Augmented Hooke's law based on alternative stress relaxation models
type: Item
instance of: scholarly article
title: Augmented Hooke's law based on alternative stress relaxation models
zbMATH Open document ID: 0983.74005
author: K. Dovstam
published in: Computational Mechanics
publication date: 2002-04-14T00:00:00Z
review text: The author presents a unified model (augmented Hooke's law, AHL) of material damping in the presence of linear vibrations. It is based on constitutive modelling of simple solid materials at the macroscopic level, on an internal anelastic strain variable, and on specific assumptions concerning the Helmholtz free energy. The existing discrete AHL model (by the same author) is extended to apply to materials with continuously distributed relaxation frequency spectra under isothermal conditions. Using experimentally estimated data, it is demonstrated that linear material damping may be simulated by using the enhanced AHL relaxation models. It is also shown that there exists a correspondence between each admissible linear damping model and a continuously distributed relaxation spectrum, where the latter can be computed using the Stieltjes-Perron inversion formula. Traditional relaxation time spectra are shown to be directly related to AHL relaxation amplitude distributions derived in the paper.
reviewed by: Nina Kirchner
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74D99
zbMATH DE Number: 1506967
zbMATH Keywords: stress relaxation
zbMATH Keywords: augmented Hooke's law
zbMATH Keywords: material damping
zbMATH Keywords: linear vibration
zbMATH Keywords: internal anelastic strain variable
zbMATH Keywords: Helmholtz free energy
zbMATH Keywords: continuously distributed relaxation frequency spectrum
zbMATH Keywords: linear damping model
zbMATH Keywords: Stieltjes-Perron inversion formula
zbMATH Keywords: relaxation time spectrum
zbMATH Keywords: relaxation amplitude distribution
MaRDI profile type: Publication
full work available at URL: s004660000157
OpenAlex ID: W2047267809
DOI: 10.1007/S004660000157
description: scientific article; zbMATH DE number 1506967