GAMM Mitteilungen最新文献

{"title":"Physics-based modeling and predictive simulation of powder bed fusion additive manufacturing across length scales","authors":"Christoph Meier,&nbsp;Sebastian L. Fuchs,&nbsp;Nils Much,&nbsp;Jonas Nitzler,&nbsp;Ryan W. Penny,&nbsp;Patrick M. Praegla,&nbsp;Sebastian D. Proell,&nbsp;Yushen Sun,&nbsp;Reimar Weissbach,&nbsp;Magdalena Schreter,&nbsp;Neil E. Hodge,&nbsp;A. John Hart,&nbsp;Wolfgang A. Wall","doi":"10.1002/gamm.202100014","DOIUrl":"10.1002/gamm.202100014","url":null,"abstract":"<p>Powder bed fusion additive manufacturing (PBFAM) of metals has the potential to enable new paradigms of product design, manufacturing and supply chains while accelerating the realization of new technologies in the medical, aerospace, and other industries. Currently, wider adoption of PBFAM is held back by difficulty in part qualification, high production costs and low production rates, as extensive process tuning, post-processing, and inspection are required before a final part can be produced and deployed. Physics-based modeling and predictive simulation of PBFAM offers the potential to advance fundamental understanding of physical mechanisms that initiate process instabilities and cause defects. In turn, these insights can help link process and feedstock parameters with resulting part and material properties, thereby predicting optimal processing conditions and inspiring the development of improved processing hardware, strategies and materials. This work presents recent developments of our research team in the modeling of metal PBFAM processes spanning length scales, namely mesoscale powder modeling, mesoscale melt pool modeling, macroscale thermo-solid-mechanical modeling and microstructure modeling. Ongoing work in experimental validation of these models is also summarized. In conclusion, we discuss the interplay of these individual submodels within an integrated overall modeling approach, along with future research directions.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89448242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Additive manufacturing applications of phase-field-based topology optimization using adaptive isogeometric analysis","authors":"Massimo Carraturo,&nbsp;Paul Hennig,&nbsp;Gianluca Alaimo,&nbsp;Leonhard Heindel,&nbsp;Ferdinando Auricchio,&nbsp;Markus Kästner,&nbsp;Alessandro Reali","doi":"10.1002/gamm.202100013","DOIUrl":"10.1002/gamm.202100013","url":null,"abstract":"In this contribution, we apply adaptive isogeometric analysis to a diffuse interface model for topology optimization. First, the influence of refinement and coarsening parameters on the optimization procedure are evaluated and discussed on a two‐dimensional problem and a possible workflow to convert smooth isogeometric solutions into 3D printed products is described. Second, to assess the required numerical accuracy of the proposed simulation framework, numerical results obtained adopting different stopping criteria are experimentally evaluated for a three‐dimensional benchmark problem.","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88085321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling crystallization kinetics for selective laser sintering of polyamide 12","authors":"Dominic Soldner,&nbsp;Paul Steinmann,&nbsp;Julia Mergheim","doi":"10.1002/gamm.202100011","DOIUrl":"10.1002/gamm.202100011","url":null,"abstract":"<p>Selective laser sintering (SLS) of polymers represents a widely used additive manufacturing process, where the part quality depends highly on the present thermal conditions. One distinct feature of SLS is the existence of separate temperature regions for melting and crystallization (solidification) and that the process optimally operates within said regions. Typically a crystallization model, such as the Nakamura model, is used to predict the degree of crystallization as a function of temperature and time. One limitation of this model is the inability to compute negative rates of the crystallization degree during remelting. As we will show in this work, such an extension is necessary, considering the varying temperature fields appearing in SLS. To this end, an extension is proposed and analyzed in detail. Furthermore, a dependency of the temperature and crystallization fields on the size of geometrical features is presented.