Thin‐walled composite structures are widely used in weight‐critical applications such as aircraft and spacecraft. However, ensuring the stability of such structures under various load cases remains a key challenge in their design and optimization. For omega‐stringer stiffened panels, the local buckling and postbuckling behavior are investigated using closed‐form analytical solutions. The stiffened panel under consideration consists of the skin plate with eccentrically attached stringer feet along the longitudinal sides of the panel, while the remaining part of the omega‐stringer is modeled by corresponding elastically restrained edges. The computational model is based on energy methods and approximates the postbuckling behavior near the bifurcation point using a simplified plate model. To evaluate the new analysis method, a comparison with the finite element analysis is being drawn. Compared to numerical methods, the present model reduces the computational effort, which is particularly advantageous in the design phase.
We consider systems of delay differential equations (DDEs), including a single delay and a quadratic right‐hand side. In a system, parameters are replaced by random variables to perform an uncertainty quantification. Thus the solution of the DDEs becomes a random process, which can be represented by a series of the generalised polynomial chaos. We investigate the application of the stochastic Galerkin method and stochastic collocation techniques to compute unknown coefficient functions of the series. Furthermore, existence and local stability of stationary solutions are discussed for each type of method. We present results of numerical computations in two illustrative examples: a logistic equation and an epidemiological model.
This paper investigates the effects of cube‐shaped neighborhoods in peridynamic theory as an alternative to the traditional spherical neighborhoods. We examine how different neighborhood geometries influence the behavior of various peridynamic formulations, including bond‐based models, state‐based formulations, and correspondence methods. The study reveals that cube‐shaped neighborhoods introduce significant anisotropic effects in standard peridynamic formulations due to directional bias in force calculations. A generalized bond constant is derived for the bond‐based model to maintain consistency with classical continuum mechanics when using cubic neighborhoods. Through numerical examples, including wave propagation and crack growth scenarios, we demonstrate that while cube‐shaped neighborhoods cause undesirable anisotropic behavior in traditional peridynamic models, correspondence‐based formulations remain unaffected due to their averaged deformation gradient approach. The results provide important insights for the selection of neighborhood shapes in peridynamic simulations and highlight the robustness of correspondence formulations against geometric variations in discretization choices.
Quantum computing utilizes the underlying principles of quantum mechanics to perform computations with unmatched performance capabilities. Rather than using classical bits, it operates on qubits, which can exist in superposition and entangled states. This enables the solution of problems that are considered intractable for classical computers. However, since qubits are realized by physical systems such as the spins of electrons, they are highly sensitive to environmental disturbances and hardware imperfections. To achieve reliable scaling and practical application in the future, addressing these errors is of utmost importance. Different classes of errors exist, such as coherent and incoherent errors, caused by imperfections in quantum operations or the decoherence of quantum states. They are inherently different, as they arise from either a lack of precision or intrinsic randomness. Current literature struggles to provide a unified framework that models both types of errors simultaneously. In this paper, an approach based on possibility theory—a theory of imprecise probabilities—is presented to model quantum uncertainty. Possibility theory is particularly useful for systems affected by both epistemic and aleatoric uncertainty, that is, uncertainty due to limited knowledge and uncertainty due to inherent randomness, respectively. By exploring noisy quantum algorithms within a possibilistic framework, different statements about robustness can be derived without requiring prior assumptions about the underlying noise model. Moreover, a possibilistic model enables the derivation of sampling criteria for guaranteed statistical performance and provides insight into the number of measurements required—an important consideration, given that such resources are costly in practice.
This work delves into the advancement of topology optimization techniques for buckling structures that are subject to size limitations. Conventional density‐based methods are prone to yielding intricate, fine‐scale geometries that are challenging to fabricate. To circumvent this challenge, this work imposes constraints on the density distribution and utilizes aggregation techniques to consolidate local volume constraints into a unified global restriction. This approach ensures a more uniform distribution of material throughout the structure, thereby reducing material clustering, avoiding excessively thin layers, and enhancing both the manufacturability and structural performance. Numerical examples are employed to optimize the topology of buckling structures with varying size constraint parameters. The optimization outcomes demonstrate that the proposed methods are capable of effectively achieving optimal topologies that exhibit enhanced stability and strength while adhering to the specified size constraints.
