ON THE FLECK AND WILLIS HOMOGENIZATION PROCEDURE IN STRAIN GRADIENT PLASTICITY

被引:4
作者
Francfort, Gilles A. [1 ]
Giacomini, Alessandro [2 ]
Musesti, Alessandro [3 ]
机构
[1] Univ Paris 13, LAGA, F-93430 Villetaneuse, France
[2] Univ Brescia, Dipartimento Matemat, Fac Ingn, I-25133 Brescia, Italy
[3] Univ Cattolica Sacro Cuore, Dipartimento Matemat & Fis Niccolo Tartaglia, I-25121 Brescia, Italy
来源
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2013年 / 6卷 / 01期
关键词
Homogenization; gradient plasticity; H-convergence; 2-SCALE HOMOGENIZATION; CONVERGENCE;
D O I
10.3934/dcdss.2013.6.43
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We revisit the homogenization process for a heterogeneous small strain gradient plasticity model considered in [5]. We derive a precise homogenized behavior, independently of any kind of periodicity assumption and demonstrate that it reduces to a model studied in [x] when periodicity is reintroduced.
引用
收藏
页码:43 / 62
页数:20
相关论文
共 14 条
[1]   HOMOGENIZATION AND 2-SCALE CONVERGENCE [J].
ALLAIRE, G .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1992, 23 (06) :1482-1518
[2]  
[Anonymous], 1997, Progr. Nonlinear Differential Equations Appl
[3]   DEFORMATION OF PLASTICALLY NON-HOMOGENEOUS MATERIALS [J].
ASHBY, MF .
PHILOSOPHICAL MAGAZINE, 1970, 21 (170) :399-&
[4]   Bounds and estimates for the effect of strain gradients upon the effective plastic properties of an isotropic two-phase composite [J].
Fleck, NA ;
Willis, JR .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2004, 52 (08) :1855-1888
[5]   A reformulation of strain gradient plasticity [J].
Fleck, NA ;
Hutchinson, JW .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2001, 49 (10) :2245-2271
[6]   Strain gradient plasticity [J].
Fleck, NA ;
Hutchinson, JW .
ADVANCES IN APPLIED MECHANICS, VOL 33, 1997, 33 :295-361
[7]  
FRANCFORT GA, 1994, J REINE ANGEW MATH, V454, P1
[8]   Gradient theory for plasticity via homogenization of discrete dislocations [J].
Garroni, Adriana ;
Leoni, Giovanni ;
Ponsiglione, Marcello .
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2010, 12 (05) :1231-1266
[9]   TWO-SCALE HOMOGENIZATION FOR A MODEL IN STRAIN GRADIENT PLASTICITY [J].
Giacomini, Alessandro ;
Musesti, Alessandro .
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2011, 17 (04) :1035-1065
[10]   A unified treatment of strain gradient plasticity [J].
Gudmundson, P .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2004, 52 (06) :1379-1406