[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122044-en":3,"doc-seo-122044-105":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":4,"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},122044,8796095462418,"Noah","https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780",8,"Research & Report","Machine learning-based sampling of virtual experiments within the full stress state","This paper presents a machine learning-based framework to study anisotropic yield surfaces of sheet metals using virtual experiments. The method adapts active learning to sample virtual experiments efficiently for the full stress state, enabling identification of parameters for anisotropic yield functions. It is applied to virtual experiments derived from crystal plasticity finite element method (CPFEM) results for DX56D deep drawing steel and benchmarked against two established sampling strategies. The parameters are then used in cylindrical cup drawing simulations to evaluate how sampling choices influence forming predictions and in-plane anisotropy representation.","Machine learning-based sampling of virtual experiments within the full  \nstress state  \nA. Wessela,b, L. Moranda, A. Butza, D. Helma, W. Volkb  \na Fraunhofer Institute for Mechanics of Materials IWM, Woehlerstrasse 11, 79108 Freiburg,  \nGermany  \nb Chair of Metal Forming and Casting, Technical University of Munich, Walther-Meissner  \nStrasse 4, 85748 Garching, Germany  \nE-mail address: alexander.wessel@iwm.fraunhofer.de  \nAbstract  \nThis paper presents a new machine learning-based approach to investigate anisotropic yield surfaces of sheet metals by means of virtual experiments. The new sampling approach is based on the machine learning technique known as active learning, which has been adapted to efficiently sample virtual experiments with respect to the full stress state in order to identify parameters of anisotropic yield functions. The approach was employed to sample virtual experiments based on the crystal plasticity finite element method (CPFEM) for a DX56D deep drawing steel and compared with two state-of-the-art sampling methods taken from the literature. The resulting points on the initial yield surface for all three sampling methods were used to identify parameters of the anisotropic yield functions Hill48, Yld91, Yld2004-18p and Yld2004-27p. These parameters were then applied to a cylindrical cup drawing simulation to analyse the effect of the three sampling methods on a typical sheet forming simulation. The results show that the new machine learning-based sampling approach has a higher sampling efficiency than the two state-of-the-art sampling methods. Consequently, fewer computationally expensive crystal plasticity simulations are required. By comparing different variants ofthe Hill48, Yld91, Yld2004-18p and Yld2004-27p yield surfaces, it was also found that identifying parameters of anisotropic yield functions based on virtual experiments sampled within the full stress state can lead to a degraded representation ofthe in-plane anisotropy. With respect to DX56D deep drawing steel, this degradation was observed for the Yld2004-18p yield function. The negative implications following from this degraded in-plane representation were  \nfurther demonstrated by the results of the cylindrical cup drawing process. As a consequence, the representation of the in-plane anisotropy must be carefully reviewed when taking the full stress state into account. In this context, Yld2004-27p was identified as being sufficiently flexible to simultaneously represent the plastic anisotropy of DX56D with respect to the inplane and out-of-plane behaviour with high accuracy.  \nKeyword: crystal plasticity, yield condition, machine learning, adaptive sampling, DX56D deep drawing steel, Yld2004-27p  \n1. Introduction  \nSheet metal forming operations play an important role in various manufacturing industries, particularly in the automotive sector. To reduce development times, minimise costs and increase the product quality of sheet metal parts, finite element simulations have become a stateof-the-art method to analyse and improve forming operations. One precondition for highquality sheet metal forming simulations is an accurate description of the plastic material behaviour. Since sheet metal typically exhibits direction-dependent, or rather anisotropic material properties due to its manufacturing process, the mathematical description of textureinduced plastic anisotropy by anisotropic yield functions is essential (Banabic et al., 2010; Banabic et al., 2020; Tekkaya, 2000) . Hence, many anisotropic yield functions have been developed for the plane and full stress state over the past decades. Apart from his well-known isotropic yield function (von Mises, 1913), von Mises (1928) also proposed the first anisotropic yield function for the plane and full stress state. It is a quadratic yield function and was initially introduced to describe the plastic anisotropy of single crystals. Using the concept of the plastic potential of von Mises (1928), Hill (1","cbCailLymvMtltwa","https://ap.wps.com/l/cbCailLymvMtltwa","pdf",20692916,1,51,"English","en",105,"# Introduction\n## Finite element simulation for sheet metal forming\n## Anisotropic yield functions for plane and full stress states\n## Background on Hill and Barlat yield criteria\n## Motivation for active learning-based sampling\n# Virtual experiment sampling and model identification\n## Active learning for full-stress virtual experiments\n## CPFEM-based virtual experiments for DX56D steel\n## Benchmark comparison with literature sampling methods\n# Parameter identification and forming validation\n## Yield function parameter fitting (Hill48, Yld91, Yld2004-18p, Yld2004-27p)\n## Cylindrical cup drawing simulations\n## Impact on in-plane and out-of-plane anisotropy","[{\"question\":\"What problem does the paper address in sheet metal forming simulations?\",\"answer\":\"It addresses the need for accurately describing plastic, direction-dependent (anisotropic) material behavior so that finite element simulations can reliably analyze and improve forming operations.\"},{\"question\":\"How does the proposed method sample virtual experiments?\",\"answer\":\"It uses active learning to adaptively sample virtual experiments with respect to the full stress state, aiming to efficiently identify parameters of anisotropic yield functions.\"},{\"question\":\"How was the approach validated?\",\"answer\":\"The method was applied to CPFEM-based virtual experiments for DX56D deep drawing steel, benchmarked against two literature sampling methods, and then used to run cylindrical cup drawing simulations to assess prediction effects.\"}]","Machine learning-based sampling of virtual experiments within the full stress state | 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problem does the paper address in sheet metal forming simulations?","Question",{"text":75,"@type":76},"It addresses the need for accurately describing plastic, direction-dependent (anisotropic) material behavior so that finite element simulations can reliably analyze and improve forming operations.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method sample virtual experiments?",{"text":80,"@type":76},"It uses active learning to adaptively sample virtual experiments with respect to the full stress state, aiming to efficiently identify parameters of anisotropic yield functions.",{"name":82,"@type":73,"acceptedAnswer":83},"How was the approach validated?",{"text":84,"@type":76},"The method was applied to CPFEM-based virtual experiments for DX56D deep drawing steel, benchmarked against two literature sampling methods, and then used to run cylindrical cup drawing simulations to assess prediction 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