# The Numerical Analysis of Textile Reinforced Concrete Shells: Basic Principles
## 3 Materials Models  
### Short Overview of Material Models for TRC  
One of the most important points is the way the calculation routines integrate the theoretical background of the TRC structures. In the present state of the art in the field of the analysis of TRC structures, three categories of numerical approaches can be summarized [19] which are given in Figure 2 as a schematic overview. The first column (a) shows parameters of the discrete crack model description. Here, the damage to the concrete is considered via the evolution of discrete cracks in the matrix and a nonlinear bond stress-slip relation between concrete and continuous fibre-based reinforcement [19]. The model gives a valuable representation of the composite behaviour but with a considerable level of complexity in the description of the governing mechanisms as well as computational efforts. For the planned iterative workflow, a high numerical complexity implies a disproportionate  
Figure 1: Overview of the workflow. Graphic: [PERSON]. numerical effort, which is why this approach was not pursued further for the project. In the smeared model (b), TRC is represented as a composite with uniform behaviour over the cross-section. The model's parameters are determined via the rule of mixtures that demands the correct estimation of the volume fractions of the constituents. With that, the material model has to be calculated for each cross-sectional configuration [19]. It should be noted here that the smeared model was the most convenient one within the selected software packages to account for the damage effects in the TRC. A more detailed description of the model used in RFEM is given later. The third model (c) contains a resolved realization of the matrix and textile layers. This behaviour is similar to the discrete model with the difference that the cracks in the matrix are smeared along the specimen. This makes the model less demanding for the numerous calibration procedures and gives the opportunity to consider the exact position of the reinforcement layers within the cross-section [19]. For the calculation in RFEM, a material description for the composite textile reinforced concrete under compressive and tensile stress is required which can be represented by the smeared approach. The stress-strain behaviour of TRC under tension is very similar to that of steel-reinforced concrete, see, e.g., refs. [20; 21]. In State I, the concrete is non-cracked, and the specimen's stiffness is high. The composite's strain \(\varepsilon_{c}\) is equal to the strains in matrix \(\varepsilon_{m}\) and the fibre reinforcement \(\varepsilon_{f}\). When the concrete's tensile strength is reached, cracks begin to form successively (State IIa). If the tensile force is increased further beyond the point of completed cracking, the number of cracks no longer changes. Only the crack widths increase (State IIb) until the textile tears. Since, in this state, only textile reinforcement bears the total tensile load, the composite section possesses the stiffness of the reinforcement. As part of the described workflow (Figure 1), a special script was developed within the scope of the Rh + GH environment, with which multiple experimental results of a test series were converted into a single average curve of the stress-strain relation. Afterwards, the script converts this average data curve into three states, I to IIb, to be able to map the curve analytically for further processing. The analytical description should reflect the material behaviour of TRC as accurately as possible. This is important for the further optimization and analysis of the textile reinforced concrete shell structures in the context of a theoretical parametrical study, as only singular structures can be tested in the experiment. However, we would like to be able to make a statement about the behaviour of structures with different geometries, material combinations and loading scenarios. There are several analytical models appropriate for TRC, each with specific advantages and disadvantages.