{"title":"具有周期性材料特性的薄膜/基底双层膜的起皱:对温克勒基础模型的评估","authors":"Yuxin Fu , Yue-Sheng Wang , Yibin Fu","doi":"10.1016/j.ijnonlinmec.2024.104815","DOIUrl":null,"url":null,"abstract":"<div><p>The Winkler foundation model is often used to analyze the wrinkling of a film/substrate bilayer under compression, and it can be rigorously justified when both the film and substrate are homogeneous and the film is much stiffer than the substrate. We assess the validity of this model when the substrate is still homogeneous but the film has periodic material properties in the direction parallel to the interface. More precisely, we assume that each unit cell is piecewise homogeneous, and each piece can be described by the Euler–Bernoulli beam theory. We provide analytical results for the critical compression when the substrate is viewed as a Winkler foundation with stiffness modeled either approximately (as in some previous studies) or exactly (using the Floquet theory). The analytical results are then compared with those from Abaqus simulations based on the three-dimensional nonlinear elasticity theory in order to assess the validity of the Euler–Bernoulli beam theory and the Winkler foundation model in the current context.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002074622400180X/pdfft?md5=a566bcbc3aca089438f449daa90e5be8&pid=1-s2.0-S002074622400180X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Wrinkling of a film/substrate bilayer with periodic material properties: An assessment of the Winkler foundation model\",\"authors\":\"Yuxin Fu , Yue-Sheng Wang , Yibin Fu\",\"doi\":\"10.1016/j.ijnonlinmec.2024.104815\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The Winkler foundation model is often used to analyze the wrinkling of a film/substrate bilayer under compression, and it can be rigorously justified when both the film and substrate are homogeneous and the film is much stiffer than the substrate. We assess the validity of this model when the substrate is still homogeneous but the film has periodic material properties in the direction parallel to the interface. More precisely, we assume that each unit cell is piecewise homogeneous, and each piece can be described by the Euler–Bernoulli beam theory. We provide analytical results for the critical compression when the substrate is viewed as a Winkler foundation with stiffness modeled either approximately (as in some previous studies) or exactly (using the Floquet theory). The analytical results are then compared with those from Abaqus simulations based on the three-dimensional nonlinear elasticity theory in order to assess the validity of the Euler–Bernoulli beam theory and the Winkler foundation model in the current context.</p></div>\",\"PeriodicalId\":50303,\"journal\":{\"name\":\"International Journal of Non-Linear Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S002074622400180X/pdfft?md5=a566bcbc3aca089438f449daa90e5be8&pid=1-s2.0-S002074622400180X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Non-Linear Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002074622400180X\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Non-Linear Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002074622400180X","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
Wrinkling of a film/substrate bilayer with periodic material properties: An assessment of the Winkler foundation model
The Winkler foundation model is often used to analyze the wrinkling of a film/substrate bilayer under compression, and it can be rigorously justified when both the film and substrate are homogeneous and the film is much stiffer than the substrate. We assess the validity of this model when the substrate is still homogeneous but the film has periodic material properties in the direction parallel to the interface. More precisely, we assume that each unit cell is piecewise homogeneous, and each piece can be described by the Euler–Bernoulli beam theory. We provide analytical results for the critical compression when the substrate is viewed as a Winkler foundation with stiffness modeled either approximately (as in some previous studies) or exactly (using the Floquet theory). The analytical results are then compared with those from Abaqus simulations based on the three-dimensional nonlinear elasticity theory in order to assess the validity of the Euler–Bernoulli beam theory and the Winkler foundation model in the current context.
期刊介绍:
The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear.
The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas.
Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.