[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82120-en":3,"doc-seo-82120-105":29,"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":13,"seo_description":14,"update_tm":27,"read_time":28},82120,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Impedance-Guided Programmable Transmission of Localized Deformation in Modular Soft Metamaterials","Soft mechanical metamaterials enable applications in robotics, biomedical devices, and flexible electronics, but transmitting controlled localized responses across modular assemblies remains underdeveloped. A key challenge is that nonuniform excitation in soft materials attenuates deformation and force over distance, limiting end-to-end and long-range functionality. The impedance-guided framework introduces a nonlinear spring model with position-dependent interactions, regulating transmission via unit-cell topology optimization. Modules are synthesized as homogeneous or heterogeneous families, supporting diverse architectures including obstacle bypassing, defect-tolerant gripping, and embodied signal processing.","Impedance-Guided Programmable Transmission of Localized Deformation in Modular Soft Metamaterials  \nAuthors Information  \nWeiyun Xu, 1 * Daewon Hong,2 Zhi Zhao, 1 Rahul Dev Kundu, 1 Xiaojia Shelly Zhang 1,2,3 *  \n1 Department of Civil and Environmental Engineering, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA.  \n2 Department of Mechanical Engineering, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA.  \n3 National Center for Supercomputing Applications, Urbana, IL 61801, USA.  \n* Correspondence to: Weiyun Xu ([weiyunxu@illinois.edu](weiyunxu@illinois.edu)) and Xiaojia Shelly Zhang ([zhangxs@illinois.edu](zhangxs@illinois.edu)).  \nAbstract  \nSoft mechanical metamaterials provide a promising platform for applications in robotics, biomedical devices, and flexible electronics. The localized mechanical responses induced by nonuniform excitation are ubiquitous in soft materials, yet their controlled transmission across modular metamaterial assemblies remains largely overlooked in metamaterial design, which critically constrains nontrivial functionalities that require end-to-end and long-range deformation transmission. Here, we introduce an impedance-guided design framework that enables programmable transmission of localized deformation in modular soft metamaterials, achieving behaviors unattainable by intuitive design. By establishing an equivalent nonlinear spring model considering position-dependent interactions and integrating the concept of mechanical impedance within soft metamaterials, we regulate assembly-level transmission solely through unit-cell topology optimization. The resulting framework enables effective synthesis of module families, allowing both homogeneous and heterogeneous assemblies to be custom-built with markedly enhanced transmission characteristics. Leveraging the highly combinatorial and extensible design space, we physically realize diverse on-demand displacement manipulation architectures, including obstacle-bypassing modular soft-metamaterial assemblies, defect-tolerant soft gripping, and embodied signal processing. Beyond deformation programming, the reconfigurability andreassemblability of these soft modules can embed electric logic signals, enabling energy-efficient and low-latency information processing through compliant-switch-controlled mechanical LED displays and wearable finger-motion-sensing controllers. Our method provides fundamental insights into localized deformation transmission in modular soft metamaterials and establishes a scalable route toward embodied-intelligence material systems, particularly for soft-metamaterialcentric actuation, sensing, and collective computing.  \nKeywords  \nSoft Metamaterials; Modular; Topology optimization; Impedance; Deformation transmission; Local deformation.  \nIntroduction  \nMetamaterials have emerged as a powerful platform for systems with physical intelligence, owing to their ability to achieve exceptional and programmable mechanical responses through the rational design of microstructures and constituent materials [1,2] . In particular, soft metamaterials, which employ compliant matrices such as elastomeric polyurethane (EPU) [3], polydimethylsiloxane (PDMS) [4], liquid crystal elastomers (LCEs) [5], and hydrogels [6], are distinguished by their large deformability and resilient recoverability. Driven by the combination of soft matter and architected geometry, extensive efforts have been devoted to nonlinear mechanical behavior [7] and multiphysics integration [8] in soft metamaterials, enabling applications in soft robotics [9], electronic skin [10], human-computer interaction [11], and material-level information processing [12] . Many of these emerging functionalities would particularly benefit from modular, scalable, and reconfigurable architectures [13-15], which are essential for large-scale and adaptive material systems. Despite these advances, most existing studies focus on the global nonlinear response of monolithic ","cbCaidIh91L51HGm","https://ap.wps.com/l/cbCaidIh91L51HGm","pdf",9449712,1,32,"English","en",105,"# Introduction\n## Localized deformation attenuation in soft modular assemblies\n## Saint-Venant-type decay and cascaded unit-cell behavior","[{\"question\":\"What problem does the impedance-guided framework address in modular soft metamaterials?\",\"answer\":\"It targets the difficulty of end-to-end, programmable transmission of localized deformation across modular assemblies, which is otherwise strongly attenuated with distance in soft materials.\"},{\"question\":\"How is transmission regulated in the proposed method?\",\"answer\":\"Transmission is regulated through unit-cell topology optimization using an equivalent nonlinear spring model that incorporates position-dependent interactions and mechanical impedance.\"},{\"question\":\"What kinds of modules and on-demand behaviors does the framework enable?\",\"answer\":\"It enables both homogeneous and heterogeneous module families, realized for architectures such as obstacle-bypassing assemblies, defect-tolerant soft gripping, and embodied signal 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problem does the impedance-guided framework address in modular soft metamaterials?","Question",{"text":75,"@type":76},"It targets the difficulty of end-to-end, programmable transmission of localized deformation across modular assemblies, which is otherwise strongly attenuated with distance in soft materials.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is transmission regulated in the proposed method?",{"text":80,"@type":76},"Transmission is regulated through unit-cell topology optimization using an equivalent nonlinear spring model that incorporates position-dependent interactions and mechanical impedance.",{"name":82,"@type":73,"acceptedAnswer":83},"What kinds of modules and on-demand behaviors does the framework enable?",{"text":84,"@type":76},"It enables both homogeneous and heterogeneous module families, realized for architectures such as obstacle-bypassing assemblies, defect-tolerant soft gripping, and embodied signal 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