# The Numerical Analysis of Textile Reinforced Concrete Shells: Basic Principles
## 3 Materials Models
### Calibrating the Selected Material Models  
To calibrate the material models and respective parameters, it was necessary to perform uniaxial tensile tests on composite samples. The concrete mixture C3-B2-HF-2-190-2 [30], optimized for fibre reinforcement, was used. With a maximum grain size of 2 mm, it is also suitable for the production of very intricate concrete components. Table 1 provides the mixture composition [30]. The binder BMK-D5-1 is outside the current cement standard due to the addition of an inert filler and was developed in a partnership between the Institute for Building Materials of TU Dresden and the Deuna cement plant (Dyckerhoff\({}^{\circledR}\) company, Wiesbaden, Germany) in the project C3-B2 as part of the C\({}^{3}\)--Carbon Concrete Composite project [31]. The compressive and bending tensile strengths of the hardened concrete from Table 2 were determined on three prisms with dimensions of 40 \(\times\) 40 \(\times\) 160 mm according to DIN EN 196-1 [32]. For tensile tests on TRC, a 1220 \(\times\) 540 \(\times\) 40 mm slab was concreted and stored for the first few days under wet cloths and afterwards at 20 \(\lx@math@degree\)C in a climate chamber with 65% relative humidity. The plate thickness and the two-layer carbon reinforcement were selected according to shell elements planned for subsequent steps. The reinforcement was located centrally with a gap of 10 mm, and the concrete covers were equal to 15 mm on both sides of the test samples. Before testing at an age of 28 days, in total, six tensile test samples with dimensions of 800 \(\times\) 62 \(\times\) 40 mm were cut off from the slab. The samples were displacement-controlled loaded with a loading speed of 0.03 mm/min until failure. In addition to the force, the deformation was recorded using two LVDTs in the measuring range. The test setup is presented in Figure 5. \begin{table}
\begin{tabular}{c c} \hline
**Raw Materials** & **Quantity (kg/m’)** \\ \hline Binder compound BMK-DS-1 (Dyckerhoff, Germany) & 815 \\ Quartz sand 0.06/0.2 & 340 \\ Sand 0/2 & 965 \\ Superplasticizer (e.g., MC-VP-16-0205-02 from MC-Bauchemie, Germany) & 17 \\ Water & 190 \\ \hline \end{tabular}
\end{table} 
Table 1: Mixture composition of concrete C3-B2-HF-2-190-2 [30]. \begin{table}
\begin{tabular}{c c c} \hline
**Property** & **Longitudinal** & **Transversal** \\ \hline Roving axis distance \(e_{tex}\) (mm) & 21 & 21 \\ Cross-section of a roving \(A_{f}\) (mm\({}^{2}\)) & 1.81 & 1.81 \\ Cross-section of the reinforcement grid \(A_{tex}\) (mm\({}^{2}\)/m) & 85.4 & 85.6 \\ Tensile strength of the roving \(\sigma_{hf}\) (MPa) & \(\geq\)3950 & \(\geq\)4250 \\ Tensile strength of the grid \(\sigma_{u,tex}\) (MPa) & \(\geq\)3950 (avg.)\(\downarrow\)3050 (char.) & \(\geq\)4250 (avg.)\(\downarrow\)\(\geq\)3250 (char.) \\ Resisting force \(F_{tex}\) (kN/m) & \(\geq\)260.5 & \(\geq\)275.0 \\ Modulus of elasticity \(E_{tex}\) (MPa) & \(\geq\)251,500 & \(\geq\)254,000 \\ \hline \end{tabular}
\end{table} 
Table 2: Properties of hardened concrete (mean values). \begin{table}
\begin{tabular}{c c c} \hline
**Property** & **Value** & **Unit** \\ \hline Compressive strength\(f_{cm}\) & 114.8 & MPa \\ Bending tensile strength\(f_{cm,fl}\) & 8.8 & MPa \\ \hline \end{tabular}
\end{table} 
Table 3: Properties of textile reinforcement solidian GRID Q85-CCE-21 [33]. The average stress-strain curve from the six individual tests is compared with the material models in the following, and the detailed results are published in [34]. Based on the material properties presented, the material models described above were calibrated. Figure 6 shows the results for the ACK material model (M1). Similarly, Figure 7 displays simulated results for the trilinear model (M2). For the comparison with the experiments, both models were calibrated with \(V_{f}=0.40\%\). Figure 5: Tensile tests on TRC; (**a**) sample geometry, (**b**) sample during testing. Graphic: [PERSON]; photo: [PERSON]. Figure 6: Calibrated ACK material model for various values of volume fraction \(V_{f}\). Graphic: [PERSON].