## 2 Model Development  
### Micromechanical Representation of Recycled Concrete  
The microstructure of recycled concrete is resolved across four length scales by means of four hierarchically-organized representative volume elements (RVEs) (see Figure 1). Separation of scales [22] is fulfilled in the sense that all RVEs are (i) significantly smaller than the structures which they form and (ii) significantly larger than the inhomogeneities inside the RVEs. As the inhomogeneities within those four RVEs are to complex to be described in full detail, quasi-homogeneous sub-domains (so-called material phases) are introduced and their micromechanical features such as shape, volume dosage, mechanical properties, and their mutual interactions are discussed next. At the largest observation scale, the centimeter-sized concrete scale, we consider a matrix phase of new cement paste hosting (natural and recycled) aggregate phases (see Figure 1a). The morphological complexity of recycled aggregates renders their representation in the micromechanical approach a challenging task. We herein aim for a representation which is able to capture the peculiarities of the (micro-)stress fields within and around typical recycled aggregates of various morphologies, while still allowing for multiscale homogenization in the framework of continuum micromechanics. Based on visual inspection of typical recycled aggregates which were used in the study of [PERSON] et al. [32], we distinguish three classes of recycled aggregates (see Figure 2):  
* A considerable fraction of the recycled aggregates are either completely free of attached mortar or cement paste covers only a negligible part of their surfaces. Recycled aggregates that exhibit such a morphology are herein labeled as class I aggregates. * A considerable fraction of the recycled aggregates are old mortar particles where none of the many small aggregates inside the mortar exhibits a dominant size, labeled herein as class II aggregates. * A considerable fraction of the recycled aggregates are single stone aggregates, whereby the majority of the aggregate surface is covered by cement paste, labeled herein as class III aggregates. Classification is not straightforward, in particular the distinction between class II and class III recycled aggregates, given that one cannot see \"inside\" the cement paste (or mortar) inclusions. In this context, we report on a study by [PERSON] et al. [17], who manufactured recycled concrete using ordinary (gray) Portland cement and recycled aggregates from a concrete produced with white cement paste. This way, the authors could readily distinguish the old (gray) and new (white) cement paste by means of image analysis of cut sections (see Figure 3a,b). The resulting images support the aforementioned classification of the recycled aggregates, as exemplarily demonstrated in Figure 3b. Notably, yet another important recycled aggregate morphology might be identified: recycled aggregates composed of a one or a few large stones with old cement paste attached or in between, whereby both stones and paste are visible in comparable proportions at the boundary (see e.g., the pictures of [33]). Herein, we do not explicitly account for such a morphology, given the applied scale separation-based homogenization approach. Rather, we consider that the stress fields inside and around such recycled aggregates are captured well by means of the three envisaged classes of recycled aggregates. Figure 1: Multiscale micromechanical representation of recycled concrete; two-dimensional sketches refer to three-dimensional representative volume elements (RVEs). Next, we discuss how the three aggregate morphology classes are translated to micromechanical phases. Class I recycled aggregates (old plain aggregates) as well as (potentially used) new natural (virgin) aggregates are modeled as spherical inclusions, see Figure 3c, analogously to earlier micromechanics models [21; 23]. Notably, these phases represent both coarse aggregates and sand particles.