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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.
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 flexibil- ity and quality of a process. Typically, before producing a whole additive manufacturing structure, a simplified experiment in form of a bead-on- 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 devel- oped, 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 tem- perature. 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.
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.
FenicsXConcrete
(2023)
FAIR (findable, accessible, interoperable and reusable) data usage is one of the main principals that many of the research and funding organizations include in their strategic plans, which means that following the main principals of FAIR data is required in many research projects. The definition of data being FAIR is very general. When implementing that for a specific application or project or even setting a standardized procedure within a working group, a company or a research community, many challenges arise. In this contribution, an overview about our experience with different methods and tools is outlined.
We begin with a motivation on potential use cases for the application of FAIR data with increasing complexity starting from a reproducible research paper over collaborative projects with multiple participants such as Round-Robin tests up to data-based models within standardization codes, applications in machine learning or parameter estimation of physics-based simulation models.
In a second part, different options for structuring the data (including metadata schema) are discussed. The first one is the openBIS system, which is an open-source lab notebook and PostgreSQL based data management system. A second option is a semantic representation using RDF based on ontologies for the domain of interest.
In a third section, requirements for workflow tools to automate data processing are discussed and their integration into reproducible data analysis is presented with an outlook on required information to be stored as metadata in the database.
Finally, the presented procedures are exemplarily demonstrated for the calibration of a temperature dependent constitutive model for additively manufactured mortar. A metadata schema for a rheological measurement setup is derived and implemented in an openBIS database. After a short review of a potential numerical model predicting the structural build-up behavior, the automatic workflow to use the stored data for model parameter estimation is demonstrated.
FAIR (findable, accessible, interoperable and reusable) data usage is one of the main principals that many of the research and funding organizations include in their strategic plans, which means that following the main principals of FAIR data is required in many research projects. The definition of data being FAIR is very general, and when implementing that for a specific application or project or even setting a standardized procedure within a working group, a company or a research community, many challenges arise. In this contribution, an overview about our experience with different methods, tools and procedures is outlined.
We begin with a motivation on potential use cases for the applications of FAIR data with increasing complexity starting from a reproducible research paper over collaborative projects with multiple participants such as Round-Robin tests up to data-based models within standardization codes, applications in machine learning or parameter estimation of physics-based simulation models.
In a second part, different options for structuring the data are discussed. On the one hand, this includes a discussion on how to define actual data structures and in particular metadata schema, and on the other hand, two different systems for storing the data are discussed. The first one is the openBIS system, which is an open-source Lab notebook and PostgreSQL based data management system. A second option are a semantic representations using RDF based ontologies for the domain of interest.
In a third section, requirements for workflow tools to automate data processing are discussed and their integration into reproducible data analysis is presented with an outlook on required information to be stored as metadata in the database.
Finally, the presented procedures are exemplarily demonstrated for the calibration of a temperature dependent constitutive model for additively manufactured mortar. Metadata schemata for a rheological measurement setup are derived and implemented in an openBIS database. After a short review of a potential numerical model predicting the structural build-up behaviour, the automatic workflow to use the stored data for model parameter estimation is demonstrated.
PGDrome
(2023)
Structural build-up describes the stability and early-age strength development of fresh mortar used in 3D printing. lt is influenced by several factors, i.e. the composition of the print able material, the printing regime, and the ambient conditions. The existing modelling approaches for structural build-up usually define the model parameters for a specific material composition with out considering the influence of the ambient conditions. The goal of this contribution is to explicitly include the temperature dependency in the modelling approach. Temperature changes have signifi cant impact on the structural build-up process: an increase of the temperature leads to a faster dissol ution of cement phases and accelerates hydration. The proposed extended model includes temperature dependency using the Arrhenius theory. The new model parameters are successfully calibrated based on Viskomat measurement data using Bayesian inference. Furthermore, a higher impact of the temperature in the re-flocculation as in the structuration stage is observed.
For extrusion-based 3D concrete printing, the early age mechanical behavior is influenced by various time dependent phenomena: structural build-up, plasticity as well as viscosity. The structural build-up is governing the stability and early-age strength development of the fresh printable cementitious materials and with that influencing the printability, buildability, and open time of the printing process. Generally, it is influenced by a number of factors, i.e. composition of the printable material, printing regime, and ambient conditions (temperature, humidity, etc.). There are several approaches to model the structural build-up of cementitious materials. All models are based on a time-dependent internal structural parameter describing the flocculation state, which is assumed to be zero after mixing and increases with time. The approaches differ in the definition of the time dependency (linear, exponential, bi-linear). Usually, the parameters are defined for a specific material composition without considering the influence of ambient conditions.
In this contribution, the bi-linear structural build-up model [Kruger et al., Construction and Building Materials 224, 2019] is extended by the temperature influence. Temperature changes will occur in real life printing processes due to changing ambient conditions (summer, winter, day, night) as well as the printing process (pressure changes etc.) and have a significant impact on the structural build-up process: an increase of the temperature leads to a faster dissolution of cement phases, accelerates hydration and boosts the Brownian motion. For that reason, the model parameters are simulated as temperature dependent using an Arrhenius function. Furthermore, the proposed extended model is calibrated based on measurement data using Bayesian inference. A very good agreement of the predicted model data with the measured control data was reached. Additionally, the structural build-up model is integrated into a viscoelastic and elastoplastic mechanical model, simulating the whole mechanical behavior during layer deposition.