Isometries between given surfaces and the isometric deformation of a single unstretchable material surface
type: Item
instance of: scholarly article
title: Isometries between given surfaces and the isometric deformation of a single unstretchable material surface
zbMATH Open document ID: 1503.53007
author: Yichao Chen
author: Eliot Fried
author: Roger Fosdick
published in: Journal of Elasticity
publication date: 2022-10-18T00:00:00Z
review text: The concept of isometry is a well known property in the theory of surfaces (and Riemannian geometry in general). The present paper discusses the 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. Further, the authors analyse some misunderstandings that have been promoted in recent works concerning the mechanics of unstretchable material surfaces and 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 presented.
reviewed by: Andreas Arvanitoyeorgos
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53A45
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 74K35
Mathematics Subject Classification ID: 57R40
zbMATH DE Number: 7603447
zbMATH Keywords: inextensible surface
zbMATH Keywords: inextensional surface
zbMATH Keywords: two-dimensional Riemannian manifold
zbMATH Keywords: embedding
zbMATH Keywords: developable surface
zbMATH Keywords: rectifying developable
zbMATH Keywords: internal constraint
MaRDI profile type: Publication
full work available at URL: s10659-022-09909-0
OpenAlex ID: W4284883686
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DOI: 10.1007/S10659-022-09909-0
description: scientific article; zbMATH DE number 7603447