## 3 Numerical Analysis
### Material Characteristics of the Model  
The concrete material characteristics were considered from the strength tests of the concrete cubes taken during specimen casting. In the numerical simulation, a brittle-plastic constitutive material model was used, which combines models for the description of the behavior of concrete under the tensile and compressive stress (3D non-linear cementitious 2). The plastic model of concrete with its compressive action is based on the Menetrey-Williams definition of the failure area's shape [32]. This surface's position is not fixed but may be varied and spread, simulating phase hardening and softening [33; 34]. The fracture model is based on the classical formulation of the \"smeared\" cracks, which uses [PERSON]'s failure criterion [35] and exponentially reduced stiffness (softening). The material model also considers the wedging of the aggregate in shear (\"Concrete Field Theory Aggregate Interlock\"). The material model's formulation is based on the decomposition of the resulting relative deformations into separate individual components of relative deformations--elastic \(\varepsilon^{e}_{ij}\), plastic \(\varepsilon^{p}_{ij}\) and fracture \(\varepsilon^{f}_{ij}\)[26]. Figure 11 shows a diagram in the form of uniaxial stress and its associated relative deformation, where \(\varepsilon_{i}\) is the relative deformation corresponding to the maximum tensile strength of the concrete, \(f_{i}\varepsilon^{g}\) is the ultimate value of concrete tensile strength, \(\varepsilon_{c}\) is the relative deformation corresponding to the concrete's maximum compressive strength, and \(f_{c}\varepsilon^{f}\) is the ultimate compressive strength of concrete.  
Figure 10: Different ways of modelling supplementary reinforcement: (**a**) 3D solid elements; (**b**) 1D elements.  
Principles of fracture mechanics are commonly used to describe the process of cracking in concrete. Its foundations were given by [PERSON]'s work published in 1921 [36]. An energy criterion has been established according to which a crack can propagate provided that the amount of energy available to create or widen the crack surface exceeds the amount of energy required for this process [37]. In contrast to the linear elastic theory of fracture mechanics, a large fracture process zone is formed in front of the crack, which is not negligible. The material in this zone is exposed to significant softening [38]. The nonlinear theory of fracture mechanics was published by [PERSON] in 1976 [39]. The global material model considers the Crack Band Model [40], which assumes that microcracks are concentrated and smeared in a specific width in the area of the fracture process zone [38]. The model indicates the relationship between the relative softening and a certain width, which is considered a material attribute [41].  
The detailed material properties of the concrete (tensile strength, elastic modulus, specific fracture energy, crack shear stiffness factor, etc.) were defined on the basis of the real cubic compressive strength according to the formulas published in [26] (default software values).  
A bilinear elastic-plastic material model of the steel is commonly used for structural analyses [42; 43; 44]. This type of material definition was used to create a model of the anchor with a forged head, supplementary reinforcement, longitudinal and shear reinforcement of the beam (Figure 12).  
The initial ascending branch represents the material's elastic action, taking into account the modulus of elasticity of the steel \(E_{s}\). After reaching the yield strength value, the  
Figure 11: Uniaxial stress–strain diagram of concrete in compression and tension.  
Figure 12: Bilinear stress–strain diagram of the steel.  
simplified ideal plastic action of the material is considered. This simplification is acceptable in most numerical analyses of reinforced concrete members or structural details [45].