## 1 Introduction
### Viscoelastic Phase Properties  
For conventional cementitious materials, the macroscopic creep behavior has been attributed to the hydration products only [32; 39; 40], while all other material phases are considered to exhibit purely elastic behavior. As for polymer-modified cement pastes, in turn, we consider that not only the hydrates, but also the polymers exhibit viscoelastic behavior, defined as [41],  
\[ \begin{split}\mathbf{\sigma}_{j}(t)&=\int_{-\infty}^{t} \mathbb{R}_{j}(t-\tau):\frac{\partial\mathbf{\varepsilon}_{j}(\tau)}{\partial\tau }d\tau,\\ \mathbf{\varepsilon}_{j}(t)&=\int_{-\infty}^{t}\mathbb{ J}_{j}(t-\tau):\frac{\partial\mathbf{\sigma}_{j}(\tau)}{\partial\tau}d\tau, \end{split} \qquad j\in\left\{\text{hyd, pol}\right\}. \tag{1}\]  
Figure 1: Micromechanical representation of polymer-modified cement pastes after [9]; the two-dimensional sketches refer to three-dimensional representative volume elements (RVEs). where \(\sigma_{j}\) and \(\epsilon_{j}\) are phase stresses and strains, \(\mathbb{R}_{j}\) and \(\mathbb{J}_{j}\) denote the phase relaxation and creep tensor functions, \(\tau\) is the time instant of loading and \(t\) is the chronological time. Notably, creep and relaxation tensor functions of any phase \(j\) are linked by means of the following convolution condition [42]:  
\[\int_{-\infty}^{t}\mathbb{J}_{j}(t-\tau):\mathbb{R}_{j}(\tau)\mathrm{d}\tau= \int_{-\infty}^{t}\mathbb{R}_{j}(t-\tau):\mathbb{J}_{j}(\tau)\mathrm{d}\tau=t \mathbb{I}\,, \tag{2}\]  
where \(\mathbb{I}\) denotes the symmetric fourth-order identity tensor with the components \(I_{ijkl}=\dfrac{1}{2}\left(\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk}\right)\) and where \(\delta_{ij}\) is the Kronecker delta, with components \(\delta_{ij}=1\) for \(i=j\), and zero, otherwise. The capillary pores, the unhydrated cement and the entrapped air phases behave elastically, expressed as:  
\[\sigma_{j}(t)=\mathbb{C}_{j}:\epsilon_{j}(t),\qquad j\in\left\{\text{por, cem, air}\right\}, \tag{3}\]  
where \(\mathbb{C}_{j}\) denotes the phase stiffness tensor. Equation (3) entails that their relaxation functions are time-invariant according to:  
\[\mathbb{R}_{j}=\mathbb{C}_{j}=3k_{j}\mathbb{I}^{\text{vol}}+2\mu_{j}\mathbb{I }^{\text{dev}},\qquad j\in\left\{\text{por, cem, air}\right\}. \tag{4}\]  
\(k_{j}\) and \(\mu_{j}\) denote the bulk and the shear moduli of phase \(j\) (see Table 1), and \(\mathbb{I}^{\text{vol}}\) and \(\mathbb{I}^{\text{dev}}\) are the volumetric and deviatoric parts of the identity tensor \(\mathbb{I}\). The creep tensor functions of hydrates and polymers are introduced as follows. [PERSON] et al. [33] performed a top-down analysis of more than 500 ultra-short early-age creep tests on conventional cement pastes, with different compositions in terms of different water-to-cement ratios. Very remarkably, the large macroscopic database could be explained based on one universal isochoric creep function of the microscopic hydrates, reading as:  
\[\mathbb{J}_{\text{hyd}}(t-\tau)=\dfrac{1}{3k_{\text{hyd}}}\mathbb{I}^{\text{ vol}}+\dfrac{1}{2}\left[\dfrac{1}{\mu_{\text{hyd}}}+\dfrac{1}{\mu_{c, \text{hyd}}}\left(\dfrac{t-\tau}{t_{\text{ref}}}\right)^{\beta_{\text{hyd}} }\right]\mathbb{I}^{\text{dev}}. \tag{5}\]  
In Equation (5), \(t_{\text{ref}}=1\,\mathrm{d}=86\),\(400\,\mathrm{s}\) is the reference time; \(k_{\text{hyd}}\) and \(\mu_{\text{hyd}}\) denote the universal bulk and shear modulus of the hydrates (see Table 1); and \(\mu_{c,\text{hyd}}\) and \(\beta_{\text{hyd}}\) are the universal shear creep modulus and the power-law creep exponent of the hydrates, amounting to [33]:  
\[\mu_{c,\text{hyd}}=20.93\text{ GPa},\qquad\beta_{\text{hyd}}=0.251. \tag{6}\]  
As for the polymers, we consider that their creep behavior is also isochoric. Furthermore, it is recalled that the creep behavior measured in macroscopic creep tests on different polymers could be modeled