## 3 Identification of Polymer Creep Properties Based on Macroscopic Creep Tests
### Age-Dependent Polymer Creep Properties
Figure 6: Comparison of experimental and computed creep strains of polymer-modified cement pastes P1 (**a**) and P2 (**b**) at ages of 40 h, 60 h and 130 h, considering age-dependent shear creep moduli and constant power-law creep exponents. The identified shear creep moduli increase, in a virtually bilinear fashion, with increasing material age; see Figure 7. For material ages up to 40 h, the identified shear creep moduli increase quite rapidly up to \(\mu_{c,P1}\approx 0.10\) GPa and \(\mu_{c,P2}\approx 0.14\) GPa, respectively. Thereafter, the hourly increase is significantly smaller. After one week of hydration, the identified values amount to \(\mu_{c,P1}\approx 0.23\) GPa and \(\mu_{c,P2}\approx 0.26\) GPa, respectively. The progressive decrease of the internal relative humidity is, on the one hand, a prime candidate for explaining the decrease of the creep activity of the polymers, but on the other hand, it is difficult to imagine how it could explain the obtained bilinear evolution of the identified creep shear moduli. Therefore, a second microstructural effect appears to be involved. [PERSON] et al. [36] observed that the polymer particles are not uniformly distributed throughout the microstructure at the time instant of casting. Instead, the polymer particles flocculate, referred to as localization. One might speculate that such polymer agglomerates exhibit a much more compliant time-dependent behavior compared to the individual polymer particles. According to [PERSON] et al. [36], the growing hydrates penetrate into the flocculated polymer particles, such that the agglomerates are progressively destroyed. [PERSON] and [PERSON] [63] and [PERSON] [64] among others also observed that the cementitious hydration products grow through the polymer layers by means of ESEM investigations. The first and strongly increasing branch of the time-evolution of the shear creep modulus might reflect this progressive destruction of polymer agglomerates, but clearly there is a need for more experimental evidence, before a convincing conclusion could be drawn. As for the second identification strategy, all 168 tests per specimen are reanalyzed, and optimal values of both the creep shear modulus and the power-law creep exponent are identified simultaneously, so as to minimize the error between modeled and measured creep strains. In other words, both the creep shear modulus and the power-law creep exponent are considered to be age-dependent and, thus, evolving quantities. The identified shear creep moduli and the identified power-law creep exponents evolve nonlinearly with increasing material age; see Figure 8. In comparison with Figure 7, the evolutions of the shear creep modulus, as well as of the power-law exponent exhibit a more pronounced scatter. Most likely, this is related to the more complex optimization problem of the second identification strategy, which involves the determination of two variables. Therewith, the two variables may span an area with several minimal values close to each other, rendering the identification of the optima more challenging. After a rather rapid increase of the shear creep modulus up to material ages of about 40 h, it is almost constant between ages of 40 and 110 h and amounts to \(\mu_{c,P1}\approx 0.08\) GPa and \(\mu_{c,P2}\approx 0.11\) GPa, respectively. Thereafter, the shear creep modulus increases again rather rapidly and reaches, one week after production, \(\mu_{c,P1}\approx 0.60\) MPa  
Figure 7: Evolutions of the shear creep modulus with respect to material age, while considering time-independent power-law exponents \(\beta_{P1}=\beta_{P2}=0.6\), for paste P1 (**a**) and paste P2 (**b**). and \(\mu_{c,P2}\approx 0.40\) MPa, respectively. The power-law creep exponents, in turn, are virtually constant, \(\beta_{P1}\approx\beta_{P2}\approx 0.9\), at material ages of less than 100 h. Subsequently, they decrease and finally stabilize around \(\beta_{P1}\approx 0.3\) or \(\beta_{P2}\approx 0.4\), respectively.