Field fluctuations in a heterogeneous elastic material - An information theory approach
type: Item
instance of: scholarly article
title: Field fluctuations in a heterogeneous elastic material - An information theory approach
zbMATH Open document ID: 0598.73004
DOI: 10.1016/0022-5096(85)90008-0
author: W. Pompe
author: Wolfgang S. Kreher
published in: Journal of the Mechanics and Physics of Solids
publication date: 1985-01-01T00:00:00Z
review text: The subject is related to randomly disordered solids as polycrystals or multiphase materials. The tensor of elastic constants is a random function of position. A joint probability density functional of elastic constants and displacements is introduced and its entropy is defined by a double functional integral. The functional which maximizes the entropy and agrees with constraints is derived. An approximate solution is given for a case when one-point probability density is available only. Effective elastic properties are connected with the topological order and fluctuations of the strain field. A composite material which consists of N isotropic components is taken as an example. The Gauss probability distributions are obtained for the stress and strain and mean values and fluctuations of stresses are calculated for a cemented metal carbide and a zinc polycrystal. A solution of the variational problem where the random field is subject to constraints, is presented in an appendix.
Mathematics Subject Classification ID: 74A40
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 82D30
Mathematics Subject Classification ID: 74E15
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74A60
Mathematics Subject Classification ID: 74M25
Mathematics Subject Classification ID: 62B10
zbMATH DE Number: 3965517
zbMATH Keywords: internal stress
zbMATH Keywords: strain fields
zbMATH Keywords: information theory entropy is maximized subject to constraints
zbMATH Keywords: equations of elasticity
zbMATH Keywords: experimental data
zbMATH Keywords: polycrystals
zbMATH Keywords: multiphase materials
zbMATH Keywords: Gauss probability distributions
reviewed by: J. Murzewski
MaRDI profile type: Publication
full work available at URL: 0022-5096(85)90008-0
OpenAlex ID: W2055531912
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description: scientific article; zbMATH DE number 3965517