Asymptotic results for bifurcations in pure bending of rubber blocks

The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length η, subject to pure bending, is considered. The two incremental equilibrium equations corresponding to a nonlinear pre-buckling state of strain are reduced to a fourth-order linear eigenproblem that displ...

Full description

Saved in:
Bibliographic Details
Published in:Quarterly journal of mechanics and applied mathematics 2008-08, Vol.61 (3), p.395-414
Main Authors: Coman, Ciprian D., Destrade, Michel
Format: Article
Language:English
Subjects:
Applied sciences
Buckling
Elastomers
Engineering Sciences
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Industrial polymers. Preparations
Materials and structures in mechanics
Mathematical methods in physics
Mechanics
Numerical approximation and analysis
Numerical simulation, solution of equations
Physics
Polymer industry, paints, wood
Solid mechanics
Structural and continuum mechanics
Technology of polymers
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c434t-179edeea45bd16d34087a49ebe707f65fc7009f28c446a8058cf5084e94326903
cites
container_end_page 414
container_issue 3
container_start_page 395
container_title Quarterly journal of mechanics and applied mathematics
container_volume 61
creator Coman, Ciprian D.
Destrade, Michel
description The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length η, subject to pure bending, is considered. The two incremental equilibrium equations corresponding to a nonlinear pre-buckling state of strain are reduced to a fourth-order linear eigenproblem that displays a multiple turning point. It is found that for 0 
doi_str_mv 10.1093/qjmam/hbn009
format article
fullrecord <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_00341387v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><oup_id>10.1093/qjmam/hbn009</oup_id><sourcerecordid>1535963541</sourcerecordid><originalsourceid>FETCH-LOGICAL-c434t-179edeea45bd16d34087a49ebe707f65fc7009f28c446a8058cf5084e94326903</originalsourceid><addsrcrecordid>eNqF0E1v1DAQBmALgcRSuPEDIiSEkAgdx-OPHLflYxELXEqFuFiO16beZuPUThD997ik2iunkazHr2ZeQp5TeEuhZac3-4M5nF51A0D7gKwoCqyZ4vwhWQEwVnNB8TF5kvMeABCVWJF363x7GKc4BVsll-d-ypWPqeqCn5M1U4hDrsJQjXNyVeeGXRh-VdFXae46V1gf7XV-Sh5502f37H6ekO8f3l-cb-rtt4-fztfb2iLDqaaydTvnDPJuR8WOIShpsHWdkyC94N7KsrhvlEUURgFX1nNQ6FpkjWiBnZDXS-6V6fWYwsGkWx1N0Jv1Vt-9lSuRMiV_02JfLHZM8WZ2edL7OKehrKcb1qBQyNuC3izIpphzcv6YSkHfVar_VaqXSgt_eZ9psjW9T2awIR__NMBLLjTFvVpcnMf_JdaLDHlyf47WpGstJJNcb3781Gefv8jLS3mhv7K_3ziTTA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>232468459</pqid></control><display><type>article</type><title>Asymptotic results for bifurcations in pure bending of rubber blocks</title><source>Oxford Journals Online</source><creator>Coman, Ciprian D. ; Destrade, Michel</creator><creatorcontrib>Coman, Ciprian D. ; Destrade, Michel</creatorcontrib><description>The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length η, subject to pure bending, is considered. The two incremental equilibrium equations corresponding to a nonlinear pre-buckling state of strain are reduced to a fourth-order linear eigenproblem that displays a multiple turning point. It is found that for 0 &lt; η &lt; ∞, the block experiences an Euler-type buckling instability which in the limit η → ∞ degenerates into a surface instability. Singular perturbation methods enable us to capture this transition, while direct numerical simulations corroborate the analytical results.</description><identifier>ISSN: 0033-5614</identifier><identifier>EISSN: 1464-3855</identifier><identifier>DOI: 10.1093/qjmam/hbn009</identifier><identifier>CODEN: QJMMAV</identifier><language>eng</language><publisher>Oxford: Oxford University Press</publisher><subject>Applied sciences ; Buckling ; Elastomers ; Engineering Sciences ; Exact sciences and technology ; Fundamental areas of phenomenology (including applications) ; Industrial polymers. Preparations ; Materials and structures in mechanics ; Mathematical methods in physics ; Mechanics ; Numerical approximation and analysis ; Numerical simulation, solution of equations ; Physics ; Polymer industry, paints, wood ; Solid mechanics ; Structural and continuum mechanics ; Technology of polymers</subject><ispartof>Quarterly journal of mechanics and applied mathematics, 2008-08, Vol.61 (3), p.395-414</ispartof><rights>Q. Jl Mech. Appl. Math, Vol. 61. No. 3 © The author 2008. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org 2008</rights><rights>2008 INIST-CNRS</rights><rights>Q. Jl Mech. Appl. Math, Vol. 61. No. 3 © The author 2008. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c434t-179edeea45bd16d34087a49ebe707f65fc7009f28c446a8058cf5084e94326903</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27922,27923</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=20546802$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-00341387$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Coman, Ciprian D.</creatorcontrib><creatorcontrib>Destrade, Michel</creatorcontrib><title>Asymptotic results for bifurcations in pure bending of rubber blocks</title><title>Quarterly journal of mechanics and applied mathematics</title><description>The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length η, subject to pure bending, is considered. The two incremental equilibrium equations corresponding to a nonlinear pre-buckling state of strain are reduced to a fourth-order linear eigenproblem that displays a multiple turning point. It is found that for 0 &lt; η &lt; ∞, the block experiences an Euler-type buckling instability which in the limit η → ∞ degenerates into a surface instability. Singular perturbation methods enable us to capture this transition, while direct numerical simulations corroborate the analytical results.