{"title":"The mechanics and morphology evolutions in stretched ribbons under torsion: A 3D phase diagram","authors":"Hao Liu , Lei Liu , Dabiao Liu","doi":"10.1016/j.ijmecsci.2024.109786","DOIUrl":null,"url":null,"abstract":"<div><div>Slender structures ubiquitously undergo complex shape transformations in both natural and artificial systems. Soft ribbons can exhibit rich morphologies when subjected to loading and geometric constraints. The competition between the macroscopic, microscopic, and transverse buckling modes results in multiple morphological transitions, revealing distinct evolution paths among helicoid, crease, cylinder, and scrolled yarn configurations. However, the roles of tension, twist, and geometry in determining the buckling modes of a stretched ribbon under torsion remain unclear. In this study, we comprehensively investigate the torsional instabilities of elastic ribbons through experiments, theory, and finite element simulations. A one-dimensional model is employed to describe the nonlinear torsional responses in the helicoid stage. We present a modeling approach to describe the crease configuration and derive a semi-analytical solution based on the finite element analysis. We find that the competition between the macroscopic and microscopic buckling modes is governed by the thickness-to-width ratio, which determines the relative magnitudes of the membrane and bending strain energy in the helicoid. Additionally, as the applied tension increases, the buckling mode shifts from the longitudinal to the transverse direction. A three-dimensional phase diagram, as a function of twist, tension, and thickness-to-width ratio, is constructed to identify the morphology transitions of elastic ribbons. This study has implications for understanding the morphological complexity and achieving precise control of slender structures.</div></div>","PeriodicalId":56287,"journal":{"name":"International Journal of Mechanical Sciences","volume":"285 ","pages":"Article 109786"},"PeriodicalIF":7.1000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mechanical Sciences","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020740324008270","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Slender structures ubiquitously undergo complex shape transformations in both natural and artificial systems. Soft ribbons can exhibit rich morphologies when subjected to loading and geometric constraints. The competition between the macroscopic, microscopic, and transverse buckling modes results in multiple morphological transitions, revealing distinct evolution paths among helicoid, crease, cylinder, and scrolled yarn configurations. However, the roles of tension, twist, and geometry in determining the buckling modes of a stretched ribbon under torsion remain unclear. In this study, we comprehensively investigate the torsional instabilities of elastic ribbons through experiments, theory, and finite element simulations. A one-dimensional model is employed to describe the nonlinear torsional responses in the helicoid stage. We present a modeling approach to describe the crease configuration and derive a semi-analytical solution based on the finite element analysis. We find that the competition between the macroscopic and microscopic buckling modes is governed by the thickness-to-width ratio, which determines the relative magnitudes of the membrane and bending strain energy in the helicoid. Additionally, as the applied tension increases, the buckling mode shifts from the longitudinal to the transverse direction. A three-dimensional phase diagram, as a function of twist, tension, and thickness-to-width ratio, is constructed to identify the morphology transitions of elastic ribbons. This study has implications for understanding the morphological complexity and achieving precise control of slender structures.
期刊介绍:
The International Journal of Mechanical Sciences (IJMS) serves as a global platform for the publication and dissemination of original research that contributes to a deeper scientific understanding of the fundamental disciplines within mechanical, civil, and material engineering.
The primary focus of IJMS is to showcase innovative and ground-breaking work that utilizes analytical and computational modeling techniques, such as Finite Element Method (FEM), Boundary Element Method (BEM), and mesh-free methods, among others. These modeling methods are applied to diverse fields including rigid-body mechanics (e.g., dynamics, vibration, stability), structural mechanics, metal forming, advanced materials (e.g., metals, composites, cellular, smart) behavior and applications, impact mechanics, strain localization, and other nonlinear effects (e.g., large deflections, plasticity, fracture).
Additionally, IJMS covers the realms of fluid mechanics (both external and internal flows), tribology, thermodynamics, and materials processing. These subjects collectively form the core of the journal's content.
In summary, IJMS provides a prestigious platform for researchers to present their original contributions, shedding light on analytical and computational modeling methods in various areas of mechanical engineering, as well as exploring the behavior and application of advanced materials, fluid mechanics, thermodynamics, and materials processing.