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.
Keywords: strain gradient plasticity, periodic homogenization, two-scale convergence, quasistatic evolutions
@article{COCV_2011__17_4_1035_0,
author = {Giacomini, Alessandro and Musesti, Alessandro},
title = {Two-scale homogenization for a model in strain gradient plasticity},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1035--1065},
year = {2011},
publisher = {EDP Sciences},
volume = {17},
number = {4},
doi = {10.1051/cocv/2010036},
mrnumber = {2859864},
zbl = {1300.74008},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2010036/}
}
TY - JOUR AU - Giacomini, Alessandro AU - Musesti, Alessandro TI - Two-scale homogenization for a model in strain gradient plasticity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 1035 EP - 1065 VL - 17 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2010036/ DO - 10.1051/cocv/2010036 LA - en ID - COCV_2011__17_4_1035_0 ER -
%0 Journal Article %A Giacomini, Alessandro %A Musesti, Alessandro %T Two-scale homogenization for a model in strain gradient plasticity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 1035-1065 %V 17 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2010036/ %R 10.1051/cocv/2010036 %G en %F COCV_2011__17_4_1035_0
Giacomini, Alessandro; Musesti, Alessandro. Two-scale homogenization for a model in strain gradient plasticity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1035-1065. doi: 10.1051/cocv/2010036
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