Vladislav Gudžulić

Cohesive zone models with interface elements are widely used for simulating crack initiation and propagation, but their practical reliability is often limited by mesh bias: cracks can only propagate along predefined elements' boundaries, so predicted crack paths and global response may be strongly controlled by mesh orientation. In badly oriented automatically generated meshes, this can make physically admissible crack trajectories inaccessible and lead to inaccurate fracture patterns and artificial stiffness.This work introduces a novel adaptive mesh reorientation method to overcome this limitation while preserving the core strengths of interface-element formulations: discrete crack representation, natural crack initiation, branching, coalescence, and closure. No crack tracking and no predefined crack initiation locations are required. After each load step, mesh nodes are relocated so that intact interface elements progressively align with locally preferred fracture directions derived from the current stress state. The update is posed as a constrained discrete variational minimization problem and solved in a staggered manner after the mechanical equilibrium step.The approach is applicable in two and three dimensions. Its performance is demonstrated on established concrete fracture benchmarks, including heterogeneous mesoscale cases. The proposed method is robust and well suited for practical engineering analysis. It is readily integrated into standard finite element frameworks and directly applicable to complex geometries, material heterogeneity, and large-scale structural fracture simulations. Across seven benchmarks considered, the results consistently show improved crack-path prediction, reduced mesh sensitivity, and capture of crack initiation in the interior of the domain.

This paper presents a discrete fracture modeling approach for simulating cracking in reinforced concrete (RC) structures. Cracks are represented using cohesive zero-thickness interface elements, with a traction-separation law by Snozzi and Molinari (Int J Numer Meth Eng 93(5):510–526, 2013. https://doi.org/10.1002/nme.4398 ) extended to account for frictional sliding and crack-roughness-induced dilatancy. An effective failure surface is derived from the extended constitutive relation. Reinforcement is modeled using elastoplastic Timoshenko beam elements, and bond behavior is modeled using coupling elements governed by an elastoplastic bond-slip law. The model is validated through simulations of size effect experiments on RC beams under four-point bending (Syroka-Korol and Tejchman in Eng Struct 58:63–78, 2014. https://doi.org/10.1016/j.engstruct.2013.10.012 ). These tests exhibit consistent shear failure modes across all sizes and serve as a reference for evaluating fracture models proposed by Bažant and Nguyen (J Eng Mech 149(8):04023047, 2023. https://doi.org/10.1061/JENMDT.EMENG-6887 ). Simulations reproduce size-dependent peak loads, crack patterns, and failure modes using material parameters derived from design codes and literature. A mesh sensitivity analysis and a parametric study on mixed-mode fracture parameters (shear strength, friction coefficient, and dilatancy) are conducted. The results highlight the importance of these parameters in capturing shear-dominated failure mechanisms and reveal the possible impact of uncertainties linked to material property identification on the model predictions. The proposed approach provides a robust, physically motivated, and modular framework for analyzing both serviceability and failure in RC structures. The model demonstrates good predictive capability, but also shows sensitivity to mixed-mode fracture properties. This result highlights the importance of advancing and more widely applying experimental methods for characterizing these parameters, which are currently difficult to obtain and rarely addressed in standard testing protocols.

In this contribution, a multi‐level Finite Element Model for steel‐fibre reinforced concrete (SFRC) is presented which allows predicting the post‐cracking response of fibre reinforced structural members. In contrast to the guidelines, which suggest that the response of SFRC should be derived indirectly, using bending tests, the post‐cracking response is here derived from the actual fibre properties. The numerical model is designed to directly track the influence of design parameters, such as fibre type, fibre orientation, fibre content and concrete strength, on the structural response. For this purpose, submodels on the level of a single fibre are combined into a crack bridging model, considering the fibre orientation and the fibre content. This is integrated into a finite element model for fiber reinforced concrete, in which a cohesive law in the context of the discrete crack approach is used to account for the opening of cracks [1]. The model has been extended to account for imperfect closure of cracks during cyclic loading and unloading, respectively, due to presence of fibres and debris within the crack, which is manifested in hysteresis loops in load‐displacement curves. The predictive capability of the proposed numerical multi‐level model for SFRC was systematically validated by means of test series performed on the fibre and the structural level [1,2]. The proposed model is validated by three‐point bending tests on notched beams with fibre content of 0 and 57 kg/m³ subjected to cyclic loading. The ability of the above‐described numerical model to capture the formation of hysteresis in cyclic loading is evaluated.

