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quasistatic evolutions

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Two-scale homogenization for a modelin strain gradient plasticity
Alessandro Giacomini, Alessandro Musesti
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 4 / October 2011

Published online by Cambridge University Press:

28 October 2010, pp. 1035-1065

Print publication:

October 2011
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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.