[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120265-en":3,"doc-seo-120265-105":30,"detail-sidebar-cat-0-en-105":91},{"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},120265,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Machine learning assisted discovery of effective viscous material laws for shear-thinning fiber suspensions","The work combines a Fast Fourier Transform-based computational method with supervised machine learning to derive models for the anisotropic effective viscosity of shear-thinning fiber suspensions. The FFT approach quantifies how fiber orientation state and macroscopic shear-rate tensor jointly shape effective viscosity across engineering-relevant shear rates, visualized in three dimensions. Four modeling requirements are synthesized from literature for Cross-type matrix fluids, then four candidate models are optimized via supervised non-convex gradient-based learning using automatic differentiation. Model selection is performed by comparing prediction accuracy on the fiber-orientation triangle, yielding engineering-accurate anisotropic shear-thinning behavior over a wide shear-rate range.","Computational Mechanics  \n[https://doi.org/10.1007/s00466-024-02490-4](https://doi.org/10.1007/s00466-024-02490-4)  \nMachine learning assisted discovery of effective viscous material laws for shear-thinning fiber suspensions  \nBenedikt Sterr1 · Andrew Hrymak2 · Matti Schneider3 · Thomas Böhlke1  \nReceived: 1 February 2024 / Accepted: 17 April 2024 © The Author(s) 2024  \nAbstract  \nIn this article, we combine a Fast Fourier Transform based computational approach and a supervised machine learning strategy to discover models for the anisotropic effective viscosity of shear-thinning fiber suspensions. Using the Fast Fourier Transform based computational approach, we study the effects of the fiber orientation state and the imposed macroscopic shear rate tensor on the effective viscosity for a broad range of shear rates of engineering process interest. We visualize the effective viscosity in three dimensions and find that the anisotropy of the effective viscosity and its shear rate dependence vary strongly with the fiber orientation state. Combining the results of this work with insights from literature, we formulate four requirements a model of the effective viscosity should satisfy for shear-thinning fiber suspensions with a Cross-type matrix fluid. Furthermore, we introduce four model candidates with differing numbers of parameters and different theoretical motivations, and use supervised machine learning techniques for non-convex optimization to identify parameter sets for the model candidates. By doing so, we leverage the flexibility of automatic differentiation and the robustness of gradient based, supervised machine learning. Finally, we identify the most suitable model by comparing the prediction accuracy of the model candidates on the fiber orientation triangle, and find that multiple models predict the anisotropic shear-thinning behavior to engineering accuracy over a broad range of shear rates.  \nKeywords Effective viscosity · Fiber-reinforced composites · Non-Newtonian suspension · Supervised machine learning · Cross-fluid  \n1 Introduction  \n1.1 State of the art  \nViscosity models for fiber polymer suspensions are widely used in molding process simulations of composite parts [1], which playa major role in the lightweight design ofengineering systems, i.e., in the automotive, aerospace, and energy sectors [2, 3] . Molding process simulations are an estab-  \nB Benedikt Sterr [benedikt.sterr@kit.edu](benedikt.sterr@kit.edu)  \nB Thomas Böhlke [thomas.boehlke@kit.edu](thomas.boehlke@kit.edu)  \n1 Karlsruhe Institute of Technology (KIT), Institute of Engineering Mechanics, Karlsruhe, Germany  \n2 Department of Chemical and Biochemical Engineering, University of Western Ontario, London, Canada  \n3 Institute of Engineering Mathematics, University of Duisburg-Essen, Essen, Germany  \nlished tool in composite part engineering, partly because of the industrial benefits of digital twins [4] and virtual process chains [2, 5, 6] . In molding simulations for fiber reinforced plastics, accurate modeling ofthe suspension viscosity iscrucial to predict various parameters of engineering interest. The suspension viscosity influences manufacturing process parameters [7, 8], as well as fiber orientation and fiber volume distributions[9]. Consequently,flowfields[10]andfinal part properties [10, 11] are also affected by the suspension viscosity. However, finding analytical models for the suspension viscosity is a challenging task, partly because of the locally inhomogeneous flow field inside the suspension, as well as the hydrodynamic interactions [12] and mechanical contacts[13]between thefibers. Furthermore, the suspension viscosity also depends strongly on the local microstructure, i.e., the fiber geometry [14], the fiber volume fraction [15], and the fiber orientation state [16] . As far as external influences are concerned, the loading direction, the shear rate [17, 18], and the melt temperature [19] also affect the suspension viscosity. Especially for suspensions with ","cbCaiozWJKRtGXCy","https://ap.wps.com/l/cbCaiozWJKRtGXCy","pdf",2689814,1,19,"English","en",105,"# Abstract\n# 1 Introduction\n## 1.1 State of the art","[{\"question\":\"What computational and machine learning methods are combined in this study?\",\"answer\":\"A Fast Fourier Transform-based computational approach is used alongside supervised machine learning. The learning component performs non-convex optimization to identify model parameters using automatic differentiation.\"},{\"question\":\"Which physical factors are analyzed for their impact on effective viscosity?\",\"answer\":\"The study examines how the fiber orientation state and the imposed macroscopic shear-rate tensor affect the effective viscosity. It covers a broad range of engineering-relevant shear rates and visualizes the results in three dimensions.\"},{\"question\":\"How are suitable effective-viscosity models chosen among multiple candidates?\",\"answer\":\"Four candidate models are proposed, then optimized and compared by evaluating prediction accuracy on the fiber orientation triangle. The best-performing model is selected based on which one captures the anisotropic shear-thinning behavior most accurately.\"}]","Machine learning assisted discovery of effective viscous material laws for shear-thinning fiber suspensions | PDF",1785729132,48,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-assisted-discovery-of-effective-viscous-material-laws-for-shear-thinning-fiber-suspensions","",{"@graph":36,"@context":85},[37,54,68],{"@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/machine-learning-assisted-discovery-of-effective-viscous-material-laws-for-shear-thinning-fiber-suspensions/120265/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What computational and machine learning methods are combined in this study?","Question",{"text":75,"@type":76},"A Fast Fourier Transform-based computational approach is used alongside supervised machine learning. The learning component performs non-convex optimization to identify model parameters using automatic differentiation.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which physical factors are analyzed for their impact on effective viscosity?",{"text":80,"@type":76},"The study examines how the fiber orientation state and the imposed macroscopic shear-rate tensor affect the effective viscosity. It covers a broad range of engineering-relevant shear rates and visualizes the results in three dimensions.",{"name":82,"@type":73,"acceptedAnswer":83},"How are suitable effective-viscosity models chosen among multiple candidates?",{"text":84,"@type":76},"Four candidate models are proposed, then optimized and compared by evaluating prediction accuracy on the fiber orientation triangle. 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