^{-1}. \tag{10}\]  
The non-zero spherical components of the interface stress concentration tensors \(\mathbb{B}_{ma}^{ncp}\), \(\mathbb{B}_{opa}^{ncp}\), \(\mathbb{B}_{oma}^{ncp}\), and \(\mathbb{B}_{ocpc}^{ncp}\), can be written as [18]  
\[ \begin{split}& B_{i,rrrr}^{ncp}=1\,,\qquad B_{i,r\phi r\theta}^{ ncp}=B_{i,r\phi r\phi\phi}^{ncp}=\frac{1}{2}\,,\qquad B_{i,\phi\theta\phi\phi}^{ncp}= \frac{\mu_{ncp}}{2\,\mu_{i}}\,,\\ & B_{i,oeoea}^{ncp}=B_{i,r\phi\phi\phi}^{ncp}=\mu_{ncp}\left(3\,k_ {i}k_{ncp}+2\,k_{i}\mu_{ncp}+2\,k_{ncp}\mu_{i}\right)\,/\Delta\,,\\ & B_{i,\theta\theta\phi\phi}^{ncp}=B_{i,r\phi\phi\phi}^{ncp}=2\, \mu_{ncp}\left(k_{ncp}\mu_{i}-k_{i}\mu_{ncp}\right)\,/\Delta\,,\\ & B_{i,\theta\theta r}^{ncp}=B_{i,\phi\theta rr}=\left[3\,k_{i}k_{ ncp}\left(\mu_{i}-\mu_{ncp}\right)-2\,\mu_{i}\mu_{ncp}\left(k_{i}-k_{ncp}\right) \right]\,/\Delta\,,\end{split}  \tag{11}\]  
with \(\Delta=k_{i}\mu_{i}\left(3\,k_{ncp}+4\,\mu_{ncp}\right)\) and with \(i\in\{na,opa,oma,ocp\}\) whereby stiffness constants of aggregates (\(k_{a}\) and \(\mu_{a}\)) are used for aggregate phases (\(i\in\{na,opa,oma\}\)) and stiffness constants of old cement paste (\(k_{ocp}\) and \(\mu_{ocp}\)) are used for the old cement paste cover (\(i=\{ocpc\}\)).