{"title":"线性摄动法与分岔分析预测变形位置的理论关系","authors":"Gilles Barbier , Ahmed Benallal , Valérie Cano","doi":"10.1016/S1251-8069(99)89001-0","DOIUrl":null,"url":null,"abstract":"<div><p>The uniqueness of mechanical response can be lost for a material with softening. For a non-viscous material, two methods are widely used to predict this phenomenon: the linear perturbation method and the bifurcation analysis. In this paper we prove that the latter method should be considered as a limit case of the former one, as already observed in some particular cases.</p></div>","PeriodicalId":100304,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1998-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1251-8069(99)89001-0","citationCount":"20","resultStr":"{\"title\":\"Relation théorique entre la méthode de perturbation linéaire et l'analyse de bifurcation pour la prédiction de la localisation des déformations\",\"authors\":\"Gilles Barbier , Ahmed Benallal , Valérie Cano\",\"doi\":\"10.1016/S1251-8069(99)89001-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The uniqueness of mechanical response can be lost for a material with softening. For a non-viscous material, two methods are widely used to predict this phenomenon: the linear perturbation method and the bifurcation analysis. In this paper we prove that the latter method should be considered as a limit case of the former one, as already observed in some particular cases.</p></div>\",\"PeriodicalId\":100304,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1251-8069(99)89001-0\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1251806999890010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1251806999890010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Relation théorique entre la méthode de perturbation linéaire et l'analyse de bifurcation pour la prédiction de la localisation des déformations
The uniqueness of mechanical response can be lost for a material with softening. For a non-viscous material, two methods are widely used to predict this phenomenon: the linear perturbation method and the bifurcation analysis. In this paper we prove that the latter method should be considered as a limit case of the former one, as already observed in some particular cases.
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