[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118151-en":3,"doc-seo-118151-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118151,8796095462418,"Noah","https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780",8,"Research & Report","A physically-informed machine learning model for freeform bending - Process model and Timoshenko beam theory","A physically-informed machine learning process model is developed to accelerate free-form bending predictions. The approach trains a regression model on experimental bending data for constant radii while embedding additional physics through Timoshenko’s beam theory. An elastic beam-theory representation of tube deformation is computed at each time step and used as input for a partially connected neural network to estimate plastic deformation after the tube exits the die. The method generalizes from constant training radii to transitional and true spline bending geometries, improving accuracy for complex kinematics and reducing computation time by four orders of magnitude versus finite element benchmarks.","A physically-informed machine learning model for freeform bending  \nPhilipp Lechner1,2 · Lorenzo Scandola3 · Daniel Maier3 · Christoph Hartmann3 · Yevgen Rizaiev3 · Mona Lieb3  \nReceived: 2 November 2023 / Accepted: 17 May 2024 © The Author(s) 2024  \nAbstract  \nThis work aims ata fast computational process model ofthe free-form bending process. It proposesa novel physically-informed machine learning model, which is trained with experimental data of bending constant radii and utilizes additional physical bending knowledge by integrating Timoshenko’s beam theory. The model is able to predict the resulting plastic deformation of the tube after exiting the die by computing an elastic representation of the tube’s deformation with beam theory at each time step. This elastic representation serves as input for a regression model similar to a partially connected neural network. This physically-informed machine learning model generalizes the constant training radii to complex bend geometries consisting of transitional sections and true spline geometries. It is compared to a benchmark finite element simulation and has an improved prediction quality for complex kinematics while reducing the computation time by four orders of magnitude.  \nKeywords Freeform bending · Physically-informed neural networks · process model · Surrogate model · Geometry prediction  \nIntroduction  \nFreeform bending is a kinematically-controlled bending process that can create complex 3D geometries. In addition to  \nPhilipp Lechner and Lorenzo Scandola have contributed equally to this work.  \nB Philipp Lechner [philipp.lechner@uni-a.de](philipp.lechner@uni-a.de)  \nLorenzo Scandola  \n[lorenzo.scandola@utg.de](lorenzo.scandola@utg.de)  \nDaniel Maier  \n[daniel.maier@utg.de](daniel.maier@utg.de)  \nChristoph Hartmann  \n[christoph.hartmann@utg.de](christoph.hartmann@utg.de)  \nYevgen Rizaiev  \n[yevgen.rizaiev@tum.de](yevgen.rizaiev@tum.de)  \nMona Lieb  \n[mona.lieb@tum.de](mona.lieb@tum.de)  \n1 Institute of Materials Resource Management, University of Augsburg, Am Technologiezentrum 8, 86159 Augsburg, Germany  \n2 Centre for Advanced Analytics and Predictive Sciences, University of Augsburg, Universitätsstraße 2, 86159 Augsburg, Germany  \n3 Technical University of Munich, Walther-Meissner-Strasse 4, 85748 Garching, Germany  \narc-shaped geometries, it also allows the bending of pure 3Dsplines. On the other hand, this increased flexibility requires a more complex design of the bending head kinematics and amore advanced set of tools to design the bending kinematics. When predicting bending processes, a distinction is made between simulations based on the physics of the process and data-based modeling.  \nPhysics-based process simulation  \nFor freeform bending processes of metal tubes, the literature mainly contains simulations and analytical approaches that predict the geometry or the stress states. Simulative approaches are listed first. Maier et al. (2021) use a numerical simulation model of freeform bending with a moving die. By varying the degrees of freedom of the machine, the simulation allows the computation of geometry and residual stresses. Stebner et al. (2021) deal with the development of a soft sensor that can derive mechanical properties of a bent tube as a basis for control. Accordingly, a simulation model for the freeform bending of tubes with a moving die is developed. Based on plasticity theories, Wang and Agarwal(2006) develop analytical models to predict the cross-sectional distortion and thickness change of tubes under different loading conditions. The publication of Zhang and Wu (2016) focuses on the simulation of bending and springback processes in  \n1 3  \ntube bending. The verification of the results is done by the finite element method(FEM). A variety ofapproaches use the finite element method to predict the bending process. Gantner et al. (2004), deal with the finite element (FE) simulation of complex bending processes using a non-linear simulation programme. E","cbCaiukGtmYmcbVZ","https://ap.wps.com/l/cbCaiukGtmYmcbVZ","pdf",1577318,1,13,"English","en",105,"# Abstract\n# Introduction\n## Physics-based process simulation\n## Data-based process models and hybrid approaches","[{\"question\":\"How does the physically-informed model incorporate physics into machine learning?\",\"answer\":\"It integrates additional bending knowledge by using Timoshenko’s beam theory, computing an elastic representation of tube deformation at each time step as ML input.\"},{\"question\":\"What experimental data is used for training the model?\",\"answer\":\"The model is trained with experimental data of bending constant radii, then adapted to more complex bend geometries.\"},{\"question\":\"How is the model evaluated and what performance benefit is reported?\",\"answer\":\"It is compared against a benchmark finite element simulation, showing improved prediction quality for complex kinematics while reducing computation time by four orders of magnitude.\"}]","A physically-informed machine learning model for freeform bending - Process model and Timoshenko beam theory | PDF",1785681896,33,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"a-physically-informed-machine-learning-model-for-freeform-bending-process-model-and-timoshenko-beam-theory","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/a-physically-informed-machine-learning-model-for-freeform-bending-process-model-and-timoshenko-beam-theory/118151/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-02",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"How does the physically-informed model incorporate physics into machine learning?","Question",{"text":76,"@type":77},"It integrates additional bending knowledge by using Timoshenko’s beam theory, computing an elastic representation of tube deformation at each time step as ML input.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What experimental data is used for training the model?",{"text":81,"@type":77},"The model is trained with experimental data of bending constant radii, then adapted to more complex bend geometries.",{"name":83,"@type":74,"acceptedAnswer":84},"How is the model evaluated and what performance benefit is reported?",{"text":85,"@type":77},"It is compared against a benchmark finite element simulation, showing improved prediction quality for complex kinematics while reducing computation time by four orders of magnitude.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]