Traditional pedagogical setups in laboratories are often outdated and do not provide the necessary support for effective learning. Teaching fluid mechanics poses additional significant challenges, particularly due to the need to visualize invisible properties, like velocity vector fields (velocity) or scalar pressure fields in time‐dependent 3D spaces. In this context, the application constructive alignment (CA) promises a more holistic approach to achieving better learning success. Here, the intended learning outcomes (ILOs), the teaching‐learning activities (TLAs), and the learning outcome monitoring (LOM), are taken as an iterative process and the three parts have to be perfectly aligned. To rate the ILOs, a cognitive taxonomy should be used. In an engineering context, we prefer the structure of observed learning outcome (SOLO) taxonomy as it helps to clarify, whether an ILO addresses surface understanding, or deep understanding. This work features a work in progress modular augmented reality (AR) mobile application called the AR FLOW for interactive fluid mechanic experiments. This application allows students to access worksheets via QR codes and explore various levels of learning. Furthermore, they can later access the laboratories that are set up in an interactive level system that helps them discover all the features of a level. The easy implementation of this application into existing lectures and courses is supported by accompanying teaching materials based on the principles of CA, featuring clear ILOs, and assessment tasks (ATs) rephrased according to SOLO taxonomy.
In aerospace transportation and propulsion systems, shock‐induced flow separation has strong detrimental effects on the aerodynamic behavior and performance. To alleviate these effects, separation control is necessary. A commonly pursued approach uses vortex generators (VG) of different design to increase the momentum transfer within the boundary layer and thus make it less prone to separation. Different mechanical vortex generators, valued in aerospace engineering for their robustness and simplicity, as well as the more flexible and less drag‐penalty prone air‐jet vortex generators (AJVGs) have been studied. A large number of parameters influence the control effectiveness of these devices, amongst them geometrical parameters, flow parameters, and the array arrangement of multiple devices. The latter aspect is particularly relevant for AJVGs, which are small enough to allow for inter‐device spacings that enable interactions between the turbulent structures induced by neighboring AJVGs, and where the intensity of these interactions strongly influence the control effect. With this great number of control parameters, vortex generators may easily encounter off‐design conditions in engineering applications, where operating conditions vary and are not as clean as in a laboratory. An overview on the relevant control parameters is provided, both for mechanical vortex generators including microramps and microvanes and for air‐jet vortex generators. Then, influences of off‐design conditions are discussed on the basis of results from recent experimental and numerical studies. A joint analysis of this rich data set allows an in‐depth interpretation of observed flow phenomena and control effects. Finally, we assess the application potential of the investigated control devices.
Crystal plasticity simulations offer insights into the anisotropic deformation of polycrystalline materials such as metals and alloys. However, rate‐independent crystal plasticity models encounter the Taylor ambiguity, where the active slip systems and plastic slip magnitudes are not uniquely defined, posing well‐known numerical challenges [1]. Interior point methods, which smooth the problem via a barrier term, have recently emerged as a promising strategy for both small‐strain [2, 3] and large‐strain [4, 5] crystal plasticity frameworks. This contribution presents a finite‐strain crystal plasticity model based on an interior point [2, 3]. Distinctly from existing large‐strain IPM implementations, our approach incorporates sequential updates for slip system rotations, which are held constant during intermediate interior point iterations, significantly enhancing algorithmic robustness. The method is evaluated at the material point level for several test cases, and its predictions are shown to be consistent with established results from various crystal plasticity algorithms in the literature, such as those based on an augmented Lagrange method.
