## 3 Identification of Polymer Creep Properties Based on Macroscopic Creep Tests
### Age-Dependent Polymer Creep Properties  
Creep tests on macroscopic polymer specimens revealed that the creep activity of polymers decreases with decreasing relative humidity to which the polymers are exposed [59; 60; 61]. The polymers within the cement pastes are also exposed to considerable decreases of the internal relative humidity, resulting from self-desiccation, i.e., from the water-consuming hydration reaction. [PERSON] et al. [62] showed that the internal relative humidity in a cement paste sample with \(w/c=0.37\) decreased, within the first few days after mixing, from 98% to 92%. Notably, the resulting capillary pressure increased virtually linearly with the hydration degree \(\xi\), in the regime \(\xi>30\%\); see [22]. As for mortars and concretes, the self-desiccation-induced capillary underpressure was shown to result in water migration from the open porosity of the aggregates into the cement paste matrix [22]. A similar mechanism is envisaged to reduce the water content of the polymers. This motivates us to consider that the creep properties of polymer phases are age-dependent. In the following, it is investigated if the reproduction quality of the multiscale model can be significantly improved, provided that age-dependent polymer creep properties are considered. In this context, two different identification strategies are implemented: (i) only the shear creep modulus is considered to be age-dependent, while the power-law exponent is considered to be constant, and (ii) both the shear creep modulus and the power-law exponent are considered to be age-dependent. As for the first identification strategy, different amplitudes of the constant power-law exponent are considered: \(\beta_{\text{pol}}\in\{0.1,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.1,1.3\}\). For each one of these values, all 168 creep tests are analyzed, in order to identify optimal values of shear creep moduli that minimize the error between experimental and modeled viscous creep functions. Interestingly, the obtained total mean errors, according to Equation (17), are virtually constant for power-law exponents within the interval \(\beta_{\text{pol}}\in[0.4,0.8]\); see Figure 5. As for the further steps of the analysis, we choose the central value \(\beta_{P1}=\beta_{P2}=0.6\). The corresponding mean errors amount to \(2.7\times 10^{-7}/\text{MPa}\) for paste P1 and to \(2.9\times 10^{-7}/\text{MPa}\) for paste P2. Remarkably, (i) these mean errors are one order of magnitude smaller than the mean errors obtained under the consideration of constant polymer creep properties (see also  
Figure 4: Comparison of experimentally-determined and model-predicted viscous strains of polymer-modified cement pastes P1 (**a**) and P2 (**b**) at material ages of 40 h, 60 h and 130 h for constant polymer creep properties. Table 2), and (ii) the corresponding modeled creep strains agree very well with the experimental data (see Figure 6). This underlines that the creep activity of polymers in hydrating cement paste might indeed change and that the decreasing relative humidity results in a decrease of the polymer creep behavior. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Shear Creep Modulus** & **Power-Law Creep Exponent** & **Polymer** & **Mean Error \(\epsilon\)** \\ \hline universal & universal & P1 & \(1.709\times 10^{-6}\) \\ universal & universal & P2 & \(1.927\times 10^{-6}\) \\ \hline age-dependent & universal & P1 & \(2.665\times 10^{-7}\) \\ age-dependent & universal & P2 & \(2.857\times 10^{-7}\) \\ \hline age-dependent & age-dependent & P1 & \(1.975\times 10^{-7}\) \\ age-dependent & age-dependent & P2 & \(2.227\times 10^{-7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean errors \(\epsilon\) according to Equation (17) for universal and age-dependent polymer creep properties. Figure 5: Mean errors according to Equation (17) for age-independent power-law creep exponents within \(\beta_{pol}\in\{0.1,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.1,1.3\}\) and for optimized age-dependent shear creep moduli for paste P1 (**a**) and paste P2 (**b**).