Isometries Between Given Surfaces and the Isometric Deformation of a Single Unstretchable Material Surface
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Published:2022-07-07
Issue:1
Volume:151
Page:159-175
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ISSN:0374-3535
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Container-title:Journal of Elasticity
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language:en
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Short-container-title:J Elast
Author:
Chen Yi-chao,Fosdick Roger,Fried Eliot
Abstract
AbstractThe difference between the differential geometric concept of an isometry between two given surfaces as purely mathematical objects and the kinematical concept of an isometric deformation of a single unstretchable material surface as a physical object is discussed. We clarify some misunderstandings that have been promoted in recent works concerning the mechanics of unstretchable material surfaces and we discuss this issue within the context of two specific examples. A revealing distinction between isometries and isometric deformations in two space dimensions is reviewed, and the use of rectifying developable surfaces to characterize the isometric deformation of rectangular material strips is analyzed.
Publisher
Springer Science and Business Media LLC
Subject
Mechanical Engineering,Mechanics of Materials,General Materials Science
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