# The Numerical Analysis of Textile Reinforced Concrete Shells: Basic Principles
## 4 FEM Model Formulation  
As mentioned previously, the commercial software RFEM (Ver. 5.19) [17] was selected for the FE calculations. The software package possesses a set of materials models with different drawbacks and benefits. The TRC material behaviour can be used as an input. In the following, we provide an overview of the three most feasible material models available in the user interface of RFEM which were verified to be used for the simulation of TRC structures via the smeared approach. * For a broad representation of the available material models in the RFEM software package (Ver. 5.19), first, a linear elastic material model was considered, called M1 in further discussions. This approach is interesting because it reflects the material model that is considered and uses it as the preinstalled model for the calculation of concrete structures in RFEM. The CUBE project shows that such approaches can be properly used [37]. Here, the force flow over the whole structure was first simulated using the linear material model coupled with an appropriate cross-sectional stiffness. Then, for an appropriate deflection calculation, the cross-section stiffness was reduced. * The next material model M2 is based on M1 but it is enriched for tension with a plastic zone and a consequent strain-hardening zone. Thus, the model is able to reflect either ACK or trilinear material behaviour as described above. Within the RFEM user interface, it is possible to find an Isotropic Nonlinear Elastic 2D/3D material model which is suitable for the calculation of non-linear materials in surfaces. One of the model's features is the possibility to provide a stress-strain curve derived from uniaxial TRC tests. A Mohr-Coulomb yield criterion is used and suitable for describing brittle materials such as concrete. The linear envelope based on the yield criteria fits for concrete with a significantly higher compressive than tensile strength. As a result, an asymmetric stress-strain diagram can be used as an input. * The further development step regarding the material models is M3. It also gives the possibility to model TRC with nonlinear behaviour and is named in the RFEM environment as the Isotropic Damage 2D/3D model. The difference is that the model is based on the assumptions of [PERSON] damage model [38; 39]. This approach provides an isotropic description of the damaged state of concrete according to [39]. The used damage function depends on scalar value D that is split into two parts, namely \(D_{t}\) for tension and \(D_{c}\) for compression, that can be determined from uniaxial tests. Such special features make the model attractive to be used for the calculation of TRC structures after the conduction of uniaxial tests. However, it is important to note that [PERSON] model according to the RFEM description [38] was developed for the calculation of materials with strain-softening behaviour like plain or steel fibre concrete. Thus, [PERSON] model does not fit the strain-hardening response of TRC via a smeared approach. Nevertheless, in the present study, the M3 model was used for the comparative simulation of TRC. Figure 8 shows a stress-strain diagram of TRC within the RFEM software(Ver. 5.19) user interface which was implemented as input data for each of the above-mentioned RFEM models. For simplification, the compressive range of the concrete material selected was solved as a bilinear curve. The numerical representation of the stress-strain diagrams for ACK and trilinear models for tensile and compressive ranges is given in Table 5.  
For numerical analysis stability and redundancy in the case of peak values of the applied load, the material model was defined with continuous behaviour after reaching the last point in the stress-strain diagram. To estimate the critical load, the calculations presented in Section 6 were performed stepwise. After each loading step in workflow Step II, the stress conditions were transferred to Step III for post-processing and the verification of the textile failure criteria (check Section 5).