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73292022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Accessing pore microstructure–property relationships for additively manufactured materials","authors":"Alexander Raßloff,&nbsp;Paul Schulz,&nbsp;Robert Kühne,&nbsp;Marreddy Ambati,&nbsp;Ilja Koch,&nbsp;André T. Zeuner,&nbsp;Maik Gude,&nbsp;Martina Zimmermann,&nbsp;Markus Kästner","doi":"10.1002/gamm.202100012","DOIUrl":"10.1002/gamm.202100012","url":null,"abstract":"<p>Understanding structure–property (SP) relationships is essential for accelerating materials innovation. Still being in the state of ongoing research and development, this is especially true for additive manufacturing (AM) in which process-induced imperfections like pores and microstructural variations significantly influence the material's properties. That is why, the present work aims at proposing an approach for accessing pore SP relationships for AM materials. For this purpose, crystal plasticity (CP) simulations on reconstructed domains based on experimental measurements are employed to allow for a microstructure-sensitive investigation. For the considered Ti–6Al–4V specimen manufactured by laser powder bed fusion, the microstructure and pore characteristics are obtained by utilizing light microscopy and X-ray computed tomography at the microscale. Employing suitable statistical analysis and reconstruction, statistical volume elements with reconstructed pore distributions are created. Using them, microscale CP simulations are performed to obtain fatigue indicating parameters. Employing a further statistical analysis, fatigue ranking parameters are derived for a comparison of different microstructures. Additionally, a comparison with the empirical <span>Murakami</span>'s square root area concept is made. Results from first numerical studies underline the potential of the approach for understanding and improving AM materials.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89507082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Structured learning of rigid-body dynamics: A survey and unified view from a robotics perspective","authors":"A. René Geist,&nbsp;Sebastian Trimpe","doi":"10.1002/gamm.202100009","DOIUrl":"10.1002/gamm.202100009","url":null,"abstract":"<p>Accurate models of mechanical system dynamics are often critical for model-based control and reinforcement learning. Fully data-driven dynamics models promise to ease the process of modeling and analysis, but require considerable amounts of data for training and often do not generalize well to unseen parts of the state space. Combining data-driven modeling with prior analytical knowledge is an attractive alternative as the inclusion of structural knowledge into a regression model improves the model's data efficiency and physical integrity. In this article, we survey supervised regression models that combine rigid-body mechanics with data-driven modeling techniques. We analyze the different latent functions (such as kinetic energy or dissipative forces) and operators (such as differential operators and projection matrices) underlying common descriptions of rigid-body mechanics. Based on this analysis, we provide a unified view on the combination of data-driven regression models, such as neural networks and Gaussian processes, with analytical model priors. Furthermore, we review and discuss key techniques for designing structured models such as automatic differentiation.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82587375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topical issue scientific machine learning (2/2)","authors":"Peter Benner,&nbsp;Axel Klawonn,&nbsp;Martin Stoll","doi":"10.1002/gamm.202100010","DOIUrl":"10.1002/gamm.202100010","url":null,"abstract":"We already have illustrated in the first issue [1] of this series that the emerging field of scientific machine learning is penetrating traditional fields within scientific computing and beyond. The second issue in this series is also devoted to demonstrating this rapid change. In this part of our special issue of the GAMM Mitteilungen, we continue the presentation of contributions on the topic of scientific machine learning in the context of complex applications across the sciences and engineering. We are pleased that again four teams of authors have accepted our invitation and are now illustrating their insights into recent research highlights as well as pointing the reader to the relevant literature and software. The four papers in this second part of the special issue are:","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82548710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Three ways to solve partial differential equations with neural networks — A review","authors":"Jan Blechschmidt,&nbsp;Oliver G. Ernst","doi":"10.1002/gamm.202100006","DOIUrl":"10.1002/gamm.202100006","url":null,"abstract":"<p>Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and their suitability for high-dimensional problems: physics-informed neural networks, methods based on the Feynman–Kac formula and methods based on the solution of backward stochastic differential equations. The article is accompanied by a suite of expository software in the form of Jupyter notebooks in which each basic methodology is explained step by step, allowing for a quick assimilation and experimentation. An extensive bibliography summarizes the state of the art.