7.7 Modellierung und Simulation
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Paper des Monats
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Despite the advances in hardware and software techniques, standard numerical methods fail in providing real-time simulations, especially for complex processes such as additive manufacturing applications. A real-time simulation enables process control through the combination of process monitoring and automated feedback, which increases the flexibility and quality of a process. Typically, before producing a whole additive manufacturing structure, a simplified experiment in the form of a beadon-plate experiment is performed to get a first insight into the process and to set parameters suitably. In this work, a reduced order model for the transient thermal problem of the bead-on-plate weld simulation is developed, allowing an efficient model calibration and control of the process. The proposed approach applies the proper generalized decomposition (PGD) method, a popular model order reduction technique, to decrease the computational effort of each model evaluation required multiple times in parameter estimation, control, and optimization. The welding torch is modeled by a moving heat source, which leads to difficulties separating space and time, a key ingredient in PGD simulations. A novel approach for separating space and time is applied and extended to 3D problems allowing the derivation of an efficient separated representation of the temperature.
The results are verified against a standard finite element model showing excellent agreement. The reduced order model is also leveraged in a Bayesian model parameter estimation setup, speeding up calibrations and ultimately leading to an optimized real-time simulation approach for welding experiment using synthetic as well as real measurement data.
Multiscale modeling of linear elastic heterogeneous structures via localized model order reduction
(2023)
In this paper, a methodology for fine scale modeling of large scale linear elastic structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse scale is modelled by the use of an additive split of the displacement field, addressing applications without a clear scale separation. Local reduced spaces are constructed by solving an oversampling problem with random boundary conditions. Herein, we inform the boundary conditions by a global reduced problem and compare our approach using physically meaningful correlated samples with existing approaches using uncorrelated samples. The local spaces are designed such that the local contribution of each subdomain can be coupled in a conforming way, which also preserves the sparsity pattern of standard finite element assembly procedures. Several numerical experiments show the accuracy and efficiency of the method, as well as its potential to reduce the size of the local spaces and the number of training samples compared to the uncorrelated sampling.
Using digital twins for decision making is a very promising concept which combines simulation models with corresponding experimental sensor data in order to support maintenance decisions or to investigate the reliability. The quality of the prognosis strongly depends on both the data quality and the quality of the digital twin. The latter comprises both the modeling assumptions as well as the correct parameters of these models. This article discusses the challenges when applying this concept to realmeasurement data for a demonstrator bridge in the lab, including the data management, the iterative development of the simulation model as well as the identification/updating procedure using Bayesian inference with a potentially large number of parameters. The investigated scenarios include both the iterative identification of the structural model parameters as well as scenarios related to a damage identification. In addition, the article aims at providing all models and data in a reproducibleway such that other researcher can use this setup to validate their methodologies.
Numerical models built as virtual-twins of a real structure (digital-twins) are considered the future ofmonitoring systems. Their setup requires the estimation of unknown parameters, which are not directly measurable. Stochastic model identification is then essential, which can be computationally costly and even unfeasible when it comes to real applications. Efficient surrogate models, such as reduced-order method, can be used to overcome this limitation and provide real time model identification. Since their numerical accuracy influences the identification process, the optimal surrogate not only has to be computationally efficient, but also accurate with respect to the identified parameters. This work aims at automatically controlling the Proper Generalized Decomposition (PGD) surrogate’s numerical accuracy for parameter identification. For this purpose, a sequence of Bayesian model identification problems, in which the surrogate’s accuracy is iteratively increased, is solved with a variational Bayesian inference procedure. The effect of the numerical accuracy on the resulting posteriors probability density functions is analyzed through two metrics, the Bayes Factor (BF) and a criterion based on the Kullback-Leibler (KL) divergence. The approach is demonstrated by a simple test example and by two structural problems. The latter aims to identify spatially distributed damage, modeled with a PGD surrogate extended for log-normal random fields, in two different structures: a truss with synthetic data and a small, reinforced bridge with real measurement data. For all examples, the evolution of the KL-based and BF criteria for increased accuracy is shown and their convergence indicates when model refinement no longer affects the identification results.
