Theory and thermohyperelasticity for near-incompressible elastomers
type: Item
instance of: scholarly article
title: Theory and thermohyperelasticity for near-incompressible elastomers
zbMATH Open document ID: 0864.73014
DOI: 10.1007/BF01171417
author: Yanyan Li
published in: Acta Mechanica
publication date: 1997-06-24T00:00:00Z
review text: Contrary to common practice which discards thermal effects by considering purely isothermal evolutions, the authors formulate a truly thermo-hyperelasticity for near-incompressible elastomers. The thermal strain ``gradient'' is a nonintegrable part of a multiplicative decomposition of the true gradient of finite deformation. Furthermore, shear and volume deformation aspects are naturally decoupled, and the thermomechanical coupling takes place essentially via the thermal expansion. Criteria for thermodynamic stability are thus derived in a rather compact form. A particular expression for Helmholtz's free energy is given which represents the thermo-mechanical counterpart of the conventional two-term incompressible Mooney-Rivlin model. These considerations are applied in a short study to the slow isothermal extension of a rubber rod and to the rapid adiabatic extension of this rod.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 952301
zbMATH Keywords: adiabatic extension of rubber red
zbMATH Keywords: isothermal extension of rubber rod
zbMATH Keywords: thermal strain ``gradient''
zbMATH Keywords: multiplicative decomposition
zbMATH Keywords: shear and volume deformation
zbMATH Keywords: thermal expansion
zbMATH Keywords: thermodynamic stability
zbMATH Keywords: Helmholtz's free energy
zbMATH Keywords: Mooney-Rivlin model
reviewed by: Gérard A. Maugin
describes a project that uses: ANSYS
describes a project that uses: ABAQUS
MaRDI profile type: Publication
cites work: A nonlinear thermoelasticity theory
cites work: Q5645108
cites work: A finite element approach for large strains of nearly incompressible rubber-like materials
cites work: Tangent modulus matrix for finite element analysis of hyperelastic materials
cites work: Q4538731
full work available at URL: https://doi.org/10.1007/bf01171417
OpenAlex ID: W2055490472
description: scientific article; zbMATH DE number 952301