| Issue |
ESAIM: COCV
Volume 17, Number 4, October-December 2011
|
|
|---|---|---|
| Page(s) | 1035 - 1065 | |
| DOI | https://doi.org/10.1051/cocv/2010036 | |
| Published online | 28 October 2010 | |
Two-scale homogenization for a model in strain gradient plasticity
1
Dipartimento di
Matematica, Facoltà di Ingegneria, Università degli Studi di
Brescia, Via Valotti 9, 25133 Brescia, Italy. alessandro.giacomini@ing.unibs.it
2
Dipartimento di Matematica e Fisica
“Niccolò Tartaglia”,
Università Cattolica del Sacro Cuore, Via dei Musei 41, 25121 Brescia, Italy. alessandro.musesti@unicatt.it
Received:
12
October
2009
Revised:
2
April
2010
Revised:
5
May
2010
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. Solids 52 (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.
Mathematics Subject Classification: 74C05 / 74G65 / 74Q05 / 35B27 / 49J45
Key words: Strain gradient plasticity / periodic homogenization / two-scale convergence / quasistatic evolutions
© EDP Sciences, SMAI, 2010
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