[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126650-en":3,"doc-seo-126650-105":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},126650,549768064778,"Finn","https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8",8,"Research & Report","Rapid inverse design of metamaterials based on prescribed mechanical behavior through machine learning","Metamaterials enable mechanical behaviors beyond their constituent materials, recorded as stress–strain response curves. Existing inverse design methods struggle to achieve full prescribed behavior because of multiple design objectives, nonlinearities, and process-dependent printing errors that distort the mapping from design to response. A rapid inverse design workflow uses generative machine learning combined with desktop additive manufacturing to generate uniaxial compressive stress–strain curves while accounting for printing variability. Experiments show nearly 90% fidelity between target and measured results.","Article [https://doi.org/10.1038/s41467-023-40854-1](https://doi.org/10.1038/s41467-023-40854-1)  \nRapid inverse design of metamaterials based on prescribed mechanical behavior through machine learning  \nReceived: 29 November 2022  \n\n| Accepted: 11 August 2023 |\n| --- |\n|  |\n| Check for updates |\n\nChan Soo Ha 1,8, Desheng Yao 2,3,8, Zhenpeng Xu2,3, Chenang Liu4, Han Liu 5, Daniel Elkins1,6, Matthew Kile1, Vikram Deshpande 7 , Zhenyu Kong 6 , Mathieu Bauchy3  & Xiaoyu (Rayne) Zheng 1,2,3   \nDesigning and printing metamaterials with customizable architectures enables the realization of unprecedented mechanical behaviors that transcend those of their constituent materials. These behaviors are recorded in the form of response curves, with stress-strain curves describing their quasi-static footprint. However, existing inverse design approaches are yet matured to capture the full desired behaviors due to challenges stemmed from multiple design objectives, nonlinear behavior, and process-dependent manufacturing errors. Here, we report a rapid inverse design methodology, leveraging generative machine learning and desktop additive manufacturing, which enables the creation of nearly all possible uniaxial compressive stress‒strain curve cases while accounting for process-dependent errors from printing. Results show that mechanical behavior with full tailorability can be achieved with nearly 90%fidelity between target and experimentally measured results. Our approach represents a starting point to inverse design materials that meet prescribed yet complex behaviors and potentially bypasses iterative design-manufacturing cycles.  \nThe intrinsic mechanical behavior of bulk materials (e.g., metals, ceramics, polymers) can be experimentally characterized by the application of force and the measurement of the resulting deformation, yielding stress‒strain curves. For example, under tensile loading, the mechanical behavior of brittle materials such as ceramics is characterized by a stress–strain curve with a linear region followed by a sharp termination; elastomers display superelasticity, characterized by a rapidly rising concave-up stress‒strain curve without a noticeable linear region. For homogenous materials such as metals, ceramics, and polymers, responses to loading are dictated by intrinsic microstructure, such as crystal structure, atomic bonding, and the size and mass of the constituent molecules/atoms, in addition to the presence  \nof stochastic microscopic defects. As a result, there is little room to tailor these materials’ responses to loads besides altering the intrinsic microstructure of the base materials.  \nAdditive manufacturing (AM) allows mechanical properties to be tailored in ways that are impossible in bulk materials, via the microarchitecture design of three-dimensional (3D) metamaterials. These materials can exhibit unusual properties such as negative Poisson’s ratio1–3, negative compressibility4,5, ultralightness and ultrastiffness, shape recoverability6–8, and multiple stable states9–11. These architected materials achieve previously unattainable region in the materialselection chart (e.g., so-called Ashby charts of density vs. Young’s modulus or strength)12,13. Architected materials manifesting these  \n1Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA. 2Department of Material Science and Engineering, University of California, Berkeley, CA, USA. 3Department of Civil and Environmental Engineering, University of California, Los Angeles, CA, USA. 4Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, USA. 5Department of Computer Science and Technology, Sichuan University, Chengdu, China. 6Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA. 7Department of Engineering, University of Cambridge, Cambridge, UK.  \n8These authors contributed equally: Chan Soo Ha, Desheng Yao. [e-mail:](e-mail: vsd20@cam.ac.uk)[ vsd20@cam.ac.uk](e-mail: vsd","cbCaio6WmQ8maBza","https://ap.wps.com/l/cbCaio6WmQ8maBza","pdf",6871671,1,11,"English","en",105,"# Background\n## Mechanical behavior and stress–strain characterization\n## Limits of bulk-material tailoring\n## Metamaterials via additive manufacturing\n## Prior design approaches and challenges\n# Methodology\n## Rapid inverse design workflow\n## Generative inverse and surrogate forward neural networks\n## Inputs: target stress–strain curve and fabrication parameters\n# Results and significance\n## Fidelity between target and experimental curves\n## Avoiding iterative design–manufacturing cycles","[{\"question\":\"Why is inverse design for metamaterials challenging for fully prescribed mechanical behavior?\",\"answer\":\"It must satisfy multiple design objectives and nonlinear behavior while also handling non-unique mappings from design to response and process-dependent manufacturing errors introduced during printing.\"},{\"question\":\"What does the proposed rapid inverse design method combine?\",\"answer\":\"It integrates generative machine learning models with desktop additive manufacturing to create metamaterial designs that replicate user-defined uniaxial compressive stress–strain curves.\"},{\"question\":\"How accurate are the experimentally realized mechanical responses compared with the targets?\",\"answer\":\"Experimental results report nearly 90% fidelity between the target stress–strain curves and experimentally measured curves.\"}]","Rapid inverse design of metamaterials based on prescribed mechanical behavior through machine learning | PDF",1785934033,28,{"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},"rapid-inverse-design-of-metamaterials-based-on-prescribed-mechanical-behavior-through-machine-learning","",{"@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/rapid-inverse-design-of-metamaterials-based-on-prescribed-mechanical-behavior-through-machine-learning/126650/",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","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is inverse design for metamaterials challenging for fully prescribed mechanical behavior?","Question",{"text":75,"@type":76},"It must satisfy multiple design objectives and nonlinear behavior while also handling non-unique mappings from design to response and process-dependent manufacturing errors introduced during printing.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What does the proposed rapid inverse design method combine?",{"text":80,"@type":76},"It integrates generative machine learning models with desktop additive manufacturing to create metamaterial designs that replicate user-defined uniaxial compressive stress–strain curves.",{"name":82,"@type":73,"acceptedAnswer":83},"How accurate are the experimentally realized mechanical responses compared with the targets?",{"text":84,"@type":76},"Experimental results report nearly 90% fidelity between the target stress–strain curves and experimentally measured curves.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]