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79161983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution","authors":"Omer San,&nbsp;Adil Rasheed,&nbsp;Trond Kvamsdal","doi":"10.1002/gamm.202100007","DOIUrl":"10.1002/gamm.202100007","url":null,"abstract":"<p>Most modeling approaches lie in either of the two categories: physics-based or data-driven. Recently, a third approach which is a combination of these deterministic and statistical models is emerging for scientific applications. To leverage these developments, our aim in this perspective paper is centered around exploring numerous principle concepts to address the challenges of (i) trustworthiness and generalizability in developing data-driven models to shed light on understanding the fundamental trade-offs in their accuracy and efficiency and (ii) seamless integration of interface learning and multifidelity coupling approaches that transfer and represent information between different entities, particularly when different scales are governed by different physics, each operating on a different level of abstraction. Addressing these challenges could enable the revolution of digital twin technologies for scientific and engineering applications.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73578201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An introduction to deep generative modeling","authors":"Lars Ruthotto,&nbsp;Eldad Haber","doi":"10.1002/gamm.202100008","DOIUrl":"10.1002/gamm.202100008","url":null,"abstract":"<p>Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions using samples. When trained successfully, we can use the DGM to estimate the likelihood of each observation and to create new samples from the underlying distribution. Developing DGMs has become one of the most hotly researched fields in artificial intelligence in recent years. The literature on DGMs has become vast and is growing rapidly. Some advances have even reached the public sphere, for example, the recent successes in generating realistic-looking images, voices, or movies; so-called deep fakes. Despite these successes, several mathematical and practical issues limit the broader use of DGMs: given a specific dataset, it remains challenging to design and train a DGM and even more challenging to find out why a particular model is or is not effective. To help advance the theoretical understanding of DGMs, we introduce DGMs and provide a concise mathematical framework for modeling the three most popular approaches: normalizing flows, variational autoencoders, and generative adversarial networks. We illustrate the advantages and disadvantages of these basic approaches using numerical experiments. Our goal is to enable and motivate the reader to contribute to this proliferating research area. Our presentation also emphasizes relations between generative modeling and optimal transport.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79434409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Classification and image processing with a semi-discrete scheme for fidelity forced Allen–Cahn on graphs","authors":"Jeremy Budd,&nbsp;Yves van Gennip,&nbsp;Jonas Latz","doi":"10.1002/gamm.202100004","DOIUrl":"10.1002/gamm.202100004","url":null,"abstract":"<p>This paper introduces a semi-discrete implicit Euler (SDIE) scheme for the Allen-Cahn equation (ACE) with fidelity forcing on graphs. The continuous-in-time version of this differential equation was pioneered by Bertozzi and Flenner in 2012 as a method for graph classification problems, such as semi-supervised learning and image segmentation. In 2013, Merkurjev et. al. used a Merriman-Bence-Osher (MBO) scheme with fidelity forcing instead, as heuristically it was expected to give similar results to the ACE. The current paper rigorously establishes the graph MBO scheme with fidelity forcing as a special case of an SDIE scheme for the graph ACE with fidelity forcing. This connection requires the use of the double-obstacle potential in the ACE, as was already demonstrated by Budd and Van Gennip in 2020 in the context of ACE without a fidelity forcing term. We also prove that solutions of the SDIE scheme converge to solutions of the graph ACE with fidelity forcing as the discrete time step converges to zero. In the second part of the paper we develop the SDIE scheme as a classification algorithm. We also introduce some innovations into the algorithms for the SDIE and MBO schemes. For large graphs, we use a QR decomposition method to compute an eigendecomposition from a Nyström extension, which outperforms the method used by, for example, Bertozzi and Flenner in 2012, in accuracy, stability, and speed. Moreover, we replace the Euler discretization for the scheme's diffusion step by a computation based on the Strang formula for matrix exponentials. We apply this algorithm to a number of image segmentation problems, and compare the performance with that of the graph MBO scheme with fidelity forcing. We find that while the general SDIE scheme does not perform better than the MBO special case at this task, our other innovations lead to a significantly better segmentation than that from previous literature. We also empirically quantify the uncertainty that this segmentation inherits from the randomness in the Nyström extension.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/gamm.202100004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90961049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}