[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120520-en":3,"doc-seo-120520-105":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},120520,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Consistent machine learning for topology optimization with microstructure-dependent neural network material models","Additive manufacturing and topology optimization enable multiscale structures with spatially varying microstructures, yet inverse design under nonlinearities is hindered by costly computational homogenization and the difficulty of differentiably parameterizing microstructural responses. A machine learning surrogate can provide efficient differentiable mappings between material response and microstructural descriptors. This work proposes a hyperelasticity-grounded consistent machine learning framework merged with homogenization-based topology optimization. The neural models enforce polyconvexity, objectivity, material symmetry, and thermodynamic consistency.","arXiv :2408 . 13843v2 [ cond-mat .mtrl-sci ] 27 Aug 2024  \nConsistent machine learning for topology optimization with microstructure-dependent neural network material models  \nHarikrishnan Vijayakumarana , Jonathan B. Russb , Glaucio H. Paulinob,c , Miguel A. Bessad  \na Department of Materials Science Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands b Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, United States c Princeton Materials Institute (PMI), Princeton University, Princeton, NJ 08544, United States d School of Engineering, Brown University, Providence, RI 02912, United States  \nAbstract  \nAdditive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such structures in the presence of nonlinearities remains a challenge due to the expense of computational homogenization methods and the complexity of differentiably parameterizing the microstructural response. A solution to this challenge lies in machine learning techniques that offer efficient, differentiable mappings between the material response and its microstructural descriptors. This work presents a framework for designing multiscale heterogeneous structures with spatially varying microstructures by merging a homogenization-based topology optimization strategy with a consistent machine learning approach grounded in hyperelasticity theory. We leverage neural architectures that adhere to critical physical principles such as polyconvexity, objectivity, material symmetry, and thermodynamic consistency to supply the framework with a reliable constitutive model that is dependent on material microstructural descriptors. Our findings highlight the potential of integrating consistent machine learning models with density-based topology optimization for enhancing design optimization of heterogeneous hyperelastic structures under finite deformations.  \nKeywords: topology optimization, material-integrated design, multi-scale structures, functionally-graded materials, neural networks, deep learning  \n1. Introduction  \nThe growth of computational resources, together with advances in additive manufacturing (AM), have brought topology optimization (TO) to the forefront of engineering design. The foundational work by Bendsøe and Kikuchi (1988), which addressed the optimization of material distribution through a homogenized treatment of the microstructure, provided the basis for the approaches we have today. Despite this, subsequently developed methods such as the solid isotropic material with penalization (SIMP) method (Bendsøe, 1989 ; Zhou and Rozvany, 1991) and the level set method (Allaire et al., 2004) were favored over homogenization-based TO because of early challenges related to manufacturability, small length scale effects, and microstructural connectivity. Today, with advances in additive manufacturing technology, it is now possible to 3D print various graded microstructures (see e.g. Schumacher et al., 2015), which has prompted a resurgence of homogenization-based methods (Pantz and Trabelsi, 2008 ; Groen and Sigmund, 2017 ; Groen et al., 2020) in multiscale TO. Structures of unprecedented complexity have been both designed and physically realized at multiple scales (Sanders et al., 2021) . Furthermore, AM methods have enabled the realization of multi-material structures (Gaynor et al., 2014), complementing the development of novel techniques in multimaterial TO (Sanders et al., 2018a,b) and its extension to hyperelastic materials under large deformations (Zhang et al., 2020) .  \n∗ Corresponding author  \nEmail address: [miguel_bessa@brown. edu](miguel_bessa@brown. edu) (Miguel A. Bessa)  \nExtending the existing single scale (e.g. Chi et al., 2021 ; Senhora et al., 2022) to two-scale concurrent design optimization methods for use with nonl","cbCaiph5dzfcLI8D","https://ap.wps.com/l/cbCaiph5dzfcLI8D","pdf",3157798,1,32,"English","en",105,"# Introduction\n## Background and motivation\n## Challenges in nonlinear multiscale topology optimization\n## Role of consistent machine learning and neural constitutive models","[{\"question\":\"What main challenge does the document address in microstructure-dependent topology optimization?\",\"answer\":\"Nonlinear inverse design remains difficult because computational homogenization is expensive and microstructural responses are complex to parameterize in a differentiable way.\"},{\"question\":\"How does the proposed method improve efficiency compared with traditional homogenization?\",\"answer\":\"It replaces costly homogenization with a machine learning framework that yields efficient, differentiable mappings between microstructural descriptors and the homogenized material response.\"},{\"question\":\"What physical principles do the neural network constitutive models enforce?\",\"answer\":\"They are designed to satisfy polyconvexity, objectivity, material symmetry, and thermodynamic consistency, providing a reliable constitutive model for hyperelastic behavior under finite deformations.\"}]","Consistent machine learning for topology optimization with microstructure-dependent neural network material models | 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main challenge does the document address in microstructure-dependent topology optimization?","Question",{"text":75,"@type":76},"Nonlinear inverse design remains difficult because computational homogenization is expensive and microstructural responses are complex to parameterize in a differentiable way.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method improve efficiency compared with traditional homogenization?",{"text":80,"@type":76},"It replaces costly homogenization with a machine learning framework that yields efficient, differentiable mappings between microstructural descriptors and the homogenized material response.",{"name":82,"@type":73,"acceptedAnswer":83},"What physical principles do the neural network constitutive models enforce?",{"text":84,"@type":76},"They are designed to satisfy polyconvexity, objectivity, material symmetry, and thermodynamic consistency, providing a reliable constitutive model for hyperelastic behavior under finite 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