This work presents a stable time‐domain boundary element method for the acoustic wave equation in three‐dimensional unbounded domains. Other formulations of time‐domain boundary element methods based on retarded potential operators are known to exhibit stability issues, which often hinder their use in industrial contexts. We have investigated the stability properties of a Galerkin first‐kind boundary integral formulation for sound emission problems, where well‐posedness can be established in both the continuous and the discrete setting. Numerical experiments confirm the accuracy and convergence of the method. We assess long‐time stability through extensive simulations focusing on fine temporal resolutions and large time ranges. The proposed formulation is compared with two alternative approaches used in practice: a space‐time single‐layer potential approach and a semi‐discretized collocation method.
Chemo‐mechanically coupled phenomena such as stress‐driven diffusion and diffusion‐induced stresses are of high interest, for example, in battery materials and metals. In this work, a chemo‐mechanically fully coupled multiphase‐field model for a multicomponent system is derived and validated with a sharp interface solution. Ensuring mechanical compatibility, the model accounts for balance equations on singular surfaces and the Hadamard jump conditions. The models' capability to address stress‐driven diffusion and diffusion‐induced stresses is demonstrated through the presentation of an illustrative diffusion example.
This study presents a numerical investigation of passive scalar mixing in homogeneous isotropic turbulence (HIT). Different volumetric forcing schemes have been used in the literature, but the side effects are rarely discussed, either because these are assumed irrelevant or because it is too costly to conduct such an analysis with a high-fidelity model. In this study, we have used One-Dimensional Turbulence (ODT) model to compare forcing schemes at low Reynolds numbers (upto Re λ = 70 ${\rm Re}_{\lambda } = 70$ ). Our analysis reveals critical flaws in the linear forcing model when applied to ODT. While both schemes exhibit spectral deviations from direct numerical simulation (DNS), the stochastic forcing scheme demonstrates superior dynamic fidelity, better capturing the turbulent energy cascade. In contrast, the linear forcing scheme suffers from a non-physical energy deficit at large scales and is approximately 10 times more computationally expensive. These artefacts directly impact scalar mixing: The stochastic scheme produces classic, multi-scale intermittency, whereas linear forcing generates extreme gradients confined only at the dissipative scales. These results demonstrate that the choice of forcing is a critical modelling decision in ODT, leading to fundamentally different model-dependent artefacts in both turbulence dynamics and scalar mixing statistics, at least in low Reynolds number regimes.
Ice shelves are large ice masses floating on the ocean that are still connected to the inland ice of a glacier. Due to high elevations in the bathymetry, the ice shelf can be partially grounded. These areas are called ice rises that act as pinning points. Satellite images show that cracks often initiate at these locations, determining the position of the calving front, which is defined as the seaward margin of an ice shelf. To better understand the crack formation, three-dimensional fracture simulations are carried out. The crack is modeled using the phase field method for fracture, where an additional scalar field represents whether the material is intact or broken. Glacier ice can be described as a Maxwell-type material with a short-term elastic and long-term viscous behavior. In addition to the viscoelastic behavior, ice is a non-Newtonian fluid with a strain-thinning behavior characterized by Glen's flow law. Therefore, the viscosity of glacier ice is not constant; instead, it is influenced by the distribution of stress and temperature within the ice shelf. These material characteristics are taken into account in the crack simulation by incorporating a nonlinear viscosity. Finite strain theory is used to adequately represent the large strains and deformations typically found in ice shelves. This approach allows the simulation of crack initiation at pinning points and contributes to the understanding of ice shelf dynamics and calving processes.
