Material symmetry and the evolution of anisotropies in a simple material. I: Change of reference configuration
type: Item
instance of: scholarly article
title: Material symmetry and the evolution of anisotropies in a simple material. I: Change of reference configuration
zbMATH Open document ID: 0706.73003
DOI: 10.1016/0020-7462(89)90017-6
author: Mehrdad Negahban
author: Alan S. Wineman
published in: International Journal of Non-Linear Mechanics
publication date: 1989-01-01T00:00:00Z
review text: In this work the authors studied the material symmetry and evolution of anisotropies in a simple material. They started by presenting the basic properties of material symmetry groups. Then they showed that for a material symmetry represented by a group of material symmetry groups (MSG); members of which are related by Noll's rule, Noll's rule allowed the generation of MSG, g, from any of its member. They next defined the apparent MSG of a MSG as its subgroup of orthogonal transformations. They showed that the apparent MSG of one MSG in g imposes a structure on all other MSG's of g. They used this property to identify all apparent MSG's realized in g. Finally, they provided particular results for the cases of an isotropic, orthotropic, and transversely isotropic material. This work might be very useful for those researchers working on the mathematical theory of simple materials.
Mathematics Subject Classification ID: 74E15
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74E10
zbMATH DE Number: 4160208
zbMATH Keywords: Noll's rule
zbMATH Keywords: isotropic
zbMATH Keywords: orthotropic
zbMATH Keywords: transversely isotropic material
reviewed by: Hilmi Demiray
MaRDI profile type: Publication
full work available at URL: 0020-7462(89)90017-6
OpenAlex ID: W2042725995
description: scientific article; zbMATH DE number 4160208