Geodesic
Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set
Carbone, Luciano  ; Cioranescu, Doina  ; Arcangelis, Riccardo De  ; Gaudiello, Antonio1 
1 Università di Cassino, Dipartimento di Automazione, Elettromagnetismo, Ingegneria dell’Informazione e Matematica Industriale, via G. Di Biasio 43, 03043 Cassino (FR), Italy;
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 53-83

Voir la notice de l'article provenant de la source Numdam

The paper is a continuation of a previous work of the same authors dealing with homogenization processes for some energies of integral type arising in the modeling of rubber-like elastomers. The previous paper took into account the general case of the homogenization of energies in presence of pointwise oscillating constraints on the admissible deformations. In the present paper homogenization processes are treated in the particular case of fixed constraints set, in which minimal coerciveness hypotheses can be assumed, and in which the results can be obtained in the general framework of BV spaces. The classical homogenization result is established for Dirichlet with affine boundary data, Neumann, and mixed problems, by proving that the limit energy is again of integral type, gradient constrained, and with an explicitly computed homogeneous density.

DOI : 10.1051/cocv:2003032
Classification : 49J45, 49N20, 74Q05
Keywords: homogenization, gradient constrained variational problems, nonlinear elastomers

Carbone, Luciano  ; Cioranescu, Doina  ; Arcangelis, Riccardo De  ; Gaudiello, Antonio 1

1 Università di Cassino, Dipartimento di Automazione, Elettromagnetismo, Ingegneria dell’Informazione e Matematica Industriale, via G. Di Biasio 43, 03043 Cassino (FR), Italy; 
@article{COCV_2004__10_1_53_0,
     author = {Carbone, Luciano and Cioranescu, Doina and Arcangelis, Riccardo De and Gaudiello, Antonio},
     title = {Homogenization of unbounded functionals and nonlinear elastomers. {The} case of the fixed constraints set},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {53--83},
     publisher = {EDP-Sciences},
     volume = {10},
     number = {1},
     year = {2004},
     doi = {10.1051/cocv:2003032},
     mrnumber = {2084255},
     zbl = {1072.49008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003032/}
}
TY  - JOUR
AU  - Carbone, Luciano
AU  - Cioranescu, Doina
AU  - Arcangelis, Riccardo De
AU  - Gaudiello, Antonio
TI  - Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2004
SP  - 53
EP  - 83
VL  - 10
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003032/
DO  - 10.1051/cocv:2003032
LA  - en
ID  - COCV_2004__10_1_53_0
ER  - 
%0 Journal Article
%A Carbone, Luciano
%A Cioranescu, Doina
%A Arcangelis, Riccardo De
%A Gaudiello, Antonio
%T Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2004
%P 53-83
%V 10
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003032/
%R 10.1051/cocv:2003032
%G en
%F COCV_2004__10_1_53_0
Carbone, Luciano; Cioranescu, Doina; Arcangelis, Riccardo De; Gaudiello, Antonio. Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 53-83. doi: 10.1051/cocv:2003032

Cité par Sources :