This research focuses on the mechanical behavior and damage evolution of additively manufactured spinodoid metamaterials under quasi-static loading. Additive manufacturing (AM), especially laser powder bed fusion (LPBF), enables the fabrication of complex geometries from digital models and is particularly suited for architected materials like spinodoids. Spinodoid metamaterials are a class of architected metamaterials derived from spinodal decomposition principles and are particularly well suited for fabrication using AM techniques like LPBF. These structures possess tunable mechanical properties, such as direction-specific strength and smooth property gradation, making them promising for applications in aerospace, biomedical, and structural engineering. Spinodoid geometries are generated using Gaussian random fields (GRFs), which produce microstructures with spatially varying densities. These variations significantly influence the mechanical response under tensile and compressive load. The onset and progression of damage are crucial in determining how these structures deform. To achieve accurate predictions of mechanical behavior, the present study incorporates a damage model into the simulation framework. By integrating damage modeling techniques, the current study aims to establish a robust framework for simulating the performance of additively manufactured structures while underscoring the immense potential of spinodoid metamaterials for applications requiring customized mechanical properties. The integration of damage modeling enables precise predictions of mechanical performance, supporting the robust design of next-generation metamaterials. The findings are particularly relevant for industries that prioritize lightweight structures, biomedical implants, and energy absorption systems. This research lays the foundation for broader adoption by demonstrating a robust framework for designing innovative and customizable materials.
Accurate modeling of cyclic damage evolution is essential for predicting the long-term performance and durability of engineering materials and structures. Traditional simulation-based approaches, while physically rigorous, are computationally expensive, especially under complex loading histories. In this work, we present a physics-based machine learning ( ϕ ML $\phi{\rm ML}$ ) framework that integrates physical laws into neural network architectures to efficiently and reliably model cyclic damage evolution. The approach leverages high-fidelity data generated from one-dimensional phase-field simulations of brittle fracture under varying cyclic loading scenarios and material properties. The proposed ϕ ML $\phi{\rm ML}$ architecture incorporates two coupled feed-forward neural networks: one to predict the phase-field damage variable and another to compute the free energy, both trained jointly using a loss function that enforces thermodynamic consistency, energy dissipation, and irreversibility of damage under cyclic loading. The model's performance is evaluated across interpolation and extrapolation scenarios, including unseen loading paths and material parameters. Compared to a purely data-driven feed-forward neural network, the ϕ ML $\phi{\rm ML}$ model demonstrates significantly improved accuracy, robustness, and physical reliability, especially in predicting long, path-dependent loading histories. These results underscore the importance of embedding physics into machine learning for modeling degradation processes and highlight the potential of hybrid models as efficient, interpretable surrogates for complex numerical simulations.
During the manufacture of mechanical structures, their calculation and experimental investigation, deviations from the deterministic state arise, which are based on uncertainties in the mechanical parameters. The propagation of such uncertainties is evaluated in two experimental setups here. A four-point bending experiment with a notched specimen and its numerical simulation are considered first. The deviations due to inexact geometric parameters were estimated using Monte Carlo simulations and correlated with deviations in the numerical calculation due to unclear model parameters in the phase-field fracture approach. As a second example, the manufacturing process of rotary draw bending is investigated. Here, we focus on the condition for failure during the bending process, and the analysis considers the propagation of geometric uncertainties to the maximum strain and the influence of the uncertain material parameter on the uniform tensile elongation. Although the examples are greatly simplified, the method presented provides a strategy for robust predictions of variability, model verification, and safety assessment.
The microlayer framework is a novel, powerful method for the numerical simulation of heterogeneous materials, such as aggregate-matrix composites across different scales. While the framework has previously only been applied to geometrically isotropic aggregates, its mathematical formulation also enables the development of material models for aggregate-matrix composites with pronounced spatial directionality, an inherent characteristic of many materials in this class. In this work, a stepwise approach is adopted: first, simplified, non-uniformed shaped representative volume elements (RVEs) are studied to investigate their macroscopic behavior. Based on the limitations identified in this initial formulation, a refined RVE is then developed that satisfies both mathematical consistency and mechanical plausibility.
