The description, classification, and reality of material and physical symmetries
type: Item
instance of: scholarly article
title: The description, classification, and reality of material and physical symmetries
zbMATH Open document ID: 0811.73002
DOI: 10.1007/BF01178519
author: J. P. Boehler
author: Quanshui Zheng
published in: Acta Mechanica
publication date: 1995-05-07T00:00:00Z
review text: We reconsider the definitions of both material symmetries and physical symmetries which are described in terms of point groups, i.e. subgroups of the full orthogonal group, because these two concepts are often confused, and the classical descriptions of physical symmetry for inelastic behaviour of materials are impracticable. All two- and three- dimensional point groups are classified into two types: compact and non- compact. The reality of every compact point group in the description of a material or a physical symmetry is justified in four aspects, that is: (i) point groups characterized by a finite set of tensors, (ii) Hilbert's theorem for integrity bases, (iii) correlation between integrity bases and function bases (generalization of Wineman and Pipkin's theorem), and (iv) physical reality.
Mathematics Subject Classification ID: 74E15
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 20F99
zbMATH DE Number: 709595
zbMATH Keywords: non-compact point group
zbMATH Keywords: compact point group
zbMATH Keywords: Hilbert's theorem for integrity bases
zbMATH Keywords: function bases
zbMATH Keywords: Wineman and Pipkin's theorem
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01178519
OpenAlex ID: W2084666333
description: scientific article; zbMATH DE number 709595