Relaxation-type equations for viscoelastic media with finite deformations
type: Item
instance of: scholarly article
title: Relaxation-type equations for viscoelastic media with finite deformations
zbMATH Open document ID: 0614.73042
DOI: 10.1016/0021-8928(85)90079-6
author: V. I. Kondaurov
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: The representation of the total deformations in the form of a composition of elastic and irreversible components is considered to describe finite deformations of viscoelastic materials of relaxation type. According to the method of internal parameters, it is assumed that the thermodynamic potential, the stress tensor, the entropy density, and thermal flux, and the rate of change of inelastic deformations are functions of the total deformation, the temperature, the temperature gradient, and the irreversible deformation. On the basic of requirements for invariance of the governing equations, a definition of isotropic ideal and hardened viscoelastic bodies is given. Necessary and sufficient conditions are formulated which the equations of state of such media should satisfy. The propagation of isothermal waves of weak discontinuity in an ideal viscoelastic medium with small elastic and finite total deformations is considered as an illustration.
Mathematics Subject Classification ID: 74D10
Mathematics Subject Classification ID: 74D05
zbMATH DE Number: 3995170
zbMATH Keywords: composition of elastic and irreversible components
zbMATH Keywords: thermodynamic potential
zbMATH Keywords: stress tensor
zbMATH Keywords: entropy density
zbMATH Keywords: thermal flux
zbMATH Keywords: rate of change of inelastic deformations
zbMATH Keywords: invariance
zbMATH Keywords: isotropic ideal and hardened viscoelastic bodies
zbMATH Keywords: Necessary and sufficient conditions
zbMATH Keywords: equations of state
zbMATH Keywords: isothermal waves of weak discontinuity
MaRDI profile type: Publication
full work available at URL: 0021-8928(85)90079-6
OpenAlex ID: W2055072959
cites work: Elastic-Plastic Deformation at Finite Strains
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description: scientific article; zbMATH DE number 3995170