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arXiv 2025年

作者： Bürchner, Tim Radtke, Lars Kopp, Philipp Computational Modeling and Simulation Technische Universität München Germany Institute for Ship Structural Design and Analysis Technische Universität Hamburg Germany Chair of Data Science in Civil Engineering Bauhaus-Universität Weimar Germany

Immersed boundary finite element methods allow the user to bypass the potentially troublesome task of boundary-conforming mesh generation. However, they suffer from the influence of cut elements, i.e., elements that are intersected by the physical domain boundaries. When combined with explicit time integration, poorly cut elements with little support in the physical domain have a detrimental effect on the critical time step size, thereby hampering the application of immersed boundary methods to wave propagation simulations. In this paper, we investigate the stabilizing effect of the finite cell method concerning explicit time integration. Starting with an analytical solution of an example with one degree of freedom, we systematically study the influence of α-stabilization on the maximum eigenvalue and thus on the critical time step size. The analysis is then complemented by a numerical study of an example with one element and an increasing polynomial degree. We demonstrate that the critical time step size does not decrease below a certain limit, even when further reducing the cut fraction of the element. This minimum critical time step size is controlled by the chosen α value and becomes less severe for higher dimensions. Increasing the polynomial degree has little effect on the degradation of the minimum critical time step size. Finally, we provide an estimate of the minimum critical time step size depending on the chosen stabilization parameter α and the dimension of the problem. Based on this estimate, we propose a modified CFL condition for the finite cell method, the validity of which we demonstrate on a numerical example of a perforated plate. © 2025, CC BY.

关键词： Boundary element method

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A new lattice Boltzmann scheme for linear elastic solids: periodic problems

arXiv

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arXiv 2022年

作者： Boolakee, Oliver Geier, Martin De Lorenzis, Laura Department of Mechanical and Process Engineering ETH Zürich Zürich8092 Switzerland Institute for Computational Modeling in Civil Engineering TU Braunschweig Braunschweig38106 Germany

We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a standard velocity set and avoids any recourse to finite difference approximations. As a result, all computational benefits of the lattice Boltzmann method can be used to full capacity. The novel scheme is systematically derived using the asymptotic expansion technique and a detailed analysis of the leading-order error behavior is provided. As demonstrated by a linear stability analysis, the method is stable for a very large range of Poisson's ratios. We consider periodic problems to focus on the governing equations and rule out the influence of boundary conditions. The analytical derivations are verified by numerical experiments and convergence studies. © 2022, CC BY.

关键词： Distribution functions

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Parameter identification and uncertainty propagation of hydrogel coupled diffusion-deformation using POD-based reduced-order modeling

arXiv

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arXiv 2024年

作者： Agarwal, Gopal Urrea-Quintero, Jorge-Humberto Wessels, Henning Wick, Thomas Leibniz University Hannover Institut für Angewandte Mathematik Welfengarten 1 Hannover Lower Saxony30167 Germany Technische Universtität Braunschweig Institute for Computational Modeling in Civil Engineering Pockelsstr. 3 Braunschweig Lower Saxony38106 Germany

This study explores reduced-order modeling for analyzing the time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in which chemical potential and displacements are coupled. This system is formulated in a monolithic fashion and solved using the finite element method. We employ proper orthogonal decomposition as a model order reduction approach. The reduced-order model performance is tested through a benchmark problem on hydrogel swelling and a case study simulating co-axial printing. Then, we embed the reduced-order model into an optimization loop to efficiently identify the coupled problem’s material parameters using full-field data. Finally, a study is conducted on the uncertainty propagation of the material parameter. © 2024, CC BY.

关键词： Hydrogels

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A comparative analysis of transient finite-strain coupled diffusion-deformation theories for hydrogels

arXiv

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arXiv 2024年

作者： Urrea-Quintero, Jorge-Humberto Marino, Michele Wick, Thomas Nackenhorst, Udo Leibniz University Hannover IBNM - Institute of Mechanics and Computational Mechanics Appelstraße 9a Hannover Lower Saxony30167 Germany Technische Universtität Braunschweig iRMB - Institute for Computational Modeling in Civil Engineering Pockelsstr. 3 Braunschweig Lower Saxony38106 Germany Department of Civil Engineering and Computer Science Engineering University of Rome Tor Vergata Via del Politecnico 1 Rome00133 Italy Leibniz University Hannover Institut für Angewandte Mathematik Welfengarten 1 Hannover Lower Saxony30167 Germany

This work presents a comparative review and classification between some well-known thermodynamically consistent models of hydrogel behavior in a large deformation setting, specifically focusing on solvent absorption/desorption and its impact on mechanical deformation and network swelling. The proposed discussion addresses formulation aspects, general mathematical classification of the governing equations, and numerical implementation issues based on the finite element method. The theories are presented in a unified framework demonstrating that, despite not being evident in some cases, all of them follow equivalent thermodynamic arguments. A detailed numerical analysis is carried out where Taylor-Hood elements are employed in the spatial discretization to satisfy the inf-sup condition and to prevent spurious numerical oscillations. The resulting discrete problems are solved using the FEniCS platform through consistent variational formulations, employing both monolithic and staggered approaches. We conduct benchmark tests on various hydrogel structures, demonstrating that major differences arise from the chosen volumetric response of the hydrogel. The significance of this choice is frequently underestimated in the state-of-the-art literature but has been shown to have substantial implications on the resulting hydrogel behavior. © 2024, CC BY.

关键词： Finite element method

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Evaluation of the Mechanisms Acting on the Atlantic Meridional Overturning Circulation in CESM2 for the 1pctCO_(2) Experiment

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Journal of Atmospheric Science Research 2024年第1期7卷 40-58页

作者： Lívia Sancho Elisa Passos Marcio Cataldi Luiz Paulo de Freitas Assad Luiz Landau Laboratory of Computational Methods in Engineering Civil Engineering ProgramAlberto Luiz Coimbra Institute for Graduate Studies and Research in EngineeringFederal University of Rio de JaneiroRio de Janeiro21941-617Brazil Civil Engineering Program Alberto Luiz Coimbra Institute for Graduate Studies and Engineering ResearchFederal University of Rio de JaneiroRio de Janeiro21941-617Brazil Physical Oceanography Laboratory Department of Physical OceanographyFaculty of OceanographyRio de Janeiro State UniversityRio de Janeiro20559-900Brazil Climate System Monitoring and Modeling Laboratory Water Resources and Environmental EngineeringFluminense Federal University24020-140Brazil Regional Atmospheric Modeling Group(MAR) Physics of the EarthDepartment of PhysicsRegional Campus of International Excellence(CEIR)“Campus Mare Nostrum”University of MurciaMurcia30100Spain Department of Meteorology Institute of GeosciencesFederal University of Rio de JaneiroRio de Janeiro21941-617Brazil

The Atlantic Meridional Overturning Circulation(AMOC)is a crucial component of the Earth’s climate system due to its fundamental role in heat distribution,carbon and oxygen transport,and the *** climate components,such as the atmosphere and sea ice,influence the *** the physical mechanisms of those interactions is paramount to increasing knowledge about AMOC’s *** this study,the authors used outputs from the Community Earth System Model version 2 and observational data to investigate changes in theAMOC and the associated physical *** DECK experiments were evaluated:piControl and 1pctCO_(2),with an annual increase of 1%of atmospheric CO_(2).The analysis revealed a significant decrease in the AMOC,associated with changes in mixed layer depth and buoyancy in high latitudes of the North Atlantic,resulting in the shutdown of deep convection and potentially affecting the formation of North Atlantic Deep Water and Antarctic Bottom Water.A vital aspect observed in this study is the association between increased runoff and reduced water evaporation,giving rise to a positive feedback ***,the rates of freshwater spreading have intensified during this period,which could lead to an accelerated disruption of the AMOC beyond the projections of existing models.

关键词： AMOC Meridional cell Climate change Deep circulation CESM2 results CMIP6

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REDUCED AND ALL-AT-ONCE APPROACHES FOR MODEL CALIBRATION AND DISCOVERY IN computational SOLID MECHANICS

arXiv

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arXiv 2024年

作者： Römer, Ulrich Hartmann, Stefan Tröger, Jendrik-Alexander Anton, David Wessels, Henning Flaschel, Moritz De Lorenzis, Laura Institute for Acoustics and Dynamics Technische Universität Braunschweig Langer Kamp 19 Braunschweig38106 Germany Institute of Applied Mechanics Clausthal University of Technology Adolph-Roemer-Straße 2a Clausthal-Zellerfeld38678 Germany Institute for Computational Modeling in Civil Engineering Technische Universität Braunschweig Pockelsstraße 3 Braunschweig38106 Germany Computational Mechanics Group Eidgenössische Technische Hochschule Zürich Tannenstraße 3 Zürich8092 Switzerland

In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently re-emerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this context, new methods such as the virtual fields method and physics-informed neural networks have been developed as alternatives to the already established least-squares and finite element-based approaches. Moreover, model discovery problems are starting to emerge and can also be addressed in a parameter estimation framework. These developments call for a new unified perspective, which is able to cover both traditional parameter estimation methods and novel approaches in which the state variables or the model structure itself are inferred as well. Adopting concepts discussed in the inverse problems community, we distinguish between all-at-once and reduced approaches. With this general framework, we are able to structure a large portion of the literature on parameter estimation in computational mechanics – and we can identify combinations that have not yet been addressed, two of which are proposed in this paper. We also discuss statistical approaches to quantify the uncertainty related to the estimated parameters, and we propose a novel two-step procedure for identification of complex material models based on both frequentist and Bayesian principles. Finally, we illustrate and compare several of the aforementioned methods with mechanical benchmarks based on synthetic and real data. Copyright © 2024, The Authors. All rights reserved.