The amount of data generated worldwide is constantly increasing. These data come from a wide variety of sources and systems, are processed differently, have a multitude of formats, and are stored in an untraceable and unstructured manner, predominantly in natural language in data silos. This problem can be equally applied to the heterogeneous research data from materials science and engineering. In this domain, ways and solutions are increasingly being generated to smartly link material data together with their contextual information in a uniform and well-structured manner on platforms, thus making them discoverable, retrievable, and reusable for research and industry. Ontologies play a key role in this context. They enable the sustainable representation of expert knowledge and the semantically structured filling of databases with computer-processable data triples.
In this perspective article, we present the project initiative Materials-open-Laboratory (Mat-o-Lab) that aims to provide a collaborative environment for domain experts to digitize their research results and processes and make them fit for data-driven materials research and development. The overarching challenge is to generate connection points to further link data from other domains to harness the promised potential of big materials data and harvest new knowledge.
In this paper, the imperialist competitive optimization algorithm is improved by damage functions to detect damage in a model steel frame test structure for offshore applications. A finite element model of the test structure is developed, validated and updated using the proposed method. As there are much more design variables, which are related to the stiffness of each finite element than the measured mode shapes, the problem is underdetermined. Therefore, damage functions are used to regularize the problem and decrease the number of design variables. A new objective function is proposed for the algorithm using the mode shapes and their l1 norm. The first ten measured mode shapes are used to solve the problem. It is shown that the proposed method is capable of predicting the damage locations with acceptable accuracy.
A three-phase transport model for high-temperature concrete simulations validated with X-ray CT data
(2021)
Concrete exposure to high temperatures induces thermo-hygral phenomena, causing water phase changes, buildup of pore pressure and vulnerability to spalling. In order to predict these phenomena under various conditions, a three-phase transport model is proposed. The model is validated on X-ray CT data up to 320 ◦C, showing good agreement of the temperature profiles and moisture changes. A dehydration description, traditionally derived from thermogravimetric analysis, was replaced by a formulation based on data from neutron radiography. In addition, treating porosity and dehydration evolution as independent processes, previous approaches do not fulfil the solid mass balance. As a consequence, a new formulation is proposed that introduces the porosity as an independent variable, ensuring the latter condition.
Simulating high-cycle fatigue with continuum models offers the possibility to model stress-redistributions, consider 3Dstress states and simplifies extensions to multi-physics problems. The computational cost of conventional cycle-by-cycle time integrations is reduced by reformulating the fatigue problem as an ordinary differential equation for the material state and solving it with high-order adaptive time integration schemes. The computational cost of calculating the Change of the material state in one cycle is further reduced by a high-order fatigue-specific time integration. The approach is exemplarily demonstrated for a fatigue extension of the implicit gradient-enhanced damage model in 3D and compared to experimental Wöhler lines.
In this paper, the impact problem and the subsequent wave Propagation are considered. For the contact discretization an intermediate non-uniform rational B-spline (NURBS) layer is added between the contacting finite element bodies, which allows a smooth contact formulation and efficient element-based integration.
The impact event is ill-posed and requires a regularization to avoid propagating stress oscillations. A nonlinear mesh-dependent penalty regularization is used, where the stiffness of the penalty regularization increases upon mesh refinement. Explicit time integration methods are well suited for wave propagation problems, but are efficient only for diagonal mass matrices. Using a spectral element discretization in combination with a NURBS contact layer the bulk part of the mass matrix is diagonal.
In this paper, the impact problem and the subsequent wave propagation are considered. For the contact discretization an intermediate NURBS layer is added between the contacting finite element bodies, which allows a smooth contact formulation and efficient element‐based integration. The impact event is ill‐posed and requires a regularization to avoid propagating stress oscillations. A nonlinear mesh dependent penalty regularization is used, where the stiffness of the penalty regularization increases upon mesh refinement. Explicit time integration methods are well suited for wave propagation problems, but are efficient only for diagonal mass matrices. Using a spectral element discretization and the coupled FE‐NURBS approach the bulk part of the mass matrix is diagonal.