Volume 17, Number 4, October-December 2011
|Page(s)||1035 - 1065|
|Published online||28 October 2010|
Two-scale homogenization for a model in strain gradient plasticity
Matematica, Facoltà di Ingegneria, Università degli Studi di
Brescia, Via Valotti 9, 25133 Brescia, Italy. firstname.lastname@example.org
2 Dipartimento di Matematica e Fisica “Niccolò Tartaglia”, Università Cattolica del Sacro Cuore, Via dei Musei 41, 25121 Brescia, Italy. email@example.com
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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