关键词： computational mechanics

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Spiking neural network for nonlinear regression

arXiv

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arXiv 2022年

作者： Henkes, Alexander Eshraghian, Jason K. Wessels, Henning Institute for Computational Modeling in Civil Engineering Technical University of Braunschweig Pockelsstr. 3 Braunschweig38106 Germany Department of Electrical and Computer Engineering University of California Santa Cruz 1156 High street Santa Cruz95064 United States

Spiking neural networks, also often referred to as the third generation of neural networks, carry the potential for a massive reduction in memory and energy consumption over traditional, second-generation neural networks. Inspired by the undisputed efficiency of the human brain, they introduce temporal and neuronal sparsity, which can be exploited by next-generation neuromorphic hardware. To open the pathway toward engineering applications, we introduce this exciting technology in the context of continuum mechanics. However, the nature of spiking neural networks poses a challenge for regression problems, which frequently arise in the modeling of engineering sciences. To overcome this problem, a framework for regression using spiking neural networks is proposed. In particular, a network topology for decoding binary spike trains to real numbers is introduced, utilizing the membrane potential of spiking neurons. As the aim of this contribution is a concise introduction to this new methodology, several different spiking neural architectures, ranging from simple spiking feedforward to complex spiking long short-term memory neural networks, are derived. Several numerical experiments directed towards regression of linear and nonlinear, history-dependent material models are carried out. A direct comparison with counterparts of traditional neural networks shows that the proposed framework is much more efficient while retaining precision and generalizability. All code has been made publicly available in the interest of reproducibility and to promote continued enhancement in this new domain. © 2022, CC BY.

关键词： Continuum mechanics

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An Inverse Neural Particle Method for Flow Field Reconstruction

引用

PAMM 2023年第1期22卷

作者： Henning Wessels Technical University of Braunschweig Institute for Computational Modeling in Civil Engineering Pockelsstr. 3 38106 Braunschweig

Physics-Informed Neural Networks (PINNs) are a novel discretization scheme for the solution of partial differential equations (PDEs), where a neural network is chosen as global ansatz function. The problem of solving the PDE is then cast as an optimization problem and addressed by training the neural network. PINNs have been promoted to perform particularly well in inverse problems. This contribution presents recent advances of the Neural Particle Method, an updated Lagrangian Physics-Informed Neural Network, in the inverse problem of reconstructing flow fields from sparse data.

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Towards model-guided feedback control of hydrogels bioprinting

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PAMM 2024年第3期24卷

作者： Jorge-Humberto Urrea-Quintero Henning Wessels Thomas Wick Institute for Computational Modeling in Civil Engineering Technische Universtität Braunschweig Braunschweig Germany Institute of Applied Mathematics Leibniz University Hannover Hannover Germany

This contribution addresses the problem of controlling the Degree of Crosslinking (DoC) in printed hydrogels through feedback control as a product quality indicator from a modeling approach. We set up a simulation that resembles co-axial printing of calcium-alginate (Ca-Alg) hydrogel as a case study. A well-known Ca-Alg gelation model composed of a set of nonlinear coupled diffusion-reactions equations is adopted as a high-fidelity model (HFM). A traditional proportional-integral (PI) controller is designed based on a reduced-order state-space linear model of the gelation process. The linear state-space model is identified from input-output data collected from the HFM. We formulate an optimization problem to find optimal PI controller parameters that minimize a closed-loop performance index. The PI controller is directly applied to the nonlinear diffusion-reaction model to guide the printing process towards a desired DoC. We show its efficacy via some numerical simulations.

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Inferring Displacement Fields from Sparse Measurements Using the Statistical Finite Element Method

arXiv

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arXiv 2022年

作者： Narouie, Vahab B. Wessels, Henning Römer, Ulrich Institute of Computational Modeling in Civil Engineering Technische Universität Braunschweig Pockelsstr. 3 Braunschweig38106 Germany Institut für Dynamik und Schwingungen Technische Universität Braunschweig Schleinitzstr. 20 Braunschweig38106 Germany

Nowadays, strain and displacement can be measured using techniques such as electronic speckle pattern interferometry and digital image correlation. However, usually, only some part of the domain of interest is accessible for measurement devices. In order to assess also inaccessible areas of the structure, a fundamental task for structural health monitoring is the inference of full-field displacements from sparse measurements. Another important task is the inference of mechanical stress from displacement or strain data. In computational mechanics, the link between such data and stress is established via constitutive models. A well-established approach for inferring full displacement and stress fields from possibly sparse data is to calibrate the parameter of a given constitutive model using a Bayesian update. After calibration, a (stochastic) forward simulation is conducted with the identified model parameters to resolve physical fields in regions that were not accessible to the measurement device. A shortcoming of model calibration is that the model is deemed to best represent reality, which is only sometimes the case, especially in the context of the aging of structures and materials. While this issue is often addressed with repeated model calibration, a different approach is followed in the recently proposed statistical Finite Element Method (statFEM). Instead of using Bayes’ theorem to update model parameters, the displacement is chosen as the stochastic prior and updated to fit the measurement data more closely. For this purpose, the statFEM framework introduces a so-called model-reality mismatch, parametrized by only three hyperparameters. This makes the inference of full-field data computationally efficient in an online stage: If the stochastic prior can be computed offline, solving the underlying partial differential equation (PDE) online is unnecessary. Compared to solving a PDE, identifying only three hyperparameters and conditioning the state on the sensor

关键词： computational efficiency

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