Unlike their crystalline counterparts, glasses have a complex structure that lacks any long-range order, resulting in the system possessing a large number of metastable states. The system transitions between these metastable states, giving rise to a complex mechanical response when subjected to mechanical deformation. These transitions manifest as localized atomic rearrangements, also known as plastic events. It has been postulated that certain regions that are prone to rearrangements can be identified in the stress-free configuration. Efforts to predict these regions have employed a wide range of methods, from computationally expensive local mechanical simulations to data-intensive machine learning techniques that require large training datasets. In contrast, we propose the use of the fabric tensor as a simple, geometry-based predictor for soft spots. The fabric tensor relies solely on atomic positions to characterize bond directionality within the system. We demonstrate a strong correlation between certain features of the fabric tensor and soft spots in two-dimensional silica samples generated using the Monte Carlo bond-switching algorithm and subjected to tension under athermal quasistatic conditions. These results show that a purely geometrical measure can effectively predict soft spots in disordered solids, independent of the underlying potential energy landscape.
Mathematical models for finite-strain poroelasticity in an Eulerian formulation are studied by constructing their energy-variational structure, which gives rise to a class of saddle-point problems. This problem is discretized using an incremental time-stepping scheme and a mixed finite element approach, resulting in a monolithic, structure-preserving discretization. The Eulerian formulation is based on the inverse deformation, the so-called reference map . We present examples from geophysical applications, where elasticity and diffusive fluid flow are fully coupled and can be used to describe porosity waves, i.e., localized ascending fluid waves driven by gravitational forces.
The pressure to reduce greenhouse gas emissions is growing, which demands new and innovative technologies to produce mobile as well as stationary energy. The CO 2 $\rm {CO_2}$ methanation offers a pathway to reduce greenhouse gas emissions by directly converting CO 2 $\rm {CO_2}$ to CH 4 $\rm {CH_4}$ . This also plays a crucial role in “power-to-gas” (P2G) technologies by providing an approach to store excess renewable energy in the form of methane in an existing natural gas infrastructure. However, methanation is a complex process due to its exothermic nature, interaction of the gas species with the catalyst, and possible catalyst degradation. Therefore, a deeper understanding is required for the methanation reaction, its different reaction pathways, and side reactions. In this work, we aim to understand the direct production of synthetic natural gas from CO 2 $\rm {CO_2}$ and H 2 $\rm {H_2}$ in a Sabatier process with the help of experiments over a Ni/ Al 2 O 3 $\rm {Al_2O_3}$ catalyst. A detailed surface reaction mechanism is developed to extend the study numerically by validating the simulation results with the experimental data. A one-dimensional model, LOGEcat, based on a single-channel catalyst model, is used for kinetic modeling. Experiments as well as simulations have been performed at various conditions, such as temperature variation and N 2 $\rm {N_2}$ dilution to the inlet composition. We have successfully captured the experimental trends using the kinetic model developed for the conditions considered for the analysis.
The conventional ring-spinning process has been used for over a century, being one of the most used processes in the textile industry. However, this process has some disadvantages at high spindle speeds, such as friction in the traveler/ring components that generates heat, resulting in yarn breakages or lower-quality production. New technological advances like superconducting magnetic bearings (SMB) systems have been implemented to face the limitations in the spindle speed. The SMBs use superconductors and permanent magnets (PM) to achieve magnetic levitation, decreasing in this way drastically the friction and enabling spindle speeds up to 50 000 rpm. Previous studies have investigated SMB dynamics, and it has been proved that the mathematical model for a six-dimensional motion can be reduced into a second-order ordinary system in matrix form that consists of mass, stiffness, and damping matrices, but due to the freedom given by the magnetic levitation, there is the presence of oscillations in the permanent magnet due to external forces. A recent study implemented an Eddy Current Damper (ECD) based on copper rings that increase the damping coefficients, resulting in the reduction of oscillations in the permanent magnet. This work analyzes the frequency response of the PM ring in an SMB system with ECDs of varying copper thicknesses, considering all motion directions. Theoretical results show that tilting modes exhibit frequency splitting due to gyroscopic effects. Experimental tests using laser sensors validated the model, and parametric identification was performed to estimate stiffness, damping, and external torque contributions.
