Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set

Luciano Carbone; Doina Cioranescu; Riccardo De Arcangelis; Antonio Gaudiello[1]

  • [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 (2004)

  • Volume: 10, Issue: 1, page 53-83
  • ISSN: 1292-8119

Abstract

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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 B V 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.

How to cite

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Carbone, Luciano, et al. "Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set." ESAIM: Control, Optimisation and Calculus of Variations 10.1 (2004): 53-83. <http://eudml.org/doc/245170>.

@article{Carbone2004,
abstract = {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.},
affiliation = {Università di Cassino, Dipartimento di Automazione, Elettromagnetismo, Ingegneria dell’Informazione e Matematica Industriale, via G. Di Biasio 43, 03043 Cassino (FR), Italy;},
author = {Carbone, Luciano, Cioranescu, Doina, Arcangelis, Riccardo De, Gaudiello, Antonio},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {homogenization; gradient constrained variational problems; nonlinear elastomers},
language = {eng},
number = {1},
pages = {53-83},
publisher = {EDP-Sciences},
title = {Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set},
url = {http://eudml.org/doc/245170},
volume = {10},
year = {2004},
}

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
PB - EDP-Sciences
VL - 10
IS - 1
SP - 53
EP - 83
AB - 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.
LA - eng
KW - homogenization; gradient constrained variational problems; nonlinear elastomers
UR - http://eudml.org/doc/245170
ER -

References

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