In the present study, the capability of high-strength short steel fibers to control the degradation in high-performance concrete was experimentally examined and numerically simulated. To this end, notched prismatic high-performance concrete specimens with (HPSFRC) and without (HPC) short steel fibers were subjected to static and cyclic tensile tests up to 100,000 cycles. The cyclic tests showed that the rate of strain increase was lower for HPSFRC specimens and that the strain stagnated after around 10,000 cycles, which was not the case with HPC specimens. The microscopic examinations showed that in HPSFRC, a larger number of microcracks developed, but they had a smaller total surface area than the microcracks in the HPC. To further investigate the influence of fibers on the behavior of HPSFRC in the cracked state, displacement-controlled crack opening tests, as well as numerical simulations thereof, were carried out. Experiments have shown, and the numerical simulations have confirmed, that the inclusion of short steel fibers did not significantly affect the ultimate strength; however, it notably increased the post-cracking ductility of the material. Finally, the unloading/reloading behavior was examined, and it was observed that the unloading stiffness was stable even for significant crack openings; however, the hysteresis loops due to unloading/reloading were very small.

Concrete is a quasi‐brittle material, characterized by a non‐negligible, finite‐sized fracture process zone (FPZ) in which various toughening mechanisms play a significant role on crack development and propagation. Concrete is often reinforced with fibers to improve the serviceability and longevity of concrete structures by controlling the maximal crack widths and providing residual carrying capacity to initiated cracks. In quasi‐brittle materials such as concrete, toughening mechanisms such as crack deflection due to the presence of large heterogeneities, contact shielding, i.e., wedging and crack closure induced by debris and rough crack faces, crack bridging by tough aggregates, unbroken ligaments and fibers (in fiber‐reinforced concretes), are mostly governing damage evolution under monotonic and especially under cyclic loadings [1]. All these items contribute to a complex non‐linear response in terms of load‐displacement curves observed in experimental investigations. Many investigations have been performed on plain concrete, but not so many for high‐performance fiber‐reinforced concrete [2] which is the main subject of investigation within the DFG Priority Program 2020. In order to better understand the influence of these toughening mechanisms on the formation of hysteresis during cyclic loading‐unloading of plain and steel fiber‐reinforced high‐performance concrete, we model these mechanisms and their evolving influence on damage development using a discrete crack approach, and take into account the imperfect closure of cracks and friction between crack faces that come in contact during loading/unloading of the specimen. Within the scope of this contribution, we present the formulation of the model and illustrate its performance through selected numerical experiments under monotonic and cyclic loading of plain and fiber‐reinforced high‐performance concrete specimens. Model predictions are compared with laboratory measurements.

Im Beitrag wird die Prognosefähigkeit eines numerischen Mehrebenen‐Modells für stahlfaserverstärkte Betonstrukturen aus hochfestem Beton anhand einer die Faser‐ und die Strukturebene umfassenden Testserie systematisch untersucht. Die experimentelle Studie umfasst Auszugsversuche an Dramix 3D 55/60 und 65/60 Fasern in hochfestem Beton mit unterschiedlichen Einbettungslängen und Neigungen zur Rissfläche auf der Mesoskala sowie Dreipunkt‐Biegezugversuche an gekerbten Balken mit drei stark unterschiedlichen Fasergehalten zur Abbildung des Strukturverhaltens. Das numerische Modell ist derart konzipiert, dass es die direkte Verfolgung des Einflusses der Entwurfsparameter wie Faserart, Faserorientierung, Fasergehalt und Betonfestigkeit auf die Strukturantwort ermöglicht. Hierzu werden Submodelle auf der Ebene der Einzelfaser zu Rissüberbrückungsmodellen in Abhängigkeit von Faserorientierung und Fasergehalt zusammengeführt und zum Zwecke numerischer Strukturanalysen in ein Finite‐Elemente‐Modell integriert. Die Validierung der Modelle für endverankerte Stahlfasern zeigt, dass die wesentlichen Interaktionsmechanismen zwischen Faser und hochfestem Beton für alle untersuchten Fälle (Faserorientierung, Einbettungslängen) wirklichkeitsnah abgebildet werden. Auf der Strukturebene zeigen die Ergebnisse der numerischen Simulationen auf Basis des Faserbetonmodells eine sehr gute Übereinstimmung für alle Fasergehalte, sowohl was die maximale Last als auch das Nachbruchverhalten betrifft.