## 2 Model Development
### Material Phase Properties  
Herein, we discuss volume dosages and elastic phase properties, which enter the micromechanics homogenization and concentration equations. The concrete-related phase volume fractions of the new cement paste matrix \(f_{ncpm}^{con}\), of the new natural aggregates \(f_{na}^{con}\), and of the recycled aggregates \(f_{na}^{con}\) are introduced first, whereby \(f_{ncpm}^{con}+f_{na}^{con}+f_{na}^{con}\!=\!1\). The recycled aggregates, in turn, contain old aggregates and old cement paste, represented by means of recycled aggregate-related phase volume fractions \(f_{ocp}^{ra}\) and \(f_{na}^{ra}\), whereby \(f_{ocp}^{ra}+f_{na}^{ra}=1\). Moreover, we introduce the (volumetric) replacement ratio \(f_{na}^{a}\) defined as the ratio between recycled aggregate volume and total aggregate volume according to  
\[f_{ra}^{a}=\frac{f_{ra}^{con}}{f_{na}^{con}+f_{ra}^{con}}\,. \tag{15}\]  
As for the distinction into the three recycled aggregate classes depicted in Figures 2 and 3, we further define the recycled aggregates-related volume fractions of the individual aggregate classes, \(f_{\text{I}}\), \(f_{\text{II}}\), \(f_{\text{III}}\), with \(f_{\text{I}}+f_{\text{II}}+f_{\text{III}}\!=\!1\). We consider that the distribution of old cement paste in recycled aggregate classes II and III is proportional to the class' volume, i.e., \(f_{ocpm}^{con}/f_{\text{II}}\!=\!f_{ocp}^{con}/f_{\text{III}}\), with \(f_{ocpm}^{con}\) and \(f_{ocp}^{con}\), denoting the concrete scale-related volume fractions of the old cement paste matrix (which is part of the class II recycled aggregate) and the old cement paste cover (which is part of the class III aggregate), respectively, whereby \(f_{ocpm}^{con}+f_{ocp}^{con}=f_{ocp}^{ra}\,f_{na}^{con}\). This way, we can express all concrete-related phase volume fractions as functions of five mix design parameters--the concrete-related new cement paste volume fraction \(f_{ncpm}^{con}\), the recycled aggregate-related old cement paste volume fraction \(f_{ocp}^{ra}\), the aggregate replacement ratio \(f_{rn}^{a}\) according to Equation (15), and the recycled aggregate-related volume fractions of class I and class II recycled aggregates, \(f_{\text{I}}\) and \(f_{\text{II}}\)--resulting in  
\[f_{na}^{con} =(1-f_{ra}^{a})\left(1-f_{ncpm}^{con}\right)\,, \tag{16}\] \[f_{opa}^{con} =f_{\text{I}}\,f_{ra}^{a}\left(1-f_{ncpm}^{con}\right)\,,\] \[f_{oma}^{con} =f_{\text{II}}\,f_{a}^{a}\left(1-f_{ncpm}^{con}\right)\,,\] \[f_{ocpc}^{con} =\frac{f_{ocp}^{ra}\,f_{ra}^{a}\left(1-f_{ncpm}^{con}\right)}{1+ \frac{f_{\text{II}}}{1-f_{\text{II}}}}\,,\] \[f_{oca}^{con} =1-f_{ncpm}^{con}-f_{na}^{con}-f_{opa}^{con}-f_{oma}^{con}-f_{ocp}^ {con}\,,\]  
with subscripts \(OPA\), \(OMA\), and \(OCA\) standing for old plain aggregates, old mortar aggregates and old covered aggregates, respectively. The old mortar-related phase volume fractions of old embedded aggregates and old cement paste, \(f_{ooea}^{oma}\) and \(f_{ocpm}^{oma}\), read as  
\[f_{ocpm}^{oma}=\frac{f_{ocp}^{ra}}{1-f_{\text{I}}}\,,\qquad f_{oea}^{oma}=1-f_{ acpm}^{oma}\,. \tag{17}\]We consider that the cement paste is a thermodynamically closed system. Modeling the absorption of the mixing water by recycled aggregates, in particular by the old cement paste matrix, as well as a potential migration of water back to the hydrating new cement paste (internal curing) is beyond the scope of the manuscript.