Model reduction by mean-field homogenization in viscoelastic composites. I. Primal theory

A homogenization scheme for viscoelastic composites proposed by Lahellec & Suquet (2007 Int. J. Solids Struct.44, 507–529 (doi:10.1016/j.ijsolstr.2006.04.038)) is revisited. The scheme relies upon an incremental variational formulation providing the inelastic strain field at a given time ste...

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Autores principales: Idiart, Martín Ignacio, Lahellec, Noël, Suquet, Pierre
Formato: Articulo
Lenguaje:Inglés
Publicado: 2020
Materias:
Ingeniería Aeronáutica
Viscoelasticity
Composites
Homogenization
Variational methods
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/137943
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-137943
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ingeniería Aeronáutica
Viscoelasticity
Composites
Homogenization
Variational methods
spellingShingle Ingeniería Aeronáutica
Viscoelasticity
Composites
Homogenization
Variational methods
Idiart, Martín Ignacio
Lahellec, Noël
Suquet, Pierre
Model reduction by mean-field homogenization in viscoelastic composites. I. Primal theory
topic_facet Ingeniería Aeronáutica
Viscoelasticity
Composites
Homogenization
Variational methods
description A homogenization scheme for viscoelastic composites proposed by Lahellec & Suquet (2007 Int. J. Solids Struct.44, 507–529 (doi:10.1016/j.ijsolstr.2006.04.038)) is revisited. The scheme relies upon an incremental variational formulation providing the inelastic strain field at a given time step in terms of the inelastic strain field from the previous time step, along with a judicious use of Legendre transforms to approximate the relevant functional by an alternative functional depending on the inelastic strain fields only through their first and second moments over each constituent phase. As a result, the approximation generates a reduced description of the microscopic state of the composite in terms of a finite set of internal variables that incorporates information on the intraphase fluctuations of the inelastic strain and that can be evaluated by mean-field homogenization techniques. In this work we provide an alternative derivation of the scheme, relying on the Cauchy–Schwarz inequality rather than the Legendre transform, and in so doing we expose the mathematical structure of the resulting approximation and generalize the exposition to fully anisotropic material systems.
format Articulo
Articulo
author Idiart, Martín Ignacio
Lahellec, Noël
Suquet, Pierre
author_facet Idiart, Martín Ignacio
Lahellec, Noël
Suquet, Pierre
author_sort Idiart, Martín Ignacio
title Model reduction by mean-field homogenization in viscoelastic composites. I. Primal theory
title_short Model reduction by mean-field homogenization in viscoelastic composites. I. Primal theory
title_full Model reduction by mean-field homogenization in viscoelastic composites. I. Primal theory
title_fullStr Model reduction by mean-field homogenization in viscoelastic composites. I. Primal theory
title_full_unstemmed Model reduction by mean-field homogenization in viscoelastic composites. I. Primal theory
title_sort model reduction by mean-field homogenization in viscoelastic composites. i. primal theory
publishDate 2020
url http://sedici.unlp.edu.ar/handle/10915/137943
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AT lahellecnoel modelreductionbymeanfieldhomogenizationinviscoelasticcompositesiprimaltheory
AT suquetpierre modelreductionbymeanfieldhomogenizationinviscoelasticcompositesiprimaltheory
bdutipo_str Repositorios
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