{"title":"弹性地基上有限长度板的剥离:一维圆柱弯曲解","authors":"R. Plaut, D. Dillard","doi":"10.1115/1.4062493","DOIUrl":null,"url":null,"abstract":"Quasi-static peeling of a finite-length, flexible, horizontal, one-dimensional (1-D) plate (strip, thin film) from a horizontal, thin, elastomeric layer (foundation) is considered. The displaced end of the plate is subjected to an upward deflection or to a rotation. The top of the interlayer is perfectly bonded to the plate, and its lower surface is bonded to a rigid, flat substrate. A transversality (debonding) condition is derived for peeling, based on the common fracture mechanics approach. Whereas debonding from a Winkler foundation can be expressed in terms of the displacement (or equivalently the foundation stress ) at the bond termination, the sixth-order formulation involves a more complex debonding criterion. Transversality relationships are used to describe this limit state (here the onset of debonding) in terms of co-state variables, herein the deflection and slope at the peel front. In the analysis, bending is assumed to be paramount, linear Kirchhoff-Love (classical) plate theory is used to model the deformation, and therefore displacements are assumed to be small. The foundation is linearly elastic and incompressible. The effects of the work of adhesion, the length of the plate, and the initial nonbonded length of the plate are investigated. The results are compared to those for a Winkler foundation. By replacing the shear modulus of the interlayer by viscosity, and displacements by their time derivatives, the results are expected to apply to viscous liquid interlayers as well.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Peeling of Finite-Length Plates From an Elastomeric Foundation: A 1-D Cylindrical Bending Solution\",\"authors\":\"R. Plaut, D. Dillard\",\"doi\":\"10.1115/1.4062493\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Quasi-static peeling of a finite-length, flexible, horizontal, one-dimensional (1-D) plate (strip, thin film) from a horizontal, thin, elastomeric layer (foundation) is considered. The displaced end of the plate is subjected to an upward deflection or to a rotation. The top of the interlayer is perfectly bonded to the plate, and its lower surface is bonded to a rigid, flat substrate. A transversality (debonding) condition is derived for peeling, based on the common fracture mechanics approach. Whereas debonding from a Winkler foundation can be expressed in terms of the displacement (or equivalently the foundation stress ) at the bond termination, the sixth-order formulation involves a more complex debonding criterion. Transversality relationships are used to describe this limit state (here the onset of debonding) in terms of co-state variables, herein the deflection and slope at the peel front. In the analysis, bending is assumed to be paramount, linear Kirchhoff-Love (classical) plate theory is used to model the deformation, and therefore displacements are assumed to be small. The foundation is linearly elastic and incompressible. The effects of the work of adhesion, the length of the plate, and the initial nonbonded length of the plate are investigated. The results are compared to those for a Winkler foundation. By replacing the shear modulus of the interlayer by viscosity, and displacements by their time derivatives, the results are expected to apply to viscous liquid interlayers as well.\",\"PeriodicalId\":54880,\"journal\":{\"name\":\"Journal of Applied Mechanics-Transactions of the Asme\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mechanics-Transactions of the Asme\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4062493\",\"RegionNum\":4,\"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":"Journal of Applied Mechanics-Transactions of the Asme","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4062493","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
Peeling of Finite-Length Plates From an Elastomeric Foundation: A 1-D Cylindrical Bending Solution
Quasi-static peeling of a finite-length, flexible, horizontal, one-dimensional (1-D) plate (strip, thin film) from a horizontal, thin, elastomeric layer (foundation) is considered. The displaced end of the plate is subjected to an upward deflection or to a rotation. The top of the interlayer is perfectly bonded to the plate, and its lower surface is bonded to a rigid, flat substrate. A transversality (debonding) condition is derived for peeling, based on the common fracture mechanics approach. Whereas debonding from a Winkler foundation can be expressed in terms of the displacement (or equivalently the foundation stress ) at the bond termination, the sixth-order formulation involves a more complex debonding criterion. Transversality relationships are used to describe this limit state (here the onset of debonding) in terms of co-state variables, herein the deflection and slope at the peel front. In the analysis, bending is assumed to be paramount, linear Kirchhoff-Love (classical) plate theory is used to model the deformation, and therefore displacements are assumed to be small. The foundation is linearly elastic and incompressible. The effects of the work of adhesion, the length of the plate, and the initial nonbonded length of the plate are investigated. The results are compared to those for a Winkler foundation. By replacing the shear modulus of the interlayer by viscosity, and displacements by their time derivatives, the results are expected to apply to viscous liquid interlayers as well.
期刊介绍:
All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation