Constitutive equations of elastic polycrystalline materials
type: Item
instance of: scholarly article
title: Constitutive equations of elastic polycrystalline materials
zbMATH Open document ID: 0958.74014
author: Roberto Paroni
author: Chi-Sing Man
published in: Archive for Rational Mechanics and Analysis
publication date: 2001-04-09T00:00:00Z
review text: The authors present a group-theoretical characterization of elastic polycrystalline materials. In order to achieve this, the constitutive equation for Cauchy stress is considered to depend not only on the deformation gradient but also on a set of so-called material ``descriptors'' (examples of which are lattice vectors of a unit cell of a crystallite, and the orientation distribution function -- ODF -- itself in a polycrystal). The group characterization is based on the assumption that, ``in so far as the mechanical response is concerned, any two configurations related by a rigid displacement and with the same material descriptors are indistinguishable''. First, the authors propose a general and abstract setting. Then this is specialized to the case of polycrystalline materials in linear elasticity with initial stresses (original motivation of the work for acousto-elastic applications). Explicit computations are given for prestressed orthorhombic aggregates of cubic crystallites, which are further specialized to the case where the descriptors are composed of the initial stress tensor and of the ODF. This allows the authors to derive equations for fourth- and sixth-order (acoustoelastic) elasticity tensors. In particular, a model-independent formula is obtained for the latter. This formula clearly exhibits the effects of texture on elastic response. This very useful paper generalizes, complements, and somewhat supersedes a part of the results of a previous work by the second author [Arch. Ration. Mech. Anal. 143, No. 1, 77-103 (1998; Zbl 0917.73007)].
Mathematics Subject Classification ID: 74E25
Mathematics Subject Classification ID: 74E15
Mathematics Subject Classification ID: 74B10
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 82D25
zbMATH DE Number: 1419579
zbMATH Keywords: acoustoelastic tensors
zbMATH Keywords: group-theoretical characterization
zbMATH Keywords: elastic polycrystalline materials
zbMATH Keywords: constitutive equation
zbMATH Keywords: Cauchy stress
zbMATH Keywords: orientation distribution function
zbMATH Keywords: material descriptors
zbMATH Keywords: linear elasticity with initial stresses
zbMATH Keywords: orthorhombic aggregates
zbMATH Keywords: cubic crystallites
zbMATH Keywords: texture
reviewed by: Gérard A. Maugin
MaRDI profile type: Publication
full work available at URL: s002050050184
OpenAlex ID: W2027409707
DOI: 10.1007/S002050050184
description: scientific article; zbMATH DE number 1419579