Alexander Popp

Max Firmbach, Ivo Steinbrecher, Alexander Popp et al.

This paper presents modified augmented Lagrangian block preconditioners for the mixed-dimensional coupling of three-dimensional solid bodies with embedded one-dimensional torsion-free Kirchhoff-Love beams using Lagrange multipliers for constraint enforcement. The finite element discretization of this mixed formulation leads to an indefinite saddle-point system. An augmented Lagrangian formulation is employed to regularize the linear system while maintaining exact enforcement of the coupling constraints. Starting from the corresponding ideal augmented Lagrangian block preconditioner, more practical block-triangular variants are derived in which the solid, beam, and Schur complement blocks can be treated independently. In addition, different variants of Schur complement approximations are introduced. Numerical experiments demonstrate robustness with respect to model parameters, near mesh-independent iteration counts, and favorable strong and weak scalability. These results indicate the suitability of the proposed approach for large-scale simulations of mixed-dimensional models in solid and structural mechanics, as demonstrated by an engineering example involving a composite sandwich plate.

Vito Pasquariello, Georg Hammerl, Felix Örley et al.

We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables sub-cell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface. The cut-cell procedure inevitably leads to non-matching interfaces, demanding for a special treatment. A Mortar method is chosen in order to obtain a conservative and consistent load transfer. We validate our method by investigating two-dimensional test cases comprising a shock-loaded rigid cylinder and a deformable panel. Moreover, the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset. Finally, we propose a three-dimensional fluid-structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations.

Linus Wunderlich, Alexander Seitz, Mert Deniz Alaydin et al.

A new construction of biorthogonal splines for isogeometric mortar methods is proposed. The biorthogonal basis has a local support and, at the same time, optimal approximation properties, which yield optimal results with mortar methods. We first present the univariate construction, which has an inherent crosspoint modification. The multivariate construction is then based on a tensor product for weighted integrals, whereby the important properties are inherited from the univariate case. Numerical results including large deformations confirm the optimality of the newly constructed biorthogonal basis.

Philip Franz, Max von Danwitz, Gregory Duthé et al.

The increasing flexibility of modern large wind turbine blades necessitates cost-efficient and reliable structural monitoring solutions. For this purpose, we propose to use aerodynamic pressure measurements obtained via Aerosense, a novel, non-intrusive and economical sensing system. In former work [Franz et al., 2025], we investigated the potential of aerodynamic pressure measurements for structural damage detection on elastic and aerodynamically loaded structures. An experimental campaign was conducted on a NACA 633418 airfoil mounted on a vertically vibrating cantilever beam within an open wind tunnel. Structural damage was introduced progressively through controlled saw cuts near the beam support. Aerodynamic pressure distributions were recorded under varying inflow conditions and structural states. Based on this data set, we developed a convolutional neural network to detect structural damage and classify its severity using only aerodynamic pressure signals. The results demonstrate that pressure measurements can effectively enable real-time detection and quantification of damage in elastic, beam-like structures subjected to mildly turbulent flow and varying operational conditions. Recognizing the limitations of pure black-box classification, in this study, we further incorporate physics-based insights and explainable machine learning methods to interpret how structural damage influences both the dynamic response and the aerodynamic pressure field. This leads to an enhanced damage detection pipeline, aiming to improve transparency, robustness, and physical consistency in data-driven monitoring of elastic, aerodynamically loaded structures.

Ivo Steinbrecher, Nora Hagmeyer, Christoph Meier et al.

Slender beam-like structures frequently occur in engineering applications and often interact at discrete locations through joints or connectors. Accurate modeling of such interactions is particularly challenging when different numerical formulations are involved in terms of underlying beam theory, interpolation schemes, and rotation parametrization. In this work, a versatile formulation-independent beam-to-beam point coupling approach is proposed within the framework of the geometrically exact beam theory discretized by the finite element method. The coupling constraints are expressed solely in terms of cross-section kinematics, namely centroid positions and orientations. Suitable generalized deformation measures for positional and rotational coupling are introduced, allowing for general coupling configurations, including relative rotations and non-coincident cross-section centroids in the reference configuration. The contribution of the coupling conditions to the weak form of the balance equations is derived in a variationally consistent manner and can be incorporated directly into the weak form of existing beam finite element models. Constraint enforcement is formulated using a Lagrange multiplier method and a penalty regularization. The proposed approach satisfies key properties such as objectivity, symmetry, and consistency with an stress-free reference configuration. Numerical examples demonstrate the robustness and flexibility of the method for coupling beams with different formulations and discretizations, even when the interaction points are located at arbitrary positions within beam elements.

Tarik Sahin, Jacopo Bonari, Sebastian Brandstaeter et al.

The effective contact area in rough surface contact plays a critical role in multi-physics phenomena such as wear, sealing, and thermal or electrical conduction. Although accurate numerical methods, like the Boundary Element Method (BEM), are available to compute this quantity, their high computational cost limits their applicability in multi-query contexts, such as uncertainty quantification, parameter identification, and multi-scale algorithms, where many repeated evaluations are required. This study proposes a surrogate modeling framework for predicting the effective contact area using fast-to-evaluate data-driven techniques. Various machine learning algorithms are trained on a precomputed dataset, where the inputs are the imposed load and statistical roughness parameters, and the output is the corresponding effective contact area. All models undergo hyperparameter optimization to enable fair comparisons in terms of predictive accuracy and computational efficiency, evaluated using established quantitative metrics. Among the models, the Kernel Ridge Regressor demonstrates the best trade-off between accuracy and efficiency, achieving high predictive accuracy, low prediction time, and minimal training overhead-making it a strong candidate for general-purpose surrogate modeling. The Gaussian Process Regressor provides an attractive alternative when uncertainty quantification is required, although it incurs additional computational cost due to variance estimation. The generalization capability of the Kernel Ridge model is validated on an unseen simulation scenario, confirming its ability to transfer to new configurations. Database generation constitutes the dominant cost in the surrogate modeling process. Nevertheless, the approach proves practical and efficient for multi-query tasks, even when accounting for this initial expense.

Marco Mattuschka, Jacopo Bonari, Max von Danwitz et al.

In an act of sabotage or terrorism, hazardous material might be released deliberately into the atmosphere to threaten individuals, e.g., those operating critical infrastructure. Hazardous materials in such a scenario include toxic industrial chemicals (TICs), which are often invisible to the human eye, making it difficult to detect and respond to releases in a timely manner. This contribution considers the scenario of an airborne hazardous release requiring rapid and reliable assessment, with a chemical, biological, radiological, and nuclear (CBRN) sensor system providing scarce and local measurements. We present a novel algorithm that couples these data with an advection-diffusion model to detect, localize, and quantify a moving and time-varying contaminant source. Unlike many existing methods, the approach identifies sources with unknown occurrence time and trajectory by incorporating spatial sparsity as prior information. The feasibility of the approach is demonstrated in a two-dimensional computational domain. To further increase the technology readiness level, we additionally propose a calibration methodology for the required three-dimensional flow models based on wind tunnel experiments. Finally, a strategy for coupling the framework with real-time sensor data within a digital twin environment is outlined to enable predictive decision support in emergency scenarios.