A note on Cauchy-Voigt dispute of independent constants in anisotropic elastic Hooke's law
type: Item
instance of: scholarly article
title: A note on Cauchy-Voigt dispute of independent constants in anisotropic elastic Hooke's law
zbMATH Open document ID: 0985.74007
DOI: 10.1016/S0093-6413(99)00027-0
author: D.-X. Du
author: Quanshui Zheng
published in: Mechanics Research Communications
publication date: 2002-05-27T00:00:00Z
review text: During the last years some publications had been devoted to the classical question of the maximum number of independent elastic constants in fully anisotropic linear elasticity (which is usually taken to be 21 due to the major symmetry of the elasticity tensor). According to Cauchy, however, this number should be 15. Here the authors show that Cauchy's elasticity tensor is the ``completely symmetric part'' (CSP) of Green's elasticity tensor. Further, they prove for two-dimensional piezoelectric problem with prescribed traction boundary conditions in a simply connected region that the stresses and electric displacements depend only on the CSP of three involved material tensors.
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74F15
zbMATH DE Number: 1445987
zbMATH Keywords: Hooke's law
zbMATH Keywords: completely symmetric part
zbMATH Keywords: maximum number of independent elastic constants
zbMATH Keywords: anisotropic linear elasticity
zbMATH Keywords: Cauchy's elasticity tensor
zbMATH Keywords: Green's elasticity tensor
zbMATH Keywords: two-dimensional piezoelectric problem
zbMATH Keywords: traction boundary conditions
zbMATH Keywords: material tensors
reviewed by: Hans Bufler
MaRDI profile type: Publication
full work available at URL: s0093-6413(99)00027-0
OpenAlex ID: W2056465309
description: scientific article; zbMATH DE number 1445987