In project C05, the extended phase-field method (XPFM) developed in the first funding period of the TRR 280 will be extended to include crack friction/aggregate interlocking within 3D mesoscale simulations. The XPFM allows for rather coarse discretizations for fracture simulations using the phase-field approach. This improves the efficiency significantly compared to phase-field simulations using classical finite element discretizations. Since aggregate interlocking is an important observable effect in carbon-reinforced concrete structures, a crack friction model for the concrete matrix will be set up and incorporated within the XPFM formulation.

In case of crack opening or sliding, carbon rovings are partially pulled out of the concrete matrix which has a significant influence on the dowel effect of carbon rovings. This delamination behavior between the roving and the matrix will be modeled by a membrane-mode-enhanced-cohesive-zone-element (MMECZE) extended by a friction model developed during the first funding period of the TRR 280. Due to the potentially complex geometry of the carbon rovings, they will be discretized using the extended finite element method (XFEM) for heterogeneous structures. The existing MMECZE formulation will be transferred to the XFEM discretization of the interface between matrix and roving.

Microcracks and the corresponding micro-friction that cannot be captured explicitly on the mesoscale will be modeled by a Drucker-Prager-cap microplane approach that has been improved during the first funding period as well. The calibration and validation of the different parts of the mesoscale model will be performed in close cooperation with several other projects of TRR 280.

To allow for predictive simulations of carbon-reinforced concrete designs on the macroscale including the detailed mesostructural crack behavior in highly strained parts of the domain, a multiscale simulation framework will be developed in close cooperation with project C03. This framework will connect the mesoscale model setup in C05 with the macroscopic solid-shell model created in C03. The coupled meso-macro model will be used to assess the resilience of carbon-reinforced concrete structures designed within TRR 280 with respect to different loading scenarios. This approach will contribute to the improvement of design strategies for carbon-reinforced concrete structures.

The aim of this project is to simulatively predict the behavior of thin-walled carbon-reinforced concrete structures under different load combinations and to ensure their sufficient robustness. Focus is the investigation of cracks in concrete at the mesoscale, including their initiation, propagation, branching and coalescence, and how these affect the macroscale behavior. These phenomena can result in complex crack patterns which discrete reproduction within the finite element (FE) method is difficult. Therefore, the phase-field method is applied, in which cracks are represented in a smeared manner. However, the accurate representation of the phase field and the high displacement gradients across the crack requires very fine FE-meshes, which leads to a considerable computational effort. For this reason, the extended phase-field method (XPFM) is developed within the scope of this project. By transforming the phase-field approach and enriching the displacement field, significantly coarser meshes can be used with the XPFM and thus the computational effort can be reduced.

In order to also capture the macroscopic behavior, efficient numerical multiscale methods are required, with which the inhomogeneous and both materially and geometrically non-linear behavior can be taken into account. Therefore, the multiscale projection method suitable for the localisation effects that occur is extended to account for heterogeneities and cracks in shell-like structures with finite deformations.

The combination of the multiscale projection method with the XPFM for three-dimensional elements enables a realistic and locking-free representation of the macroscopic structural behavior with moderate numerical effort. Thus, the resilience of carbon-reinforced concrete structures designed with the strategies developed in CRC/Transregio 280 can be reliably evaluated against different combined external loads.

Within the framework of C05, the seed fund project "Simulation of the fatigue behavior of carbon-reinforced concrete components under changing cyclic loads" (1^st round 2022) was carried out. Furthermore, in the seed fund project "Numerical modelling and experimental validation of fibre pull-out behavior in carbon-reinforced concrete" (2^nd round 2022), methods were developed to investigate fiber pull-out numerically.