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Two-scale homogenization for a model in strain gradient plasticity

Published online by Cambridge University Press:  28 October 2010

Alessandro Giacomini  and
Alessandro Musesti
Alessandro Giacomini
Affiliation:
Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy. alessandro.giacomini@ing.unibs.it
Alessandro Musesti
Affiliation:
Dipartimento di Matematica e Fisica “Niccolò Tartaglia”, Università Cattolica del Sacro Cuore, Via dei Musei 41, 25121 Brescia, Italy. alessandro.musesti@unicatt.it
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Abstract

Using the tool of two-scale convergence, we provide a rigorous mathematical setting for the homogenization result obtained by Fleck and Willis [J. Mech. Phys. Solids52 (2004) 1855–1888] concerning the effective plastic behaviour of a strain gradient composite material. Moreover, moving from deformation theory to flow theory, we prove a convergence result for the homogenization of quasistatic evolutions in the presence of isotropic linear hardening.

Keywords

Strain gradient plasticityperiodic homogenizationtwo-scale convergencequasistatic evolutions
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 4 , October 2011 , pp. 1035 - 1065
Copyright
© EDP Sciences, SMAI, 2010

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