Axisymmetric necking versus Treloar–Kearsley instability in a hyperelastic sheet under equibiaxial stretching

Wang, Mi; Jin, Lishuai; Fu, Yibin

doi:10.1177/10812865211072897

Cited by 8 publications

(3 citation statements)

References 79 publications

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“…Such extra fields and new geometries (e.g. axisymmetric necking of a stretched plate (Wang et al, 2022) ) will be considered in our future studies.…”

Section: Discussionmentioning

confidence: 99%

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

Fu¹

2023

Preprint

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We derive a one-dimensional (1d) model for the analysis of bulging or necking in an inflated hyperelastic tube of finite wall thickness from the three-dimensional finite elasticity theory by applying the dimension reduction methodology proposed by Audoly and Hutchinson (J. Mech. Phys. Solids, 97, 2016). The 1d model makes it much easier to characterize fully nonlinear axisymmetric deformations of a thick-walled tube using simple numerical schemes such as the finite difference method. The new model recovers the diffuse interface model for analyzing bulging in a membrane tube and the 1d model for investigating necking in a stretched solid cylinder as two limiting cases. It is consistent with, but significantly refines, the exact linear and weakly nonlinear bifurcation analyses. Comparisons with finite element simulations show that for the bulging problem, the 1d model is capable of describing the entire bulging process accurately, from initiation, growth, to propagation. The 1d model provides a stepping stone from which similar 1d models can be derived and used to study other effects such as anisotropy and electric loading, and other phenomena such as rupture.

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“…Such extra fields and new geometries (e.g. axisymmetric necking of a stretched plate (Wang et al, 2022) ) will be considered in our future studies.…”

Section: Discussionmentioning

confidence: 99%

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

Fu¹

2023

Preprint

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“…The sensitivity of the wrinkling stress to changes in material parameters has been verified by parametric analysis, and the feasibility of the theoretical criterion is proven. Wang et al [ 168 , 169 ] performed a theoretical analysis of the local instability of thin-walled sheet metal during stretching. Under the boundary conditions of force or displacement control, the axisymmetric necking of circular or square hyper-elastic sheets was subjected to equivalent biaxial tension.…”

Section: Analytical Methods Of Deformation Instabilitymentioning

confidence: 99%

Theory, Method and Practice of Metal Deformation Instability: A Review

Wan

Yao

et al. 2023

Materials

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Deformation instability is a macroscopic and microscopic phenomenon of non-uniformity and unstable deformation of materials under stress loading conditions, and it is affected by the intrinsic characteristics of materials, the structural geometry of materials, stress state and environmental conditions. Whether deformation instability is positive and constructive or negative and destructive, it objectively affects daily life at all times and the deformation instability based on metal-bearing analysis in engineering design has always been the focus of attention. Currently, the literature on deformation instability in review papers mainly focuses on the theoretical analysis of deformation instability (instability criteria). However, there are a limited number of papers that comprehensively classify and review the subject from the perspectives of material characteristic response, geometric structure response, analysis method and engineering application. Therefore, this paper aims to provide a comprehensive review of the existing literature on metal deformation instability, covering its fundamental principles, analytical methods, and engineering practices. The phenomenon and definition of deformation instability, the principle and viewpoint of deformation instability, the theoretical analysis, experimental research and simulation calculation of deformation instability, and the engineering application and prospect of deformation instability are described. This will provide a reference for metal bearing analysis and deformation instability design according to material deformation instability, structural deformation instability and localization conditions of deformation instability, etc. From the perspective of practical engineering applications, regarding the key problems in researching deformation instability, using reverse thinking to deduce and analyze the characteristics of deformation instability is the main trend of future research.

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“…Zhang and Zhao [15] investigate the pull-in instability and eigenfrequency variations of a graphene resonator under electrostatic loading. Finally, Wang et al [16] investigate axisymmetric necking in a hyperelastic sheet under equibiaxial stretching and how it competes with the Treloar–Kearsley instability.…”

mentioning

confidence: 99%

In memory of Prof. Hui-Hui Dai

Chen¹,

Fu²,

Zhong³

2022

Mathematics and Mechanics of Solids

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This special issue of Mathematics and Mechanics of Solids is dedicated to the memory of Professor Hui-Hui Dai who passed away on 5 January 2021 in Hong Kong. Hui-Hui was born on 24 March 1964 in Anhui Province, China. He grew up in Ming Guang, a small town in Jia Shan County, where he attended Ming Guang Primary School and Ming Guang No 1 High School. He was the top scorer in the county in the national university entrance examination at the young age of 16. The years around 1980 were an exciting period in which China had just opened up to the outside world, and universities had an electric atmosphere about science and knowledge after reopening following a 10-year close-down. Hui-Hui must have really enjoyed his studies like his peers. He obtained his BSc from the Department of Mechanics, Zhejiang University, in 1984 and entered Dalian University of Science and Technology in 1984 as an MSc student. Two years into his MSc study, he was awarded a competitive KC Wong Scholarship to study in the United Kingdom. Supervised by Professor Alan Jeffrey in the Department of Engineering Mathematics, University of Newcastle upon Tyne, he obtained his PhD in 1990. After spending just over a year in the University of Western Ontario as a postdoctoral research fellow, he spent another 3 years in the University of Manitoba. He went there as postdoctoral research fellow and was later offered a tenure-tracked position as an Assistant Professor. He moved to the

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Axisymmetric necking versus Treloar–Kearsley instability in a hyperelastic sheet under equibiaxial stretching

Cited by 8 publications

References 79 publications

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

Theory, Method and Practice of Metal Deformation Instability: A Review

In memory of Prof. Hui-Hui Dai

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