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

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

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

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topCarbone, 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 (2010): 53-83. <http://eudml.org/doc/90721>.

@article{Carbone2010,

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.
},

author = {Carbone, Luciano, Cioranescu, Doina, De Arcangelis, Riccardo, Gaudiello, Antonio},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Homogenization; gradient constrained variational problems; nonlinear elastomers; homogenization},

language = {eng},

month = {3},

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/90721},

volume = {10},

year = {2010},

}

TY - JOUR

AU - Carbone, Luciano

AU - Cioranescu, Doina

AU - De Arcangelis, Riccardo

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

DA - 2010/3//

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; homogenization

UR - http://eudml.org/doc/90721

ER -

## References

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