A coordinate-free approach to the kinematics of membranes
type: Item
instance of: scholarly article
title: A coordinate-free approach to the kinematics of membranes
zbMATH Open document ID: 0582.73011
DOI: 10.1007/BF00041068
author: Chi-Sing Man
author: H. Cohen
published in: Journal of Elasticity
publication date: 1986-01-01T00:00:00Z
review text: In the kinematics of a three-dimensional continuum the polar decomposition of the so-called deformation gradient into a stretch tensor and a rotation tensor is well known. An analogous decomposition can be developed with respect to a two-dimensional membrane. The standard polar decomposition, however, is connected with some problems resulting from the fact that the two-dimensional tangent space changes with the deformations of the membrane. These difficulties can be removed by introducing a supplementary new polar decomposition taking into account the embedding of the two-dimensional membrane into the three-dimensional Euclidean space.
Mathematics Subject Classification ID: 74A99
Mathematics Subject Classification ID: 74Axx
Mathematics Subject Classification ID: 53A45
zbMATH DE Number: 3932480
zbMATH Keywords: kinematics
zbMATH Keywords: three-dimensional continuum
zbMATH Keywords: polar decomposition
zbMATH Keywords: deformation gradient
zbMATH Keywords: stretch tensor
zbMATH Keywords: rotation tensor
zbMATH Keywords: two-dimensional membrane
zbMATH Keywords: supplementary new polar decomposition
zbMATH Keywords: embedding of the two-dimensional membrane into the three-dimensional Euclidean space
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00041068
OpenAlex ID: W1989537474
description: scientific article; zbMATH DE number 3932480