Representation of a smooth isometric deformation of a planar material region into a curved surface
type: Item
instance of: scholarly article
title: Representation of a smooth isometric deformation of a planar material region into a curved surface
zbMATH Open document ID: 1396.53003
author: Yichao Chen
author: Eliot Fried
author: Roger Fosdick
published in: Journal of Elasticity
publication date: 2018-02-07T00:00:00Z
review text: The authors provide necessary and sufficient conditions, as well as the corresponding coordinate representations, for the smooth (\({\mathcal C}^3\)-class) isometric deformations of a planar material region (identified with an open connected subset \({\mathcal D}\subset {\mathbb E}^2\)) into a surface \({\mathcal S}\subset {\mathbb E}^3\). Kinematic aspects of the two-dimensional continuous material regions (stretches of material filaments, distortion of material reference configuration) impose a stronger definition of isometric deformation than the classic one that is used in differential geometry. A strategy for determining such kinematic isometric deformations is presented together with explicit examples of the corresponding representations.
reviewed by: Ioan Bucataru
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 74K35
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 53A45
zbMATH DE Number: 6835479
zbMATH Keywords: kinematic isometry
zbMATH Keywords: planar material region, coordinate representation
MaRDI profile type: Publication
full work available at URL: s10659-017-9637-2
OpenAlex ID: W2607060675
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DOI: 10.1007/S10659-017-9637-2
description: scientific article; zbMATH DE number 6835479