On Hamilton's principle for thermo-elastic fluids and solids, and internal constraints in thermo-elasticity
type: Item
instance of: scholarly article
title: On Hamilton's principle for thermo-elastic fluids and solids, and internal constraints in thermo-elasticity
zbMATH Open document ID: 0634.76002
DOI: 10.1007/BF00251390
author: Gautam Batra
published in: Archive for Rational Mechanics and Analysis
publication date: 1987-01-01T00:00:00Z
review text: We have shown here that Hamilton's principle may be used to obtain the equations of motion and to deduce the Cauchy stress principle and the Gibbs relations for one of the simplest models from continuum mechanics, viz., thermo-elastic fluids and solids. We have not limited our theory to isentropic processes; specifically, these models allow for heat conduction. However, we do assume the existence of a thermodynamical potential, but show that the stress and entropy/temperature are obtained from its partial derivatives. Further study will be required to determine whether a similar principle, which is not simply ``little more than a reformulation of the equations of motion'', can be developed for, say, viscous heat-conducting fluids. It is hoped that some of the considerations arising in this work will prove useful in studies of mixtures, liquid crystals, granular solids, etc., where variational principles are sometimes used to obtain equations of motion.
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 76A02
zbMATH DE Number: 4033310
zbMATH Keywords: Hamilton's principle
zbMATH Keywords: Cauchy stress principle
zbMATH Keywords: Gibbs relations
zbMATH Keywords: continuum mechanics
zbMATH Keywords: thermo-elastic fluids
zbMATH Keywords: heat conduction
zbMATH Keywords: thermodynamical potential
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4033310