Saint-Venant's principle in linear viscoelasticity
type: Item
instance of: scholarly article
title: Saint-Venant's principle in linear viscoelasticity
zbMATH Open document ID: 0917.73028
DOI: 10.1016/S0020-7225(97)00028-1
author: M. Ciarletta
author: Mauro Fabrizio
author: S. Chiriţă
published in: International Journal of Engineering Science
publication date: 1999-08-05T00:00:00Z
review text: We consider an anisotropic and inhomogeneous viseoelastic body that is subjected on the time interval \([0,T]\) to body forces and initial and boundary data having a bounded support. Then a complete description is given upon what happen in the outside of the support region \(D_T\) of the data. More precisely, when the dynamic linear viscoelasticity is considered, we prove that, for each \(t\in[0,T]\), there exists a bounded domain \(D_{ct}\) so that the whole activity vanishes in the outside of \(D_{ct}\); while into the region \(D_{ct} \setminus D_T\) an appropriate measure of the dynamic viscoelastic process in question decays spatially with the distance \(r\) from the bounded support \(D_T\), the decay rate being controlled by the factor \((1-r/ct)\). As a direct consequence of this analysis, we establish a uniqueness theorem for linear viscoelastodynamics, that is valid for infinite domains and is free of any kind of a priori assumptions on the orders of growth of the velocity and stress fields at infinity. When the quasi-static linear viscoelasticity is considered for a bounded body, we associate with the quasi-static viscoelastic process an appropriate energetic volume measure and we establish a spatial decay estimate of exponential type similar to that presented by Toupin for linear elastostatics.
Mathematics Subject Classification ID: 74D99
Mathematics Subject Classification ID: 74G50
zbMATH DE Number: 1162234
zbMATH Keywords: anisotropic viscoelastic body
zbMATH Keywords: domain of dependence
zbMATH Keywords: uniqueness theorem
zbMATH Keywords: quasi-static linear viscoelasticity
zbMATH Keywords: energetic volume measure
zbMATH Keywords: spatial decay estimate of exponential type
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1162234