</description><subject>Applied sciences</subject><subject>Buckling</subject><subject>Elastomers</subject><subject>Engineering Sciences</subject><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Industrial polymers. Preparations</subject><subject>Materials and structures in mechanics</subject><subject>Mathematical methods in physics</subject><subject>Mechanics</subject><subject>Numerical approximation and analysis</subject><subject>Numerical simulation, solution of equations</subject><subject>Physics</subject><subject>Polymer industry, paints, wood</subject><subject>Solid mechanics</subject><subject>Structural and continuum mechanics</subject><subject>Technology of polymers</subject><issn>0033-5614</issn><issn>1464-3855</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNqF0E1v1DAQBmALgcRSuPEDIiSEkAgdx-OPHLflYxELXEqFuFiO16beZuPUThD997ik2iunkazHr2ZeQp5TeEuhZac3-4M5nF51A0D7gKwoCqyZ4vwhWQEwVnNB8TF5kvMeABCVWJF363x7GKc4BVsll-d-ypWPqeqCn5M1U4hDrsJQjXNyVeeGXRh-VdFXae46V1gf7XV-Sh5502f37H6ekO8f3l-cb-rtt4-fztfb2iLDqaaydTvnDPJuR8WOIShpsHWdkyC94N7KsrhvlEUURgFX1nNQ6FpkjWiBnZDXS-6V6fWYwsGkWx1N0Jv1Vt-9lSuRMiV_02JfLHZM8WZ2edL7OKehrKcb1qBQyNuC3izIpphzcv6YSkHfVar_VaqXSgt_eZ9psjW9T2awIR__NMBLLjTFvVpcnMf_JdaLDHlyf47WpGstJJNcb3781Gefv8jLS3mhv7K_3ziTTA</recordid><startdate>20080801</startdate><enddate>20080801</enddate><creator>Coman, Ciprian D.</creator><creator>Destrade, Michel</creator><general>Oxford University Press</general><general>Oxford Publishing Limited (England)</general><general>Oxford University Press (OUP)</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>20080801</creationdate><title>Asymptotic results for bifurcations in pure bending of rubber blocks</title><author>Coman, Ciprian D. ; Destrade, Michel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c434t-179edeea45bd16d34087a49ebe707f65fc7009f28c446a8058cf5084e94326903</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Applied sciences</topic><topic>Buckling</topic><topic>Elastomers</topic><topic>Engineering Sciences</topic><topic>Exact sciences and technology</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Industrial polymers. Preparations</topic><topic>Materials and structures in mechanics</topic><topic>Mathematical methods in physics</topic><topic>Mechanics</topic><topic>Numerical approximation and analysis</topic><topic>Numerical simulation, solution of equations</topic><topic>Physics</topic><topic>Polymer industry, paints, wood</topic><topic>Solid mechanics</topic><topic>Structural and continuum mechanics</topic><topic>Technology of polymers</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Coman, Ciprian D.</creatorcontrib><creatorcontrib>Destrade, Michel</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Quarterly journal of mechanics and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Coman, Ciprian D.</au><au>Destrade, Michel</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic results for bifurcations in pure bending of rubber blocks</atitle><jtitle>Quarterly journal of mechanics and applied mathematics</jtitle><date>2008-08-01</date><risdate>2008</risdate><volume>61</volume><issue>3</issue><spage>395</spage><epage>414</epage><pages>395-414</pages><issn>0033-5614</issn><eissn>1464-3855</eissn><coden>QJMMAV</coden><abstract>The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length η, subject to pure bending, is considered. The two incremental equilibrium equations corresponding to a nonlinear pre-buckling state of strain are reduced to a fourth-order linear eigenproblem that displays a multiple turning point. It is found that for 0 &lt; η &lt; ∞, the block experiences an Euler-type buckling instability which in the limit η → ∞ degenerates into a surface instability. Singular perturbation methods enable us to capture this transition, while direct numerical simulations corroborate the analytical results.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><doi>10.1093/qjmam/hbn009</doi><tpages>20</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0033-5614
ispartof Quarterly journal of mechanics and applied mathematics, 2008-08, Vol.61 (3), p.395-414
issn 0033-5614
1464-3855
language eng
recordid cdi_hal_primary_oai_HAL_hal_00341387v1
source Oxford Journals Online
subjects Applied sciences
Buckling
Elastomers
Engineering Sciences
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Industrial polymers. Preparations
Materials and structures in mechanics
Mathematical methods in physics
Mechanics
Numerical approximation and analysis
Numerical simulation, solution of equations
Physics
Polymer industry, paints, wood
Solid mechanics
Structural and continuum mechanics
Technology of polymers
title Asymptotic results for bifurcations in pure bending of rubber blocks
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T12%3A20%3A20IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Asymptotic%20results%20for%20bifurcations%20in%20pure%20bending%20of%20rubber%20blocks&rft.jtitle=Quarterly%20journal%20of%20mechanics%20and%20applied%20mathematics&rft.au=Coman,%20Ciprian%20D.&rft.date=2008-08-01&rft.volume=61&rft.issue=3&rft.spage=395&rft.epage=414&rft.pages=395-414&rft.issn=0033-5614&rft.eissn=1464-3855&rft.coden=QJMMAV&rft_id=info:doi/10.1093/qjmam/hbn009&rft_dat=%3Cproquest_hal_p%3E1535963541%3C/proquest_hal_p%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c434t-179edeea45bd16d34087a49ebe707f65fc7009f28c446a8058cf5084e94326903%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=232468459&rft_id=info:pmid/&rft_oup_id=10.1093/qjmam/hbn009&rfr_iscdi=true